id	sid	tid	token	lemma	pos
bracis-19052	1	1	optimizing	optimize	VERB
bracis-19052	1	2	diffusion	diffusion	NOUN
bracis-19052	1	3	rate	rate	NOUN
bracis-19052	1	4	and	and	CCONJ
bracis-19052	1	5	label	label	NOUN
bracis-19052	1	6	reliability	reliability	NOUN
bracis-19052	1	7	in	in	ADP
bracis-19052	1	8	a	a	DET
bracis-19052	1	9	graph	graph	NOUN
bracis-19052	1	10	-	-	PUNCT
bracis-19052	1	11	based	base	VERB
bracis-19052	1	12	semi	semi	ADJ
bracis-19052	1	13	-	-	ADJ
bracis-19052	1	14	supervised	supervised	ADJ
bracis-19052	1	15	classifier	classifier	NOUN
bracis-19052	1	16	|	|	NOUN
bracis-19052	1	17	springer	springer	NOUN
bracis-19052	1	18	nature	nature	PROPN
bracis-19052	1	19	link	link	PROPN
bracis-19052	1	20	(	(	PUNCT
bracis-19052	1	21	formerly	formerly	ADV
bracis-19052	1	22	springerlink	springerlink	NOUN
bracis-19052	1	23	)	)	PUNCT
bracis-19052	1	24	skip	skip	VERB
bracis-19052	1	25	to	to	ADP
bracis-19052	1	26	main	main	ADJ
bracis-19052	1	27	content	content	NOUN
bracis-19052	1	28	advertisement	advertisement	NOUN
bracis-19052	1	29	log	log	NOUN
bracis-19052	1	30	in	in	ADP
bracis-19052	1	31	menu	menu	NOUN
bracis-19052	1	32	find	find	VERB
bracis-19052	1	33	a	a	DET
bracis-19052	1	34	journal	journal	NOUN
bracis-19052	1	35	publish	publish	VERB
bracis-19052	1	36	with	with	ADP
bracis-19052	1	37	us	we	PRON
bracis-19052	1	38	track	track	VERB
bracis-19052	1	39	your	your	PRON
bracis-19052	1	40	research	research	NOUN
bracis-19052	1	41	search	search	NOUN
bracis-19052	1	42	cart	cart	NOUN
bracis-19052	1	43	home	home	NOUN
bracis-19052	1	44	intelligent	intelligent	ADJ
bracis-19052	1	45	systems	system	NOUN
bracis-19052	1	46	conference	conference	NOUN
bracis-19052	1	47	paper	paper	NOUN
bracis-19052	1	48	optimizing	optimizing	NOUN
bracis-19052	1	49	diffusion	diffusion	NOUN
bracis-19052	1	50	rate	rate	NOUN
bracis-19052	1	51	and	and	CCONJ
bracis-19052	1	52	label	label	NOUN
bracis-19052	1	53	reliability	reliability	NOUN
bracis-19052	1	54	in	in	ADP
bracis-19052	1	55	a	a	DET
bracis-19052	1	56	graph	graph	NOUN
bracis-19052	1	57	-	-	PUNCT
bracis-19052	1	58	based	base	VERB
bracis-19052	1	59	semi	semi	ADJ
bracis-19052	1	60	-	-	ADJ
bracis-19052	1	61	supervised	supervised	ADJ
bracis-19052	1	62	classifier	classifier	NOUN
bracis-19052	1	63	conference	conference	NOUN
bracis-19052	1	64	paper	paper	NOUN
bracis-19052	1	65	first	first	ADV
bracis-19052	1	66	online	online	ADV
bracis-19052	2	1	:	:	PUNCT
bracis-19052	2	2	28	28	NUM
bracis-19052	2	3	november	november	NOUN
bracis-19052	2	4	2021	2021	NUM
bracis-19052	3	1	pp	pp	PRON
bracis-19052	3	2	514–527	514–527	NUM
bracis-19052	3	3	cite	cite	VERB
bracis-19052	3	4	this	this	DET
bracis-19052	3	5	conference	conference	NOUN
bracis-19052	3	6	paper	paper	NOUN
bracis-19052	3	7	access	access	NOUN
bracis-19052	3	8	provided	provide	VERB
bracis-19052	3	9	by	by	ADP
bracis-19052	3	10	university	university	PROPN
bracis-19052	3	11	of	of	ADP
bracis-19052	3	12	notre	notre	PROPN
bracis-19052	3	13	dame	dame	PROPN
bracis-19052	3	14	hesburgh	hesburgh	PROPN
bracis-19052	3	15	library	library	PROPN
bracis-19052	3	16	download	download	PROPN
bracis-19052	3	17	book	book	NOUN
bracis-19052	3	18	pdf	pdf	PROPN
bracis-19052	3	19	download	download	NOUN
bracis-19052	3	20	book	book	NOUN
bracis-19052	3	21	epub	epub	PROPN
bracis-19052	3	22	intelligent	intelligent	ADJ
bracis-19052	3	23	systems	system	NOUN
bracis-19052	3	24	(	(	PUNCT
bracis-19052	3	25	bracis	bracis	NOUN
bracis-19052	3	26	2021	2021	NUM
bracis-19052	3	27	)	)	PUNCT
bracis-19052	3	28	optimizing	optimize	VERB
bracis-19052	3	29	diffusion	diffusion	NOUN
bracis-19052	3	30	rate	rate	NOUN
bracis-19052	3	31	and	and	CCONJ
bracis-19052	3	32	label	label	NOUN
bracis-19052	3	33	reliability	reliability	NOUN
bracis-19052	3	34	in	in	ADP
bracis-19052	3	35	a	a	DET
bracis-19052	3	36	graph	graph	NOUN
bracis-19052	3	37	-	-	PUNCT
bracis-19052	3	38	based	base	VERB
bracis-19052	3	39	semi	semi	ADJ
bracis-19052	3	40	-	-	ADJ
bracis-19052	3	41	supervised	supervised	ADJ
bracis-19052	3	42	classifier	classifier	NOUN
bracis-19052	3	43	download	download	NOUN
bracis-19052	3	44	book	book	NOUN
bracis-19052	3	45	pdf	pdf	PROPN
bracis-19052	3	46	download	download	NOUN
bracis-19052	3	47	book	book	PROPN
bracis-19052	3	48	epub	epub	PROPN
bracis-19052	3	49	bruno	bruno	PROPN
bracis-19052	3	50	klaus	klaus	PROPN
bracis-19052	3	51	de	de	PROPN
bracis-19052	3	52	aquino	aquino	PROPN
bracis-19052	3	53	afonso	afonso	PROPN
bracis-19052	3	54	  	  	SPACE
bracis-19052	3	55	orcid	orcid	NOUN
bracis-19052	3	56	:	:	PUNCT
bracis-19052	3	57	orcid.org/0000-0003-2086-105410	orcid.org/0000-0003-2086-105410	PROPN
bracis-19052	3	58	&	&	CCONJ
bracis-19052	3	59	lilian	lilian	PROPN
bracis-19052	3	60	berton	berton	PROPN
bracis-19052	3	61	  	  	SPACE
bracis-19052	3	62	orcid	orcid	NOUN
bracis-19052	3	63	:	:	PUNCT
bracis-19052	3	64	orcid.org/0000-0003-1397-600510	orcid.org/0000-0003-1397-600510	VERB
bracis-19052	3	65	  	  	SPACE
bracis-19052	3	66	part	part	NOUN
bracis-19052	3	67	of	of	ADP
bracis-19052	3	68	the	the	DET
bracis-19052	3	69	book	book	NOUN
bracis-19052	3	70	series	series	NOUN
bracis-19052	3	71	:	:	PUNCT
bracis-19052	3	72	lecture	lecture	NOUN
bracis-19052	3	73	notes	note	NOUN
bracis-19052	3	74	in	in	ADP
bracis-19052	3	75	computer	computer	NOUN
bracis-19052	3	76	science	science	NOUN
bracis-19052	3	77	(	(	PUNCT
bracis-19052	3	78	(	(	PUNCT
bracis-19052	3	79	lnai	lnai	ADJ
bracis-19052	3	80	,	,	PUNCT
bracis-19052	3	81	volume	volume	NOUN
bracis-19052	3	82	13073	13073	NUM
bracis-19052	3	83	)	)	PUNCT
bracis-19052	3	84	)	)	PUNCT
bracis-19052	3	85	included	include	VERB
bracis-19052	3	86	in	in	ADP
bracis-19052	3	87	the	the	DET
bracis-19052	3	88	following	follow	VERB
bracis-19052	3	89	conference	conference	NOUN
bracis-19052	3	90	series	series	NOUN
bracis-19052	3	91	:	:	PUNCT
bracis-19052	3	92	brazilian	brazilian	ADJ
bracis-19052	3	93	conference	conference	NOUN
bracis-19052	3	94	on	on	ADP
bracis-19052	3	95	intelligent	intelligent	ADJ
bracis-19052	3	96	systems	system	NOUN
bracis-19052	3	97	753	753	NUM
bracis-19052	3	98	accesses	access	VERB
bracis-19052	3	99	3	3	NUM
bracis-19052	3	100	citations	citation	NOUN
bracis-19052	3	101	1	1	NUM
bracis-19052	3	102	altmetric	altmetric	ADJ
bracis-19052	3	103	abstract	abstract	ADJ
bracis-19052	3	104	semi	semi	ADJ
bracis-19052	3	105	-	-	ADJ
bracis-19052	3	106	supervised	supervised	ADJ
bracis-19052	3	107	learning	learning	NOUN
bracis-19052	3	108	has	have	AUX
bracis-19052	3	109	received	receive	VERB
bracis-19052	3	110	attention	attention	NOUN
bracis-19052	3	111	from	from	ADP
bracis-19052	3	112	researchers	researcher	NOUN
bracis-19052	3	113	,	,	PUNCT
bracis-19052	3	114	as	as	SCONJ
bracis-19052	3	115	it	it	PRON
bracis-19052	3	116	allows	allow	VERB
bracis-19052	3	117	one	one	PRON
bracis-19052	3	118	to	to	PART
bracis-19052	3	119	exploit	exploit	VERB
bracis-19052	3	120	the	the	DET
bracis-19052	3	121	structure	structure	NOUN
bracis-19052	3	122	of	of	ADP
bracis-19052	3	123	unlabeled	unlabeled	ADJ
bracis-19052	3	124	data	datum	NOUN
bracis-19052	3	125	to	to	PART
bracis-19052	3	126	achieve	achieve	VERB
bracis-19052	3	127	competitive	competitive	ADJ
bracis-19052	3	128	classification	classification	NOUN
bracis-19052	3	129	results	result	NOUN
bracis-19052	3	130	with	with	ADP
bracis-19052	3	131	much	much	ADV
bracis-19052	3	132	fewer	few	ADJ
bracis-19052	3	133	labels	label	NOUN
bracis-19052	3	134	than	than	ADP
bracis-19052	3	135	supervised	supervised	ADJ
bracis-19052	3	136	approaches	approach	NOUN
bracis-19052	3	137	.	.	PUNCT
bracis-19052	4	1	the	the	DET
bracis-19052	4	2	local	local	ADJ
bracis-19052	4	3	and	and	CCONJ
bracis-19052	4	4	global	global	ADJ
bracis-19052	4	5	consistency	consistency	NOUN
bracis-19052	4	6	(	(	PUNCT
bracis-19052	4	7	lgc	lgc	ADJ
bracis-19052	4	8	)	)	PUNCT
bracis-19052	4	9	algorithm	algorithm	NOUN
bracis-19052	4	10	is	be	AUX
bracis-19052	4	11	one	one	NUM
bracis-19052	4	12	of	of	ADP
bracis-19052	4	13	the	the	DET
bracis-19052	4	14	most	most	ADV
bracis-19052	4	15	well	well	ADV
bracis-19052	4	16	-	-	PUNCT
bracis-19052	4	17	known	know	VERB
bracis-19052	4	18	graph	graph	NOUN
bracis-19052	4	19	-	-	PUNCT
bracis-19052	4	20	based	base	VERB
bracis-19052	4	21	semi	semi	ADJ
bracis-19052	4	22	-	-	ADJ
bracis-19052	4	23	supervised	supervised	ADJ
bracis-19052	4	24	(	(	PUNCT
bracis-19052	4	25	gssl	gssl	NOUN
bracis-19052	4	26	)	)	PUNCT
bracis-19052	4	27	classifiers	classifier	NOUN
bracis-19052	4	28	.	.	PUNCT
bracis-19052	5	1	notably	notably	ADV
bracis-19052	5	2	,	,	PUNCT
bracis-19052	5	3	its	its	PRON
bracis-19052	5	4	solution	solution	NOUN
bracis-19052	5	5	can	can	AUX
bracis-19052	5	6	be	be	AUX
bracis-19052	5	7	written	write	VERB
bracis-19052	5	8	as	as	ADP
bracis-19052	5	9	a	a	DET
bracis-19052	5	10	linear	linear	ADJ
bracis-19052	5	11	combination	combination	NOUN
bracis-19052	5	12	of	of	ADP
bracis-19052	5	13	the	the	DET
bracis-19052	5	14	known	know	VERB
bracis-19052	5	15	labels	label	NOUN
bracis-19052	5	16	.	.	PUNCT
bracis-19052	6	1	the	the	DET
bracis-19052	6	2	coefficients	coefficient	NOUN
bracis-19052	6	3	of	of	ADP
bracis-19052	6	4	this	this	DET
bracis-19052	6	5	linear	linear	ADJ
bracis-19052	6	6	combination	combination	NOUN
bracis-19052	6	7	depend	depend	VERB
bracis-19052	6	8	on	on	ADP
bracis-19052	6	9	a	a	DET
bracis-19052	6	10	parameter	parameter	NOUN
bracis-19052	6	11	\(\alpha	\(\alpha	X
bracis-19052	6	12	\	\	NOUN
bracis-19052	6	13	)	)	PUNCT
bracis-19052	6	14	,	,	PUNCT
bracis-19052	6	15	determining	determine	VERB
bracis-19052	6	16	the	the	DET
bracis-19052	6	17	decay	decay	NOUN
bracis-19052	6	18	of	of	ADP
bracis-19052	6	19	the	the	DET
bracis-19052	6	20	reward	reward	NOUN
bracis-19052	6	21	over	over	ADP
bracis-19052	6	22	time	time	NOUN
bracis-19052	6	23	when	when	SCONJ
bracis-19052	6	24	reaching	reach	VERB
bracis-19052	6	25	labeled	label	VERB
bracis-19052	6	26	vertices	vertex	NOUN
bracis-19052	6	27	in	in	ADP
bracis-19052	6	28	a	a	DET
bracis-19052	6	29	random	random	ADJ
bracis-19052	6	30	walk	walk	NOUN
bracis-19052	6	31	.	.	PUNCT
bracis-19052	7	1	in	in	ADP
bracis-19052	7	2	this	this	DET
bracis-19052	7	3	work	work	NOUN
bracis-19052	7	4	,	,	PUNCT
bracis-19052	7	5	we	we	PRON
bracis-19052	7	6	discuss	discuss	VERB
bracis-19052	7	7	how	how	SCONJ
bracis-19052	7	8	removing	remove	VERB
bracis-19052	7	9	the	the	DET
bracis-19052	7	10	self	self	NOUN
bracis-19052	7	11	-	-	PUNCT
bracis-19052	7	12	influence	influence	NOUN
bracis-19052	7	13	of	of	ADP
bracis-19052	7	14	a	a	DET
bracis-19052	7	15	labeled	label	VERB
bracis-19052	7	16	instance	instance	NOUN
bracis-19052	7	17	may	may	AUX
bracis-19052	7	18	be	be	AUX
bracis-19052	7	19	beneficial	beneficial	ADJ
bracis-19052	7	20	,	,	PUNCT
bracis-19052	7	21	and	and	CCONJ
bracis-19052	7	22	how	how	SCONJ
bracis-19052	7	23	it	it	PRON
bracis-19052	7	24	relates	relate	VERB
bracis-19052	7	25	to	to	PART
bracis-19052	7	26	leave	leave	VERB
bracis-19052	7	27	-	-	PUNCT
bracis-19052	7	28	one	one	NUM
bracis-19052	7	29	-	-	PUNCT
bracis-19052	7	30	out	out	NOUN
bracis-19052	7	31	error	error	NOUN
bracis-19052	7	32	.	.	PUNCT
bracis-19052	8	1	moreover	moreover	ADV
bracis-19052	8	2	,	,	PUNCT
bracis-19052	8	3	we	we	PRON
bracis-19052	8	4	propose	propose	VERB
bracis-19052	8	5	to	to	PART
bracis-19052	8	6	minimize	minimize	VERB
bracis-19052	8	7	this	this	DET
bracis-19052	8	8	leave	leave	VERB
bracis-19052	8	9	-	-	PUNCT
bracis-19052	8	10	one	one	NUM
bracis-19052	8	11	-	-	PUNCT
bracis-19052	8	12	out	out	ADP
bracis-19052	8	13	loss	loss	NOUN
bracis-19052	8	14	with	with	ADP
bracis-19052	8	15	automatic	automatic	ADJ
bracis-19052	8	16	differentiation	differentiation	NOUN
bracis-19052	8	17	.	.	PUNCT
bracis-19052	9	1	within	within	ADP
bracis-19052	9	2	this	this	DET
bracis-19052	9	3	framework	framework	NOUN
bracis-19052	9	4	,	,	PUNCT
bracis-19052	9	5	we	we	PRON
bracis-19052	9	6	propose	propose	VERB
bracis-19052	9	7	methods	method	NOUN
bracis-19052	9	8	to	to	PART
bracis-19052	9	9	estimate	estimate	VERB
bracis-19052	9	10	label	label	NOUN
bracis-19052	9	11	reliability	reliability	NOUN
bracis-19052	9	12	and	and	CCONJ
bracis-19052	9	13	diffusion	diffusion	NOUN
bracis-19052	9	14	rate	rate	NOUN
bracis-19052	9	15	.	.	PUNCT
bracis-19052	10	1	optimizing	optimize	VERB
bracis-19052	10	2	the	the	DET
bracis-19052	10	3	diffusion	diffusion	NOUN
bracis-19052	10	4	rate	rate	NOUN
bracis-19052	10	5	is	be	AUX
bracis-19052	10	6	more	more	ADV
bracis-19052	10	7	efficiently	efficiently	ADV
bracis-19052	10	8	accomplished	accomplish	VERB
bracis-19052	10	9	with	with	ADP
bracis-19052	10	10	a	a	DET
bracis-19052	10	11	spectral	spectral	ADJ
bracis-19052	10	12	representation	representation	NOUN
bracis-19052	10	13	.	.	PUNCT
bracis-19052	11	1	results	result	NOUN
bracis-19052	11	2	show	show	VERB
bracis-19052	11	3	that	that	SCONJ
bracis-19052	11	4	the	the	DET
bracis-19052	11	5	label	label	NOUN
bracis-19052	11	6	reliability	reliability	NOUN
bracis-19052	11	7	approach	approach	NOUN
bracis-19052	11	8	competes	compete	VERB
bracis-19052	11	9	with	with	ADP
bracis-19052	11	10	robust	robust	ADJ
bracis-19052	11	11	\(\ell	\(\ell	NOUN
bracis-19052	12	1	_	_	PUNCT
bracis-19052	12	2	1\)-norm	1\)-norm	NOUN
bracis-19052	12	3	methods	method	NOUN
bracis-19052	12	4	and	and	CCONJ
bracis-19052	12	5	that	that	SCONJ
bracis-19052	12	6	removing	remove	VERB
bracis-19052	12	7	diagonal	diagonal	ADJ
bracis-19052	12	8	entries	entry	NOUN
bracis-19052	12	9	reduces	reduce	VERB
bracis-19052	12	10	the	the	DET
bracis-19052	12	11	risk	risk	NOUN
bracis-19052	12	12	of	of	ADP
bracis-19052	12	13	overfitting	overfitte	VERB
bracis-19052	12	14	and	and	CCONJ
bracis-19052	12	15	leads	lead	VERB
bracis-19052	12	16	to	to	ADP
bracis-19052	12	17	suitable	suitable	ADJ
bracis-19052	12	18	criteria	criterion	NOUN
bracis-19052	12	19	for	for	ADP
bracis-19052	12	20	parameter	parameter	NOUN
bracis-19052	12	21	selection	selection	NOUN
bracis-19052	12	22	.	.	PUNCT
bracis-19052	13	1	this	this	DET
bracis-19052	13	2	study	study	NOUN
bracis-19052	13	3	was	be	AUX
bracis-19052	13	4	financed	finance	VERB
bracis-19052	13	5	in	in	ADP
bracis-19052	13	6	part	part	NOUN
bracis-19052	13	7	by	by	ADP
bracis-19052	13	8	the	the	DET
bracis-19052	13	9	coordenação	coordenação	PROPN
bracis-19052	13	10	de	de	PROPN
bracis-19052	13	11	aperfeiçoamento	aperfeiçoamento	PROPN
bracis-19052	13	12	de	de	X
bracis-19052	13	13	nível	nível	PROPN
bracis-19052	13	14	superior	superior	PROPN
bracis-19052	13	15	brasil	brasil	PROPN
bracis-19052	13	16	(	(	PUNCT
bracis-19052	13	17	capes	cape	NOUN
bracis-19052	13	18	)	)	PUNCT
bracis-19052	13	19	finance	finance	NOUN
bracis-19052	13	20	code	code	NOUN
bracis-19052	13	21	001	001	NUM
bracis-19052	13	22	,	,	PUNCT
bracis-19052	13	23	and	and	CCONJ
bracis-19052	13	24	são	são	PROPN
bracis-19052	13	25	paulo	paulo	PROPN
bracis-19052	13	26	research	research	PROPN
bracis-19052	13	27	foundation	foundation	PROPN
bracis-19052	13	28	(	(	PUNCT
bracis-19052	13	29	fapesp	fapesp	NOUN
bracis-19052	13	30	)	)	PUNCT
bracis-19052	13	31	grant	grant	VERB
bracis-19052	13	32	#	#	SYM
bracis-19052	13	33	18/01722	18/01722	NUM
bracis-19052	13	34	-	-	SYM
bracis-19052	13	35	3	3	NUM
bracis-19052	13	36	.	.	PUNCT
bracis-19052	14	1	access	access	NOUN
bracis-19052	14	2	provided	provide	VERB
bracis-19052	14	3	by	by	ADP
bracis-19052	14	4	university	university	PROPN
bracis-19052	14	5	of	of	ADP
bracis-19052	14	6	notre	notre	PROPN
bracis-19052	14	7	dame	dame	PROPN
bracis-19052	14	8	hesburgh	hesburgh	PROPN
bracis-19052	14	9	library	library	PROPN
bracis-19052	14	10	.	.	PUNCT
bracis-19052	15	1	download	download	PROPN
bracis-19052	15	2	conference	conference	NOUN
bracis-19052	15	3	paper	paper	NOUN
bracis-19052	15	4	pdf	pdf	NOUN
bracis-19052	15	5	similar	similar	ADJ
bracis-19052	15	6	content	content	NOUN
bracis-19052	15	7	being	be	AUX
bracis-19052	15	8	viewed	view	VERB
bracis-19052	15	9	by	by	ADP
bracis-19052	15	10	others	other	NOUN
bracis-19052	15	11	discriminative	discriminative	NOUN
bracis-19052	15	12	clustering	cluster	VERB
bracis-19052	15	13	with	with	ADP
bracis-19052	15	14	representation	representation	NOUN
bracis-19052	15	15	learning	learn	VERB
bracis-19052	15	16	with	with	ADP
bracis-19052	15	17	any	any	DET
bracis-19052	15	18	ratio	ratio	NOUN
bracis-19052	15	19	of	of	ADP
bracis-19052	15	20	labeled	label	VERB
bracis-19052	15	21	to	to	ADP
bracis-19052	15	22	unlabeled	unlabeled	ADJ
bracis-19052	15	23	data	datum	NOUN
bracis-19052	15	24	article	article	NOUN
bracis-19052	15	25	29	29	NUM
bracis-19052	15	26	january	january	PROPN
bracis-19052	15	27	2022	2022	NUM
bracis-19052	15	28	model	model	NOUN
bracis-19052	15	29	change	change	VERB
bracis-19052	15	30	active	active	ADJ
bracis-19052	15	31	learning	learning	NOUN
bracis-19052	15	32	in	in	ADP
bracis-19052	15	33	graph	graph	NOUN
bracis-19052	15	34	-	-	PUNCT
bracis-19052	15	35	based	base	VERB
bracis-19052	15	36	semi	semi	ADJ
bracis-19052	15	37	-	-	ADJ
bracis-19052	15	38	supervised	supervised	ADJ
bracis-19052	15	39	learning	learning	NOUN
bracis-19052	15	40	article	article	NOUN
bracis-19052	15	41	open	open	ADJ
bracis-19052	15	42	access	access	NOUN
bracis-19052	15	43	17	17	NUM
bracis-19052	15	44	february	february	NOUN
bracis-19052	15	45	2024	2024	NUM
bracis-19052	15	46	semi	semi	ADJ
bracis-19052	15	47	-	-	ADJ
bracis-19052	15	48	supervised	supervised	ADJ
bracis-19052	15	49	uncertain	uncertain	ADJ
bracis-19052	15	50	linear	linear	ADJ
bracis-19052	15	51	discriminant	discriminant	ADJ
bracis-19052	15	52	analysis	analysis	NOUN
bracis-19052	15	53	chapter	chapter	NOUN
bracis-19052	15	54	©	©	PROPN
bracis-19052	15	55	2020	2020	NUM
bracis-19052	15	56	explore	explore	VERB
bracis-19052	15	57	related	relate	VERB
bracis-19052	15	58	subjects	subject	NOUN
bracis-19052	15	59	discover	discover	VERB
bracis-19052	15	60	the	the	DET
bracis-19052	15	61	latest	late	ADJ
bracis-19052	15	62	articles	article	NOUN
bracis-19052	15	63	,	,	PUNCT
bracis-19052	15	64	books	book	NOUN
bracis-19052	15	65	and	and	CCONJ
bracis-19052	15	66	news	news	NOUN
bracis-19052	15	67	in	in	ADP
bracis-19052	15	68	related	related	ADJ
bracis-19052	15	69	subjects	subject	NOUN
bracis-19052	15	70	,	,	PUNCT
bracis-19052	15	71	suggested	suggest	VERB
bracis-19052	15	72	using	use	VERB
bracis-19052	15	73	machine	machine	NOUN
bracis-19052	15	74	learning	learning	NOUN
bracis-19052	15	75	.	.	PUNCT
bracis-19052	16	1	algorithms	algorithm	NOUN
bracis-19052	16	2	graph	graph	NOUN
bracis-19052	16	3	theory	theory	NOUN
bracis-19052	16	4	graph	graph	NOUN
bracis-19052	16	5	theory	theory	NOUN
bracis-19052	16	6	in	in	ADP
bracis-19052	16	7	probability	probability	NOUN
bracis-19052	16	8	learning	learn	VERB
bracis-19052	16	9	algorithms	algorithm	NOUN
bracis-19052	16	10	machine	machine	NOUN
bracis-19052	16	11	learning	learn	VERB
bracis-19052	16	12	statistical	statistical	ADJ
bracis-19052	16	13	learning	learn	VERB
bracis-19052	16	14	1	1	NUM
bracis-19052	16	15	introduction	introduction	NOUN
bracis-19052	16	16	machine	machine	NOUN
bracis-19052	16	17	learning	learning	NOUN
bracis-19052	16	18	(	(	PUNCT
bracis-19052	16	19	ml	ml	NOUN
bracis-19052	16	20	)	)	PUNCT
bracis-19052	16	21	is	be	AUX
bracis-19052	16	22	the	the	DET
bracis-19052	16	23	subfield	subfield	NOUN
bracis-19052	16	24	of	of	ADP
bracis-19052	16	25	computer	computer	NOUN
bracis-19052	16	26	science	science	NOUN
bracis-19052	16	27	that	that	PRON
bracis-19052	16	28	aims	aim	VERB
bracis-19052	16	29	to	to	PART
bracis-19052	16	30	make	make	VERB
bracis-19052	16	31	a	a	DET
bracis-19052	16	32	computer	computer	NOUN
bracis-19052	16	33	learn	learn	VERB
bracis-19052	16	34	from	from	ADP
bracis-19052	16	35	data	datum	NOUN
bracis-19052	16	36	[	[	X
bracis-19052	16	37	11	11	NUM
bracis-19052	16	38	]	]	PUNCT
bracis-19052	16	39	.	.	PUNCT
bracis-19052	17	1	the	the	DET
bracis-19052	17	2	task	task	NOUN
bracis-19052	17	3	we	we	PRON
bracis-19052	17	4	’ll	’ll	AUX
bracis-19052	17	5	be	be	AUX
bracis-19052	17	6	considering	consider	VERB
bracis-19052	17	7	is	be	AUX
bracis-19052	17	8	the	the	DET
bracis-19052	17	9	problem	problem	NOUN
bracis-19052	17	10	of	of	ADP
bracis-19052	17	11	classification	classification	NOUN
bracis-19052	17	12	,	,	PUNCT
bracis-19052	17	13	which	which	PRON
bracis-19052	17	14	requires	require	VERB
bracis-19052	17	15	the	the	DET
bracis-19052	17	16	prediction	prediction	NOUN
bracis-19052	17	17	of	of	ADP
bracis-19052	17	18	a	a	DET
bracis-19052	17	19	discrete	discrete	ADJ
bracis-19052	17	20	label	label	NOUN
bracis-19052	17	21	corresponding	correspond	VERB
bracis-19052	17	22	to	to	ADP
bracis-19052	17	23	a	a	DET
bracis-19052	17	24	class	class	NOUN
bracis-19052	17	25	.	.	PUNCT
bracis-19052	18	1	before	before	SCONJ
bracis-19052	18	2	the	the	DET
bracis-19052	18	3	data	datum	NOUN
bracis-19052	18	4	can	can	AUX
bracis-19052	18	5	be	be	AUX
bracis-19052	18	6	presented	present	VERB
bracis-19052	18	7	to	to	ADP
bracis-19052	18	8	an	an	DET
bracis-19052	18	9	ml	ml	NOUN
bracis-19052	18	10	model	model	NOUN
bracis-19052	18	11	,	,	PUNCT
bracis-19052	18	12	it	it	PRON
bracis-19052	18	13	must	must	AUX
bracis-19052	18	14	be	be	AUX
bracis-19052	18	15	represented	represent	VERB
bracis-19052	18	16	in	in	ADP
bracis-19052	18	17	some	some	DET
bracis-19052	18	18	way	way	NOUN
bracis-19052	18	19	.	.	PUNCT
bracis-19052	19	1	our	our	PRON
bracis-19052	19	2	input	input	NOUN
bracis-19052	19	3	is	be	AUX
bracis-19052	19	4	nothing	nothing	PRON
bracis-19052	19	5	more	more	ADJ
bracis-19052	19	6	than	than	ADP
bracis-19052	19	7	a	a	DET
bracis-19052	19	8	collection	collection	NOUN
bracis-19052	19	9	of	of	ADP
bracis-19052	19	10	n	n	DET
bracis-19052	19	11	examples	example	NOUN
bracis-19052	19	12	.	.	PUNCT
bracis-19052	20	1	each	each	DET
bracis-19052	20	2	object	object	NOUN
bracis-19052	20	3	of	of	ADP
bracis-19052	20	4	this	this	DET
bracis-19052	20	5	collection	collection	NOUN
bracis-19052	20	6	is	be	AUX
bracis-19052	20	7	called	call	VERB
bracis-19052	20	8	an	an	DET
bracis-19052	20	9	instance	instance	NOUN
bracis-19052	20	10	.	.	PUNCT
bracis-19052	21	1	for	for	ADP
bracis-19052	21	2	most	most	ADJ
bracis-19052	21	3	practical	practical	ADJ
bracis-19052	21	4	applications	application	NOUN
bracis-19052	21	5	,	,	PUNCT
bracis-19052	21	6	we	we	PRON
bracis-19052	21	7	may	may	AUX
bracis-19052	21	8	consider	consider	VERB
bracis-19052	21	9	an	an	DET
bracis-19052	21	10	instance	instance	NOUN
bracis-19052	21	11	to	to	PART
bracis-19052	21	12	be	be	AUX
bracis-19052	21	13	a	a	DET
bracis-19052	21	14	vector	vector	NOUN
bracis-19052	21	15	of	of	ADP
bracis-19052	21	16	d	d	PROPN
bracis-19052	21	17	dimensions	dimension	NOUN
bracis-19052	21	18	.	.	PUNCT
bracis-19052	22	1	graph	graph	NOUN
bracis-19052	22	2	-	-	PUNCT
bracis-19052	22	3	based	base	VERB
bracis-19052	22	4	semi	semi	ADJ
bracis-19052	22	5	-	-	ADJ
bracis-19052	22	6	supervised	supervised	ADJ
bracis-19052	22	7	learning	learning	NOUN
bracis-19052	22	8	(	(	PUNCT
bracis-19052	22	9	gssl	gssl	NOUN
bracis-19052	22	10	)	)	PUNCT
bracis-19052	22	11	relies	rely	VERB
bracis-19052	22	12	a	a	DET
bracis-19052	22	13	lot	lot	NOUN
bracis-19052	22	14	on	on	ADP
bracis-19052	22	15	matrix	matrix	NOUN
bracis-19052	22	16	representations	representation	NOUN
bracis-19052	22	17	,	,	PUNCT
bracis-19052	22	18	so	so	SCONJ
bracis-19052	22	19	we	we	PRON
bracis-19052	22	20	will	will	AUX
bracis-19052	22	21	be	be	AUX
bracis-19052	22	22	representing	represent	VERB
bracis-19052	22	23	the	the	DET
bracis-19052	22	24	observed	observe	VERB
bracis-19052	22	25	instances	instance	NOUN
bracis-19052	22	26	as	as	ADP
bracis-19052	22	27	an	an	DET
bracis-19052	22	28	input	input	NOUN
bracis-19052	22	29	matrix	matrix	NOUN
bracis-19052	22	30	(	(	PUNCT
bracis-19052	22	31	1	1	X
bracis-19052	22	32	)	)	PUNCT
bracis-19052	22	33	a	a	DET
bracis-19052	22	34	ml	ml	NOUN
bracis-19052	22	35	classifier	classifier	NOUN
bracis-19052	22	36	should	should	AUX
bracis-19052	22	37	learn	learn	VERB
bracis-19052	22	38	to	to	PART
bracis-19052	22	39	map	map	VERB
bracis-19052	22	40	an	an	DET
bracis-19052	22	41	input	input	NOUN
bracis-19052	22	42	instance	instance	NOUN
bracis-19052	22	43	to	to	ADP
bracis-19052	22	44	the	the	DET
bracis-19052	22	45	desired	desire	VERB
bracis-19052	22	46	output	output	NOUN
bracis-19052	22	47	.	.	PUNCT
bracis-19052	23	1	to	to	PART
bracis-19052	23	2	do	do	VERB
bracis-19052	23	3	this	this	PRON
bracis-19052	23	4	,	,	PUNCT
bracis-19052	23	5	it	it	PRON
bracis-19052	23	6	needs	need	VERB
bracis-19052	23	7	to	to	PART
bracis-19052	23	8	know	know	VERB
bracis-19052	23	9	the	the	DET
bracis-19052	23	10	labels	label	NOUN
bracis-19052	23	11	(	(	PUNCT
bracis-19052	23	12	i.e.	i.e.	X
bracis-19052	23	13	the	the	DET
bracis-19052	23	14	output	output	NOUN
bracis-19052	23	15	)	)	PUNCT
bracis-19052	23	16	associated	associate	VERB
bracis-19052	23	17	with	with	ADP
bracis-19052	23	18	instances	instance	NOUN
bracis-19052	23	19	contained	contain	VERB
bracis-19052	23	20	in	in	ADP
bracis-19052	23	21	the	the	DET
bracis-19052	23	22	training	training	NOUN
bracis-19052	23	23	set	set	NOUN
bracis-19052	23	24	.	.	PUNCT
bracis-19052	24	1	in	in	ADP
bracis-19052	24	2	semi	semi	ADJ
bracis-19052	24	3	-	-	ADJ
bracis-19052	24	4	supervised	supervised	ADJ
bracis-19052	24	5	learning	learning	NOUN
bracis-19052	24	6	,	,	PUNCT
bracis-19052	24	7	only	only	ADV
bracis-19052	24	8	some	some	PRON
bracis-19052	24	9	of	of	ADP
bracis-19052	24	10	the	the	DET
bracis-19052	24	11	labels	label	NOUN
bracis-19052	24	12	are	be	AUX
bracis-19052	24	13	known	know	VERB
bracis-19052	24	14	in	in	ADP
bracis-19052	24	15	advance	advance	NOUN
bracis-19052	24	16	[	[	X
bracis-19052	24	17	3	3	NUM
bracis-19052	24	18	]	]	PUNCT
bracis-19052	24	19	.	.	PUNCT
bracis-19052	25	1	once	once	ADV
bracis-19052	25	2	again	again	ADV
bracis-19052	25	3	,	,	PUNCT
bracis-19052	25	4	it	it	PRON
bracis-19052	25	5	is	be	AUX
bracis-19052	25	6	quite	quite	ADV
bracis-19052	25	7	convenient	convenient	ADJ
bracis-19052	25	8	to	to	PART
bracis-19052	25	9	use	use	VERB
bracis-19052	25	10	a	a	DET
bracis-19052	25	11	matrix	matrix	NOUN
bracis-19052	25	12	representation	representation	NOUN
bracis-19052	25	13	,	,	PUNCT
bracis-19052	25	14	referred	refer	VERB
bracis-19052	25	15	to	to	ADP
bracis-19052	25	16	as	as	ADP
bracis-19052	25	17	the	the	DET
bracis-19052	25	18	(	(	PUNCT
bracis-19052	25	19	true	true	ADJ
bracis-19052	25	20	)	)	PUNCT
bracis-19052	25	21	label	label	NOUN
bracis-19052	25	22	matrix	matrix	NOUN
bracis-19052	25	23	$	$	SYM
bracis-19052	25	24	$	$	SYM
bracis-19052	25	25	\begin{aligned	\begin{aligne	VERB
bracis-19052	25	26	}	}	PUNCT
bracis-19052	25	27	\mathbf	\mathbf	PROPN
bracis-19052	25	28	{	{	PUNCT
bracis-19052	25	29	y}_{ij	y}_{ij	NOUN
bracis-19052	25	30	}	}	PUNCT
bracis-19052	25	31	=	=	SYM
bracis-19052	25	32	{	{	PUNCT
bracis-19052	25	33	\left\	\left\	PROPN
bracis-19052	25	34	{	{	PUNCT
bracis-19052	25	35	\begin{array}{ll	\begin{array}{ll	PROPN
bracis-19052	25	36	}	}	PUNCT
bracis-19052	25	37	1	1	NUM
bracis-19052	25	38	&	&	CCONJ
bracis-19052	25	39	{	{	PUNCT
bracis-19052	25	40	}	}	PUNCT
bracis-19052	25	41	\text	\text	PROPN
bracis-19052	25	42	{	{	PUNCT
bracis-19052	25	43	if	if	SCONJ
bracis-19052	25	44	the	the	DET
bracis-19052	25	45	}	}	PUNCT
bracis-19052	25	46	i\text	i\text	NOUN
bracis-19052	25	47	{	{	PUNCT
bracis-19052	25	48	-th	-th	NOUN
bracis-19052	25	49	instance	instance	NOUN
bracis-19052	25	50	is	be	AUX
bracis-19052	25	51	associated	associate	VERB
bracis-19052	25	52	with	with	ADP
bracis-19052	25	53	the	the	DET
bracis-19052	25	54	}	}	PUNCT
bracis-19052	25	55	j\text	j\text	PROPN
bracis-19052	25	56	{	{	PUNCT
bracis-19052	25	57	-th	-th	NOUN
bracis-19052	25	58	class}\\	class}\\	PROPN
bracis-19052	25	59	0	0	PROPN
bracis-19052	25	60	&	&	CCONJ
bracis-19052	25	61	{	{	PUNCT
bracis-19052	25	62	}	}	PUNCT
bracis-19052	25	63	\text	\text	PROPN
bracis-19052	25	64	{	{	PUNCT
bracis-19052	25	65	otherwise	otherwise	ADV
bracis-19052	25	66	}	}	PUNCT
bracis-19052	25	67	\end{array}\right	\end{array}\right	PROPN
bracis-19052	25	68	.	.	PUNCT
bracis-19052	25	69	}	}	PUNCT
bracis-19052	25	70	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	25	71	(	(	PUNCT
bracis-19052	25	72	2	2	X
bracis-19052	25	73	)	)	PUNCT
bracis-19052	25	74	most	most	ADJ
bracis-19052	25	75	approaches	approach	NOUN
bracis-19052	25	76	are	be	AUX
bracis-19052	25	77	inductive	inductive	ADJ
bracis-19052	25	78	in	in	ADP
bracis-19052	25	79	nature	nature	NOUN
bracis-19052	25	80	so	so	SCONJ
bracis-19052	25	81	that	that	SCONJ
bracis-19052	25	82	we	we	PRON
bracis-19052	25	83	can	can	AUX
bracis-19052	25	84	predict	predict	VERB
bracis-19052	25	85	the	the	DET
bracis-19052	25	86	labels	label	NOUN
bracis-19052	25	87	of	of	ADP
bracis-19052	25	88	instances	instance	NOUN
bracis-19052	25	89	not	not	PART
bracis-19052	25	90	seen	see	VERB
bracis-19052	25	91	before	before	ADP
bracis-19052	25	92	deployment	deployment	NOUN
bracis-19052	25	93	.	.	PUNCT
bracis-19052	26	1	however	however	ADV
bracis-19052	26	2	,	,	PUNCT
bracis-19052	26	3	most	most	ADV
bracis-19052	26	4	gssl	gssl	ADJ
bracis-19052	26	5	methods	method	NOUN
bracis-19052	26	6	are	be	AUX
bracis-19052	26	7	transductive	transductive	ADJ
bracis-19052	26	8	,	,	PUNCT
bracis-19052	26	9	which	which	PRON
bracis-19052	26	10	simply	simply	ADV
bracis-19052	26	11	means	mean	VERB
bracis-19052	26	12	that	that	SCONJ
bracis-19052	26	13	we	we	PRON
bracis-19052	26	14	are	be	AUX
bracis-19052	26	15	only	only	ADV
bracis-19052	26	16	interested	interested	ADJ
bracis-19052	26	17	in	in	ADP
bracis-19052	26	18	the	the	DET
bracis-19052	26	19	fixed	fix	VERB
bracis-19052	26	20	but	but	CCONJ
bracis-19052	26	21	unknown	unknown	ADJ
bracis-19052	26	22	set	set	NOUN
bracis-19052	26	23	of	of	ADP
bracis-19052	26	24	labels	label	NOUN
bracis-19052	26	25	corresponding	correspond	VERB
bracis-19052	26	26	to	to	ADP
bracis-19052	26	27	unlabeled	unlabeled	ADJ
bracis-19052	26	28	instances	instance	NOUN
bracis-19052	26	29	[	[	X
bracis-19052	26	30	17	17	NUM
bracis-19052	26	31	]	]	PUNCT
bracis-19052	26	32	.	.	PUNCT
bracis-19052	27	1	accordingly	accordingly	ADV
bracis-19052	27	2	,	,	PUNCT
bracis-19052	27	3	we	we	PRON
bracis-19052	27	4	may	may	AUX
bracis-19052	27	5	represent	represent	VERB
bracis-19052	27	6	this	this	PRON
bracis-19052	27	7	with	with	ADP
bracis-19052	27	8	a	a	DET
bracis-19052	27	9	classification	classification	NOUN
bracis-19052	27	10	matrix	matrix	NOUN
bracis-19052	27	11	:	:	PUNCT
bracis-19052	27	12	(	(	PUNCT
bracis-19052	27	13	3	3	X
bracis-19052	27	14	)	)	PUNCT
bracis-19052	27	15	in	in	ADP
bracis-19052	27	16	order	order	NOUN
bracis-19052	27	17	to	to	PART
bracis-19052	27	18	separate	separate	VERB
bracis-19052	27	19	the	the	DET
bracis-19052	27	20	labeled	label	VERB
bracis-19052	27	21	data	datum	NOUN
bracis-19052	27	22	\(\mathcal	\(\mathcal	ADJ
bracis-19052	27	23	{	{	PUNCT
bracis-19052	27	24	l}\	l}\	PROPN
bracis-19052	27	25	)	)	PUNCT
bracis-19052	27	26	from	from	ADP
bracis-19052	27	27	the	the	DET
bracis-19052	27	28	unlabeled	unlabeled	ADJ
bracis-19052	27	29	data	datum	NOUN
bracis-19052	27	30	\(\mathcal	\(\mathcal	ADJ
bracis-19052	27	31	{	{	PUNCT
bracis-19052	27	32	u}\	u}\	PROPN
bracis-19052	27	33	)	)	PUNCT
bracis-19052	27	34	,	,	PUNCT
bracis-19052	27	35	we	we	PRON
bracis-19052	27	36	divide	divide	VERB
bracis-19052	27	37	our	our	PRON
bracis-19052	27	38	matrices	matrix	NOUN
bracis-19052	27	39	as	as	ADP
bracis-19052	27	40	following	follow	VERB
bracis-19052	27	41	:	:	PUNCT
bracis-19052	27	42	$	$	SYM
bracis-19052	27	43	$	$	SYM
bracis-19052	27	44	\begin{aligned	\begin{aligne	VERB
bracis-19052	27	45	}	}	PUNCT
bracis-19052	27	46	\mathbf	\mathbf	PROPN
bracis-19052	27	47	{	{	PUNCT
bracis-19052	27	48	x}&=	x}&=	PROPN
bracis-19052	27	49	\left	\left	PROPN
bracis-19052	27	50	[	[	PUNCT
bracis-19052	27	51	\mathbf	\mathbf	PROPN
bracis-19052	27	52	{	{	PUNCT
bracis-19052	27	53	x_\mathcal	x_\mathcal	PROPN
bracis-19052	27	54	{	{	PUNCT
bracis-19052	27	55	l}}^\top	l}}^\top	NOUN
bracis-19052	27	56	,	,	PUNCT
bracis-19052	27	57	\mathbf	\mathbf	PROPN
bracis-19052	27	58	{	{	PUNCT
bracis-19052	27	59	x_\mathcal	x_\mathcal	PROPN
bracis-19052	27	60	{	{	PUNCT
bracis-19052	27	61	u}}^\top	u}}^\top	NOUN
bracis-19052	27	62	\right	\right	NOUN
bracis-19052	27	63	]	]	PUNCT
bracis-19052	27	64	^\top	^\top	X
bracis-19052	27	65	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	27	66	(	(	PUNCT
bracis-19052	27	67	4	4	NUM
bracis-19052	27	68	)	)	PUNCT
bracis-19052	27	69	$	$	SYM
bracis-19052	27	70	$	$	SYM
bracis-19052	27	71	\begin{aligned	\begin{aligne	VERB
bracis-19052	27	72	}	}	PUNCT
bracis-19052	27	73	\mathbf	\mathbf	PROPN
bracis-19052	27	74	{	{	PUNCT
bracis-19052	27	75	y}&=	y}&=	PROPN
bracis-19052	27	76	\left	\left	PROPN
bracis-19052	27	77	[	[	PUNCT
bracis-19052	27	78	\mathbf	\mathbf	PROPN
bracis-19052	27	79	{	{	PUNCT
bracis-19052	27	80	y_\mathcal	y_\mathcal	ADJ
bracis-19052	27	81	{	{	PUNCT
bracis-19052	27	82	l}}^\top	l}}^\top	NOUN
bracis-19052	27	83	,	,	PUNCT
bracis-19052	27	84	\mathbf	\mathbf	PROPN
bracis-19052	27	85	{	{	PUNCT
bracis-19052	27	86	y_\mathcal	y_\mathcal	ADJ
bracis-19052	27	87	{	{	PUNCT
bracis-19052	27	88	u}}^\top	u}}^\top	NOUN
bracis-19052	27	89	\right	\right	NOUN
bracis-19052	27	90	]	]	PUNCT
bracis-19052	27	91	^\top	^\top	X
bracis-19052	27	92	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	27	93	(	(	PUNCT
bracis-19052	27	94	5	5	NUM
bracis-19052	27	95	)	)	PUNCT
bracis-19052	27	96	$	$	SYM
bracis-19052	27	97	$	$	SYM
bracis-19052	27	98	\begin{aligned	\begin{aligne	VERB
bracis-19052	27	99	}	}	PUNCT
bracis-19052	27	100	\mathbf	\mathbf	PROPN
bracis-19052	27	101	{	{	PUNCT
bracis-19052	27	102	f}&=	f}&=	PROPN
bracis-19052	27	103	\left	\left	PROPN
bracis-19052	27	104	[	[	PUNCT
bracis-19052	27	105	\mathbf	\mathbf	PROPN
bracis-19052	27	106	{	{	PUNCT
bracis-19052	27	107	f_\mathcal	f_\mathcal	NOUN
bracis-19052	27	108	{	{	PUNCT
bracis-19052	27	109	l}}^\top	l}}^\top	NOUN
bracis-19052	27	110	,	,	PUNCT
bracis-19052	27	111	\mathbf	\mathbf	PROPN
bracis-19052	27	112	{	{	PUNCT
bracis-19052	27	113	f_\mathcal	f_\mathcal	PROPN
bracis-19052	27	114	{	{	PUNCT
bracis-19052	27	115	u}}^\top	u}}^\top	NOUN
bracis-19052	27	116	\right	\right	NOUN
bracis-19052	27	117	]	]	PUNCT
bracis-19052	27	118	^\top	^\top	X
bracis-19052	27	119	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	27	120	(	(	PUNCT
bracis-19052	27	121	6	6	NUM
bracis-19052	27	122	)	)	PUNCT
bracis-19052	27	123	the	the	DET
bracis-19052	27	124	idea	idea	NOUN
bracis-19052	27	125	of	of	ADP
bracis-19052	27	126	ssl	ssl	PROPN
bracis-19052	27	127	is	be	AUX
bracis-19052	27	128	appealing	appeal	VERB
bracis-19052	27	129	for	for	ADP
bracis-19052	27	130	many	many	ADJ
bracis-19052	27	131	reasons	reason	NOUN
bracis-19052	27	132	.	.	PUNCT
bracis-19052	28	1	one	one	NUM
bracis-19052	28	2	of	of	ADP
bracis-19052	28	3	them	they	PRON
bracis-19052	28	4	is	be	AUX
bracis-19052	28	5	the	the	DET
bracis-19052	28	6	possibility	possibility	NOUN
bracis-19052	28	7	to	to	PART
bracis-19052	28	8	integrate	integrate	VERB
bracis-19052	28	9	the	the	DET
bracis-19052	28	10	toolset	toolset	NOUN
bracis-19052	28	11	developed	develop	VERB
bracis-19052	28	12	for	for	ADP
bracis-19052	28	13	unsupervised	unsupervised	ADJ
bracis-19052	28	14	learning	learning	NOUN
bracis-19052	28	15	.	.	PUNCT
bracis-19052	29	1	namely	namely	ADV
bracis-19052	29	2	,	,	PUNCT
bracis-19052	29	3	we	we	PRON
bracis-19052	29	4	may	may	AUX
bracis-19052	29	5	use	use	VERB
bracis-19052	29	6	unlabeled	unlabeled	ADJ
bracis-19052	29	7	data	datum	NOUN
bracis-19052	29	8	to	to	PART
bracis-19052	29	9	measure	measure	VERB
bracis-19052	29	10	the	the	DET
bracis-19052	29	11	density	density	NOUN
bracis-19052	29	12	\(p	\(p	NOUN
bracis-19052	29	13	(	(	PUNCT
bracis-19052	29	14	\mathbf	\mathbf	PROPN
bracis-19052	29	15	{	{	PUNCT
bracis-19052	29	16	x})\	x})\	PROPN
bracis-19052	29	17	)	)	PUNCT
bracis-19052	29	18	within	within	ADP
bracis-19052	29	19	our	our	PRON
bracis-19052	29	20	d	d	ADJ
bracis-19052	29	21	-	-	ADJ
bracis-19052	29	22	dimensional	dimensional	ADJ
bracis-19052	29	23	input	input	NOUN
bracis-19052	29	24	space	space	NOUN
bracis-19052	29	25	.	.	PUNCT
bracis-19052	30	1	once	once	ADV
bracis-19052	30	2	that	that	PRON
bracis-19052	30	3	is	be	AUX
bracis-19052	30	4	achieved	achieve	VERB
bracis-19052	30	5	,	,	PUNCT
bracis-19052	30	6	the	the	DET
bracis-19052	30	7	only	only	ADJ
bracis-19052	30	8	thing	thing	NOUN
bracis-19052	30	9	left	leave	VERB
bracis-19052	30	10	is	be	AUX
bracis-19052	30	11	to	to	PART
bracis-19052	30	12	take	take	VERB
bracis-19052	30	13	advantage	advantage	NOUN
bracis-19052	30	14	of	of	ADP
bracis-19052	30	15	this	this	DET
bracis-19052	30	16	information	information	NOUN
bracis-19052	30	17	.	.	PUNCT
bracis-19052	31	1	to	to	PART
bracis-19052	31	2	do	do	VERB
bracis-19052	31	3	this	this	PRON
bracis-19052	31	4	,	,	PUNCT
bracis-19052	31	5	we	we	PRON
bracis-19052	31	6	have	have	VERB
bracis-19052	31	7	to	to	PART
bracis-19052	31	8	make	make	VERB
bracis-19052	31	9	use	use	NOUN
bracis-19052	31	10	of	of	ADP
bracis-19052	31	11	assumptions	assumption	NOUN
bracis-19052	31	12	about	about	ADP
bracis-19052	31	13	the	the	DET
bracis-19052	31	14	relationship	relationship	NOUN
bracis-19052	31	15	between	between	ADP
bracis-19052	31	16	the	the	DET
bracis-19052	31	17	input	input	NOUN
bracis-19052	31	18	density	density	NOUN
bracis-19052	31	19	\(p	\(p	PROPN
bracis-19052	31	20	(	(	PUNCT
bracis-19052	31	21	\mathbf	\mathbf	PROPN
bracis-19052	31	22	{	{	PUNCT
bracis-19052	31	23	x})\	x})\	PROPN
bracis-19052	31	24	)	)	PUNCT
bracis-19052	31	25	and	and	CCONJ
bracis-19052	31	26	the	the	DET
bracis-19052	31	27	conditional	conditional	ADJ
bracis-19052	31	28	class	class	NOUN
bracis-19052	31	29	distribution	distribution	NOUN
bracis-19052	31	30	\(p(y\!\mid	\(p(y\!\mid	X
bracis-19052	31	31	\	\	PROPN
bracis-19052	31	32	!	!	PUNCT
bracis-19052	32	1	\mathbf	\mathbf	PROPN
bracis-19052	32	2	{	{	PUNCT
bracis-19052	32	3	x})\	x})\	PROPN
bracis-19052	32	4	)	)	PUNCT
bracis-19052	32	5	.	.	PUNCT
bracis-19052	33	1	if	if	SCONJ
bracis-19052	33	2	we	we	PRON
bracis-19052	33	3	are	be	AUX
bracis-19052	33	4	not	not	PART
bracis-19052	33	5	assuming	assume	VERB
bracis-19052	33	6	that	that	SCONJ
bracis-19052	33	7	our	our	PRON
bracis-19052	33	8	datasets	dataset	NOUN
bracis-19052	33	9	satisfy	satisfy	VERB
bracis-19052	33	10	any	any	DET
bracis-19052	33	11	kind	kind	NOUN
bracis-19052	33	12	of	of	ADP
bracis-19052	33	13	assumption	assumption	NOUN
bracis-19052	33	14	,	,	PUNCT
bracis-19052	33	15	ssl	ssl	PROPN
bracis-19052	33	16	can	can	AUX
bracis-19052	33	17	potentially	potentially	ADV
bracis-19052	33	18	cause	cause	VERB
bracis-19052	33	19	a	a	DET
bracis-19052	33	20	significant	significant	ADJ
bracis-19052	33	21	decrease	decrease	NOUN
bracis-19052	33	22	compared	compare	VERB
bracis-19052	33	23	to	to	ADP
bracis-19052	33	24	baseline	baseline	VERB
bracis-19052	33	25	performance	performance	NOUN
bracis-19052	33	26	[	[	X
bracis-19052	33	27	14	14	NUM
bracis-19052	33	28	]	]	PUNCT
bracis-19052	33	29	.	.	PUNCT
bracis-19052	34	1	this	this	PRON
bracis-19052	34	2	is	be	AUX
bracis-19052	34	3	currently	currently	ADV
bracis-19052	34	4	an	an	DET
bracis-19052	34	5	active	active	ADJ
bracis-19052	34	6	area	area	NOUN
bracis-19052	34	7	of	of	ADP
bracis-19052	34	8	research	research	NOUN
bracis-19052	34	9	:	:	PUNCT
bracis-19052	34	10	safe	safe	ADJ
bracis-19052	34	11	semi	semi	ADJ
bracis-19052	34	12	-	-	ADJ
bracis-19052	34	13	supervised	supervised	ADJ
bracis-19052	34	14	learning	learning	NOUN
bracis-19052	34	15	is	be	AUX
bracis-19052	34	16	said	say	VERB
bracis-19052	34	17	to	to	PART
bracis-19052	34	18	be	be	AUX
bracis-19052	34	19	attained	attain	VERB
bracis-19052	34	20	when	when	SCONJ
bracis-19052	34	21	ssl	ssl	PROPN
bracis-19052	34	22	never	never	ADV
bracis-19052	34	23	performs	perform	VERB
bracis-19052	34	24	worse	bad	ADJ
bracis-19052	34	25	than	than	ADP
bracis-19052	34	26	the	the	DET
bracis-19052	34	27	baseline	baseline	NOUN
bracis-19052	34	28	,	,	PUNCT
bracis-19052	34	29	for	for	ADP
bracis-19052	34	30	any	any	DET
bracis-19052	34	31	choice	choice	NOUN
bracis-19052	34	32	of	of	ADP
bracis-19052	34	33	labels	label	NOUN
bracis-19052	34	34	for	for	ADP
bracis-19052	34	35	the	the	DET
bracis-19052	34	36	unlabeled	unlabeled	ADJ
bracis-19052	34	37	data	datum	NOUN
bracis-19052	34	38	.	.	PUNCT
bracis-19052	35	1	this	this	PRON
bracis-19052	35	2	is	be	AUX
bracis-19052	35	3	indeed	indeed	ADV
bracis-19052	35	4	possible	possible	ADJ
bracis-19052	35	5	in	in	ADP
bracis-19052	35	6	some	some	DET
bracis-19052	35	7	limited	limited	ADJ
bracis-19052	35	8	circumstances	circumstance	NOUN
bracis-19052	35	9	,	,	PUNCT
bracis-19052	35	10	but	but	CCONJ
bracis-19052	35	11	also	also	ADV
bracis-19052	35	12	provably	provably	ADV
bracis-19052	35	13	impossible	impossible	ADJ
bracis-19052	35	14	for	for	ADP
bracis-19052	35	15	others	other	NOUN
bracis-19052	35	16	,	,	PUNCT
bracis-19052	35	17	such	such	ADJ
bracis-19052	35	18	as	as	ADP
bracis-19052	35	19	for	for	ADP
bracis-19052	35	20	a	a	DET
bracis-19052	35	21	specific	specific	ADJ
bracis-19052	35	22	class	class	NOUN
bracis-19052	35	23	of	of	ADP
bracis-19052	35	24	margin	margin	NOUN
bracis-19052	35	25	-	-	PUNCT
bracis-19052	35	26	based	base	VERB
bracis-19052	35	27	classifiers	classifier	NOUN
bracis-19052	35	28	[	[	X
bracis-19052	35	29	9	9	NUM
bracis-19052	35	30	]	]	PUNCT
bracis-19052	35	31	.	.	PUNCT
bracis-19052	36	1	in	in	ADP
bracis-19052	36	2	fig	fig	NOUN
bracis-19052	36	3	.	.	PUNCT
bracis-19052	36	4	 	 	SPACE
bracis-19052	36	5	1	1	NUM
bracis-19052	36	6	,	,	PUNCT
bracis-19052	36	7	we	we	PRON
bracis-19052	36	8	illustrate	illustrate	VERB
bracis-19052	36	9	which	which	DET
bracis-19052	36	10	kind	kind	NOUN
bracis-19052	36	11	of	of	ADP
bracis-19052	36	12	dataset	dataset	NOUN
bracis-19052	36	13	is	be	AUX
bracis-19052	36	14	suitable	suitable	ADJ
bracis-19052	36	15	for	for	ADP
bracis-19052	36	16	gssl	gssl	NOUN
bracis-19052	36	17	.	.	PUNCT
bracis-19052	37	1	there	there	PRON
bracis-19052	37	2	are	be	VERB
bracis-19052	37	3	two	two	NUM
bracis-19052	37	4	clear	clear	ADJ
bracis-19052	37	5	spirals	spiral	NOUN
bracis-19052	37	6	,	,	PUNCT
bracis-19052	37	7	one	one	NUM
bracis-19052	37	8	corresponding	correspond	VERB
bracis-19052	37	9	to	to	ADP
bracis-19052	37	10	each	each	DET
bracis-19052	37	11	class	class	NOUN
bracis-19052	37	12	.	.	PUNCT
bracis-19052	38	1	in	in	ADP
bracis-19052	38	2	a	a	DET
bracis-19052	38	3	bad	bad	ADJ
bracis-19052	38	4	dataset	dataset	NOUN
bracis-19052	38	5	for	for	ADP
bracis-19052	38	6	ssl	ssl	PROPN
bracis-19052	38	7	,	,	PUNCT
bracis-19052	38	8	we	we	PRON
bracis-19052	38	9	can	can	AUX
bracis-19052	38	10	imagine	imagine	VERB
bracis-19052	38	11	the	the	DET
bracis-19052	38	12	spiral	spiral	ADJ
bracis-19052	38	13	structure	structure	NOUN
bracis-19052	38	14	to	to	PART
bracis-19052	38	15	be	be	AUX
bracis-19052	38	16	a	a	DET
bracis-19052	38	17	red	red	ADJ
bracis-19052	38	18	herring	herring	NOUN
bracis-19052	38	19	,	,	PUNCT
bracis-19052	38	20	i.e.	i.e.	X
bracis-19052	38	21	something	something	PRON
bracis-19052	38	22	misguiding	misguide	VERB
bracis-19052	38	23	.	.	PUNCT
bracis-19052	39	1	a	a	DET
bracis-19052	39	2	very	very	ADV
bracis-19052	39	3	common	common	ADJ
bracis-19052	39	4	assumption	assumption	NOUN
bracis-19052	39	5	for	for	ADP
bracis-19052	39	6	ssl	ssl	PROPN
bracis-19052	39	7	is	be	AUX
bracis-19052	39	8	the	the	DET
bracis-19052	39	9	smoothness	smoothness	ADJ
bracis-19052	39	10	assumption	assumption	NOUN
bracis-19052	39	11	,	,	PUNCT
bracis-19052	39	12	which	which	PRON
bracis-19052	39	13	is	be	AUX
bracis-19052	39	14	one	one	NUM
bracis-19052	39	15	of	of	ADP
bracis-19052	39	16	the	the	DET
bracis-19052	39	17	cornerstones	cornerstone	NOUN
bracis-19052	39	18	for	for	ADP
bracis-19052	39	19	gssl	gssl	ADJ
bracis-19052	39	20	classifiers	classifier	NOUN
bracis-19052	39	21	.	.	PUNCT
bracis-19052	40	1	it	it	PRON
bracis-19052	40	2	states	state	VERB
bracis-19052	40	3	that	that	SCONJ
bracis-19052	40	4	“	"	PUNCT
bracis-19052	40	5	if	if	SCONJ
bracis-19052	40	6	two	two	NUM
bracis-19052	40	7	instances	instance	NOUN
bracis-19052	40	8	\	\	X
bracis-19052	40	9	(	(	PUNCT
bracis-19052	40	10	\mathbf	\mathbf	PROPN
bracis-19052	40	11	{	{	PUNCT
bracis-19052	40	12	x}_1\	x}_1\	PROPN
bracis-19052	40	13	)	)	PUNCT
bracis-19052	40	14	,	,	PUNCT
bracis-19052	40	15	\	\	PROPN
bracis-19052	40	16	(	(	PUNCT
bracis-19052	40	17	\mathbf	\mathbf	PROPN
bracis-19052	40	18	{	{	PUNCT
bracis-19052	40	19	x}_2\	x}_2\	NUM
bracis-19052	40	20	)	)	PUNCT
bracis-19052	40	21	in	in	ADP
bracis-19052	40	22	a	a	DET
bracis-19052	40	23	high	high	ADJ
bracis-19052	40	24	-	-	PUNCT
bracis-19052	40	25	density	density	NOUN
bracis-19052	40	26	region	region	NOUN
bracis-19052	40	27	are	be	AUX
bracis-19052	40	28	close	close	ADJ
bracis-19052	40	29	,	,	PUNCT
bracis-19052	40	30	then	then	ADV
bracis-19052	40	31	so	so	ADV
bracis-19052	40	32	should	should	AUX
bracis-19052	40	33	be	be	AUX
bracis-19052	40	34	the	the	DET
bracis-19052	40	35	corresponding	corresponding	ADJ
bracis-19052	40	36	outputs	output	NOUN
bracis-19052	40	37	\(y_1\	\(y_1\	PROPN
bracis-19052	40	38	)	)	PUNCT
bracis-19052	40	39	,	,	PUNCT
bracis-19052	40	40	\(y_2\	\(y_2\	PROPN
bracis-19052	40	41	)	)	PUNCT
bracis-19052	40	42	”	"	PUNCT
bracis-19052	41	1	[	[	X
bracis-19052	41	2	3	3	NUM
bracis-19052	41	3	]	]	PUNCT
bracis-19052	41	4	.	.	PUNCT
bracis-19052	42	1	another	another	DET
bracis-19052	42	2	important	important	ADJ
bracis-19052	42	3	assumption	assumption	NOUN
bracis-19052	42	4	is	be	AUX
bracis-19052	42	5	that	that	SCONJ
bracis-19052	42	6	the	the	DET
bracis-19052	42	7	(	(	PUNCT
bracis-19052	42	8	high	high	ADV
bracis-19052	42	9	-	-	PUNCT
bracis-19052	42	10	dimensional	dimensional	ADJ
bracis-19052	42	11	)	)	PUNCT
bracis-19052	42	12	data	datum	NOUN
bracis-19052	42	13	lie	lie	NOUN
bracis-19052	42	14	(	(	PUNCT
bracis-19052	42	15	roughly	roughly	ADV
bracis-19052	42	16	)	)	PUNCT
bracis-19052	42	17	on	on	ADP
bracis-19052	42	18	a	a	DET
bracis-19052	42	19	low	low	ADJ
bracis-19052	42	20	-	-	PUNCT
bracis-19052	42	21	dimensional	dimensional	ADJ
bracis-19052	42	22	manifold	manifold	NOUN
bracis-19052	42	23	,	,	PUNCT
bracis-19052	42	24	also	also	ADV
bracis-19052	42	25	known	know	VERB
bracis-19052	42	26	as	as	ADP
bracis-19052	42	27	the	the	DET
bracis-19052	42	28	manifold	manifold	ADJ
bracis-19052	42	29	assumption	assumption	NOUN
bracis-19052	42	30	[	[	X
bracis-19052	42	31	3	3	NUM
bracis-19052	42	32	]	]	PUNCT
bracis-19052	42	33	.	.	PUNCT
bracis-19052	43	1	if	if	SCONJ
bracis-19052	43	2	the	the	DET
bracis-19052	43	3	data	datum	NOUN
bracis-19052	43	4	lie	lie	VERB
bracis-19052	43	5	on	on	ADP
bracis-19052	43	6	a	a	DET
bracis-19052	43	7	low	low	ADJ
bracis-19052	43	8	-	-	PUNCT
bracis-19052	43	9	dimensional	dimensional	ADJ
bracis-19052	43	10	manifold	manifold	NOUN
bracis-19052	43	11	,	,	PUNCT
bracis-19052	43	12	the	the	DET
bracis-19052	43	13	local	local	ADJ
bracis-19052	43	14	similarities	similarity	NOUN
bracis-19052	43	15	will	will	AUX
bracis-19052	43	16	approximate	approximate	VERB
bracis-19052	43	17	the	the	DET
bracis-19052	43	18	manifold	manifold	ADJ
bracis-19052	43	19	well	well	NOUN
bracis-19052	43	20	.	.	PUNCT
bracis-19052	44	1	as	as	ADP
bracis-19052	44	2	a	a	DET
bracis-19052	44	3	result	result	NOUN
bracis-19052	44	4	,	,	PUNCT
bracis-19052	44	5	we	we	PRON
bracis-19052	44	6	can	can	AUX
bracis-19052	44	7	,	,	PUNCT
bracis-19052	44	8	for	for	ADP
bracis-19052	44	9	example	example	NOUN
bracis-19052	44	10	,	,	PUNCT
bracis-19052	44	11	increase	increase	VERB
bracis-19052	44	12	the	the	DET
bracis-19052	44	13	resolution	resolution	NOUN
bracis-19052	44	14	of	of	ADP
bracis-19052	44	15	our	our	PRON
bracis-19052	44	16	image	image	NOUN
bracis-19052	44	17	data	datum	NOUN
bracis-19052	44	18	without	without	ADP
bracis-19052	44	19	impacting	impact	VERB
bracis-19052	44	20	performance	performance	NOUN
bracis-19052	44	21	.	.	PUNCT
bracis-19052	45	1	graph	graph	NOUN
bracis-19052	45	2	-	-	PUNCT
bracis-19052	45	3	based	base	VERB
bracis-19052	45	4	semi	semi	ADJ
bracis-19052	45	5	-	-	ADJ
bracis-19052	45	6	supervised	supervised	ADJ
bracis-19052	45	7	learning	learning	NOUN
bracis-19052	45	8	has	have	AUX
bracis-19052	45	9	been	be	AUX
bracis-19052	45	10	used	use	VERB
bracis-19052	45	11	extensively	extensively	ADV
bracis-19052	45	12	for	for	ADP
bracis-19052	45	13	many	many	ADJ
bracis-19052	45	14	different	different	ADJ
bracis-19052	45	15	applications	application	NOUN
bracis-19052	45	16	across	across	ADP
bracis-19052	45	17	different	different	ADJ
bracis-19052	45	18	domains	domain	NOUN
bracis-19052	45	19	.	.	PUNCT
bracis-19052	46	1	in	in	ADP
bracis-19052	46	2	computer	computer	NOUN
bracis-19052	46	3	vision	vision	NOUN
bracis-19052	46	4	,	,	PUNCT
bracis-19052	46	5	these	these	PRON
bracis-19052	46	6	include	include	VERB
bracis-19052	46	7	car	car	NOUN
bracis-19052	46	8	plate	plate	NOUN
bracis-19052	46	9	character	character	NOUN
bracis-19052	46	10	recognition	recognition	NOUN
bracis-19052	46	11	[	[	X
bracis-19052	46	12	19	19	NUM
bracis-19052	46	13	]	]	PUNCT
bracis-19052	46	14	and	and	CCONJ
bracis-19052	46	15	hyperspectral	hyperspectral	ADJ
bracis-19052	46	16	image	image	NOUN
bracis-19052	46	17	classification	classification	NOUN
bracis-19052	46	18	[	[	X
bracis-19052	46	19	13	13	NUM
bracis-19052	46	20	]	]	PUNCT
bracis-19052	46	21	.	.	PUNCT
bracis-19052	47	1	gssl	gssl	PROPN
bracis-19052	47	2	is	be	AUX
bracis-19052	47	3	particularly	particularly	ADV
bracis-19052	47	4	appealing	appealing	ADJ
bracis-19052	47	5	if	if	SCONJ
bracis-19052	47	6	the	the	DET
bracis-19052	47	7	underlying	underlying	ADJ
bracis-19052	47	8	data	datum	NOUN
bracis-19052	47	9	has	have	VERB
bracis-19052	47	10	a	a	DET
bracis-19052	47	11	natural	natural	ADJ
bracis-19052	47	12	representation	representation	NOUN
bracis-19052	47	13	as	as	ADP
bracis-19052	47	14	a	a	DET
bracis-19052	47	15	graph	graph	NOUN
bracis-19052	47	16	.	.	PUNCT
bracis-19052	48	1	as	as	ADP
bracis-19052	48	2	such	such	ADJ
bracis-19052	48	3	,	,	PUNCT
bracis-19052	48	4	it	it	PRON
bracis-19052	48	5	has	have	AUX
bracis-19052	48	6	been	be	AUX
bracis-19052	48	7	a	a	DET
bracis-19052	48	8	promising	promising	ADJ
bracis-19052	48	9	approach	approach	NOUN
bracis-19052	48	10	for	for	ADP
bracis-19052	48	11	drug	drug	NOUN
bracis-19052	48	12	property	property	NOUN
bracis-19052	48	13	prediction	prediction	NOUN
bracis-19052	48	14	from	from	ADP
bracis-19052	48	15	the	the	DET
bracis-19052	48	16	structure	structure	NOUN
bracis-19052	48	17	of	of	ADP
bracis-19052	48	18	molecules	molecule	NOUN
bracis-19052	48	19	[	[	X
bracis-19052	48	20	8	8	NUM
bracis-19052	48	21	]	]	PUNCT
bracis-19052	48	22	.	.	PUNCT
bracis-19052	49	1	moreover	moreover	ADV
bracis-19052	49	2	,	,	PUNCT
bracis-19052	49	3	it	it	PRON
bracis-19052	49	4	has	have	AUX
bracis-19052	49	5	had	have	VERB
bracis-19052	49	6	much	much	ADJ
bracis-19052	49	7	application	application	NOUN
bracis-19052	49	8	in	in	ADP
bracis-19052	49	9	knowledge	knowledge	NOUN
bracis-19052	49	10	graphs	graph	NOUN
bracis-19052	49	11	,	,	PUNCT
bracis-19052	49	12	such	such	ADJ
bracis-19052	49	13	as	as	ADP
bracis-19052	49	14	the	the	DET
bracis-19052	49	15	development	development	NOUN
bracis-19052	49	16	of	of	ADP
bracis-19052	49	17	web	web	NOUN
bracis-19052	49	18	-	-	ADJ
bracis-19052	49	19	scale	scale	ADJ
bracis-19052	49	20	recommendation	recommendation	NOUN
bracis-19052	49	21	systems	system	NOUN
bracis-19052	49	22	[	[	X
bracis-19052	49	23	16	16	NUM
bracis-19052	49	24	]	]	PUNCT
bracis-19052	49	25	.	.	PUNCT
bracis-19052	50	1	fig	fig	NOUN
bracis-19052	50	2	.	.	PUNCT
bracis-19052	51	1	1	1	X
bracis-19052	51	2	.	.	X
bracis-19052	51	3	an	an	DET
bracis-19052	51	4	ideal	ideal	ADJ
bracis-19052	51	5	scenario	scenario	NOUN
bracis-19052	51	6	for	for	ADP
bracis-19052	51	7	semi	semi	ADJ
bracis-19052	51	8	-	-	ADJ
bracis-19052	51	9	supervised	supervised	ADJ
bracis-19052	51	10	learning	learning	NOUN
bracis-19052	51	11	full	full	ADJ
bracis-19052	51	12	size	size	NOUN
bracis-19052	51	13	image	image	NOUN
bracis-19052	51	14	gssl	gssl	NOUN
bracis-19052	51	15	methods	method	NOUN
bracis-19052	51	16	put	put	VERB
bracis-19052	51	17	a	a	DET
bracis-19052	51	18	greater	great	ADJ
bracis-19052	51	19	emphasis	emphasis	NOUN
bracis-19052	51	20	on	on	ADP
bracis-19052	51	21	using	use	VERB
bracis-19052	51	22	geodesics	geodesic	NOUN
bracis-19052	51	23	by	by	ADP
bracis-19052	51	24	expressing	express	VERB
bracis-19052	51	25	connectivity	connectivity	NOUN
bracis-19052	51	26	between	between	ADP
bracis-19052	51	27	instances	instance	NOUN
bracis-19052	51	28	through	through	ADP
bracis-19052	51	29	the	the	DET
bracis-19052	51	30	creation	creation	NOUN
bracis-19052	51	31	of	of	ADP
bracis-19052	51	32	a	a	DET
bracis-19052	51	33	graph	graph	NOUN
bracis-19052	51	34	.	.	PUNCT
bracis-19052	52	1	many	many	ADJ
bracis-19052	52	2	successful	successful	ADJ
bracis-19052	52	3	deep	deep	ADJ
bracis-19052	52	4	semi	semi	ADJ
bracis-19052	52	5	-	-	ADJ
bracis-19052	52	6	supervised	supervised	ADJ
bracis-19052	52	7	approaches	approach	NOUN
bracis-19052	52	8	use	use	VERB
bracis-19052	52	9	a	a	DET
bracis-19052	52	10	similar	similar	ADJ
bracis-19052	52	11	yet	yet	ADV
bracis-19052	52	12	slightly	slightly	ADV
bracis-19052	52	13	weaker	weak	ADJ
bracis-19052	52	14	assumption	assumption	NOUN
bracis-19052	52	15	,	,	PUNCT
bracis-19052	52	16	namely	namely	ADV
bracis-19052	52	17	that	that	SCONJ
bracis-19052	52	18	small	small	ADJ
bracis-19052	52	19	perturbations	perturbation	NOUN
bracis-19052	52	20	in	in	ADP
bracis-19052	52	21	input	input	NOUN
bracis-19052	52	22	space	space	NOUN
bracis-19052	52	23	should	should	AUX
bracis-19052	52	24	cause	cause	VERB
bracis-19052	52	25	little	little	ADJ
bracis-19052	52	26	corresponding	corresponding	ADJ
bracis-19052	52	27	perturbation	perturbation	NOUN
bracis-19052	52	28	on	on	ADP
bracis-19052	52	29	the	the	DET
bracis-19052	52	30	output	output	NOUN
bracis-19052	52	31	space	space	NOUN
bracis-19052	52	32	[	[	X
bracis-19052	52	33	12	12	NUM
bracis-19052	52	34	]	]	PUNCT
bracis-19052	52	35	.	.	PUNCT
bracis-19052	53	1	it	it	PRON
bracis-19052	53	2	turns	turn	VERB
bracis-19052	53	3	out	out	ADP
bracis-19052	53	4	that	that	SCONJ
bracis-19052	53	5	we	we	PRON
bracis-19052	53	6	can	can	AUX
bracis-19052	53	7	best	well	ADV
bracis-19052	53	8	express	express	VERB
bracis-19052	53	9	our	our	PRON
bracis-19052	53	10	concepts	concept	NOUN
bracis-19052	53	11	by	by	ADP
bracis-19052	53	12	defining	define	VERB
bracis-19052	53	13	a	a	DET
bracis-19052	53	14	measure	measure	NOUN
bracis-19052	53	15	of	of	ADP
bracis-19052	53	16	similarity	similarity	NOUN
bracis-19052	53	17	,	,	PUNCT
bracis-19052	53	18	instead	instead	ADV
bracis-19052	53	19	of	of	ADP
bracis-19052	53	20	distance	distance	NOUN
bracis-19052	53	21	.	.	PUNCT
bracis-19052	54	1	in	in	ADP
bracis-19052	54	2	particular	particular	ADJ
bracis-19052	54	3	,	,	PUNCT
bracis-19052	54	4	we	we	PRON
bracis-19052	54	5	search	search	VERB
bracis-19052	54	6	for	for	ADP
bracis-19052	54	7	an	an	DET
bracis-19052	54	8	affinity	affinity	NOUN
bracis-19052	54	9	matrix	matrix	NOUN
bracis-19052	54	10	,	,	PUNCT
bracis-19052	54	11	such	such	ADJ
bracis-19052	54	12	that	that	SCONJ
bracis-19052	54	13	$	$	SYM
bracis-19052	54	14	$	$	SYM
bracis-19052	54	15	\begin{aligned	\begin{aligne	VERB
bracis-19052	54	16	}	}	PUNCT
bracis-19052	54	17	\mathbf	\mathbf	PROPN
bracis-19052	54	18	{	{	PUNCT
bracis-19052	54	19	w}_{ij	w}_{ij	NOUN
bracis-19052	54	20	}	}	PUNCT
bracis-19052	54	21	=	=	SYM
bracis-19052	54	22	{	{	PUNCT
bracis-19052	54	23	\left\	\left\	PROPN
bracis-19052	54	24	{	{	PUNCT
bracis-19052	54	25	\begin{array}{ll	\begin{array}{ll	PROPN
bracis-19052	54	26	}	}	PUNCT
bracis-19052	54	27	w	w	PROPN
bracis-19052	54	28	(	(	PUNCT
bracis-19052	54	29	\mathbf	\mathbf	PROPN
bracis-19052	54	30	{	{	PUNCT
bracis-19052	54	31	x}_i	x}_i	PROPN
bracis-19052	54	32	,	,	PUNCT
bracis-19052	54	33	\mathbf	\mathbf	PROPN
bracis-19052	54	34	{	{	PUNCT
bracis-19052	54	35	x}_j)\in	x}_j)\in	PROPN
bracis-19052	54	36	\mathbb	\mathbb	PROPN
bracis-19052	54	37	{	{	PUNCT
bracis-19052	54	38	r	r	AUX
bracis-19052	54	39	}	}	PUNCT
bracis-19052	54	40	&	&	CCONJ
bracis-19052	54	41	{	{	PUNCT
bracis-19052	54	42	}	}	PUNCT
bracis-19052	54	43	\text	\text	PROPN
bracis-19052	54	44	{	{	PUNCT
bracis-19052	54	45	if	if	SCONJ
bracis-19052	54	46	}	}	PUNCT
bracis-19052	54	47	\mathbf	\mathbf	PROPN
bracis-19052	54	48	{	{	PUNCT
bracis-19052	54	49	x}_i\text	x}_i\text	PROPN
bracis-19052	54	50	{	{	PUNCT
bracis-19052	54	51	and	and	CCONJ
bracis-19052	54	52	}	}	PUNCT
bracis-19052	54	53	\mathbf	\mathbf	PROPN
bracis-19052	54	54	{	{	PUNCT
bracis-19052	54	55	x}_j\text	x}_j\text	PROPN
bracis-19052	54	56	{	{	PUNCT
bracis-19052	54	57	are	be	AUX
bracis-19052	54	58	considered	consider	VERB
bracis-19052	54	59	neighbors}\\	neighbors}\\	ADJ
bracis-19052	54	60	0	0	NUM
bracis-19052	54	61	&	&	CCONJ
bracis-19052	54	62	{	{	PUNCT
bracis-19052	54	63	}	}	PUNCT
bracis-19052	54	64	\text	\text	PROPN
bracis-19052	54	65	{	{	PUNCT
bracis-19052	54	66	otherwise	otherwise	ADV
bracis-19052	54	67	}	}	PUNCT
bracis-19052	54	68	\end{array}\right	\end{array}\right	PROPN
bracis-19052	54	69	.	.	PUNCT
bracis-19052	54	70	}	}	PUNCT
bracis-19052	54	71	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	54	72	(	(	PUNCT
bracis-19052	54	73	7	7	NUM
bracis-19052	54	74	)	)	PUNCT
bracis-19052	54	75	where	where	SCONJ
bracis-19052	54	76	w	w	NOUN
bracis-19052	54	77	is	be	AUX
bracis-19052	54	78	some	some	DET
bracis-19052	54	79	function	function	NOUN
bracis-19052	54	80	determining	determine	VERB
bracis-19052	54	81	the	the	DET
bracis-19052	54	82	similarity	similarity	NOUN
bracis-19052	54	83	between	between	ADP
bracis-19052	54	84	any	any	DET
bracis-19052	54	85	two	two	NUM
bracis-19052	54	86	instances	instance	NOUN
bracis-19052	54	87	\	\	NOUN
bracis-19052	54	88	(	(	PUNCT
bracis-19052	54	89	\mathbf	\mathbf	PROPN
bracis-19052	54	90	{	{	PUNCT
bracis-19052	54	91	x}_i	x}_i	PROPN
bracis-19052	54	92	,	,	PUNCT
bracis-19052	54	93	\mathbf	\mathbf	PROPN
bracis-19052	54	94	{	{	PUNCT
bracis-19052	54	95	x}_j\	x}_j\	PROPN
bracis-19052	54	96	)	)	PUNCT
bracis-19052	54	97	.	.	PUNCT
bracis-19052	55	1	when	when	SCONJ
bracis-19052	55	2	constructing	construct	VERB
bracis-19052	55	3	an	an	DET
bracis-19052	55	4	affinity	affinity	NOUN
bracis-19052	55	5	matrix	matrix	NOUN
bracis-19052	55	6	in	in	ADP
bracis-19052	55	7	practice	practice	NOUN
bracis-19052	55	8	,	,	PUNCT
bracis-19052	55	9	instances	instance	NOUN
bracis-19052	55	10	are	be	AUX
bracis-19052	55	11	not	not	PART
bracis-19052	55	12	considered	consider	VERB
bracis-19052	55	13	neighbors	neighbor	NOUN
bracis-19052	55	14	of	of	ADP
bracis-19052	55	15	themselves	themselves	PRON
bracis-19052	55	16	,	,	PUNCT
bracis-19052	55	17	i.e.	i.e.	X
bracis-19052	55	18	we	we	PRON
bracis-19052	55	19	have	have	VERB
bracis-19052	55	20	\(\forall	\(\forall	ADV
bracis-19052	55	21	i	i	PRON
bracis-19052	55	22	\in	\in	PROPN
bracis-19052	55	23	\{1	\{1	PROPN
bracis-19052	55	24	..	..	PUNCT
bracis-19052	55	25	n\	n\	NOUN
bracis-19052	55	26	}	}	PUNCT
bracis-19052	55	27	:	:	PUNCT
bracis-19052	55	28	\mathbf	\mathbf	PROPN
bracis-19052	55	29	{	{	PUNCT
bracis-19052	55	30	w}_{ii	w}_{ii	PROPN
bracis-19052	55	31	}	}	PUNCT
bracis-19052	55	32	=	=	SYM
bracis-19052	55	33	0\	0\	PROPN
bracis-19052	55	34	)	)	PUNCT
bracis-19052	55	35	.	.	PUNCT
bracis-19052	56	1	the	the	DET
bracis-19052	56	2	specification	specification	NOUN
bracis-19052	56	3	of	of	ADP
bracis-19052	56	4	an	an	DET
bracis-19052	56	5	affinity	affinity	NOUN
bracis-19052	56	6	matrix	matrix	NOUN
bracis-19052	56	7	is	be	AUX
bracis-19052	56	8	a	a	DET
bracis-19052	56	9	necessary	necessary	ADJ
bracis-19052	56	10	step	step	NOUN
bracis-19052	56	11	for	for	ADP
bracis-19052	56	12	any	any	DET
bracis-19052	56	13	gssl	gssl	ADJ
bracis-19052	56	14	classifier	classifier	NOUN
bracis-19052	56	15	,	,	PUNCT
bracis-19052	56	16	and	and	CCONJ
bracis-19052	56	17	its	its	PRON
bracis-19052	56	18	sparsity	sparsity	NOUN
bracis-19052	56	19	is	be	AUX
bracis-19052	56	20	often	often	ADV
bracis-19052	56	21	crucial	crucial	ADJ
bracis-19052	56	22	for	for	ADP
bracis-19052	56	23	reducing	reduce	VERB
bracis-19052	56	24	computational	computational	ADJ
bracis-19052	56	25	costs	cost	NOUN
bracis-19052	56	26	.	.	PUNCT
bracis-19052	57	1	there	there	PRON
bracis-19052	57	2	are	be	VERB
bracis-19052	57	3	many	many	ADJ
bracis-19052	57	4	ways	way	NOUN
bracis-19052	57	5	to	to	PART
bracis-19052	57	6	choose	choose	VERB
bracis-19052	57	7	a	a	DET
bracis-19052	57	8	neighborhood	neighborhood	NOUN
bracis-19052	57	9	.	.	PUNCT
bracis-19052	58	1	most	most	ADV
bracis-19052	58	2	frequently	frequently	ADV
bracis-19052	58	3	,	,	PUNCT
bracis-19052	58	4	it	it	PRON
bracis-19052	58	5	is	be	AUX
bracis-19052	58	6	constructed	construct	VERB
bracis-19052	58	7	by	by	ADP
bracis-19052	58	8	looking	look	VERB
bracis-19052	58	9	at	at	ADP
bracis-19052	58	10	the	the	DET
bracis-19052	58	11	k	k	NOUN
bracis-19052	58	12	-	-	PUNCT
bracis-19052	58	13	nearest	near	ADJ
bracis-19052	58	14	neighbors	neighbor	NOUN
bracis-19052	58	15	(	(	PUNCT
bracis-19052	58	16	knn	knn	PROPN
bracis-19052	58	17	)	)	PUNCT
bracis-19052	58	18	of	of	ADP
bracis-19052	58	19	a	a	DET
bracis-19052	58	20	given	give	VERB
bracis-19052	58	21	instance	instance	NOUN
bracis-19052	58	22	.	.	PUNCT
bracis-19052	59	1	one	one	NUM
bracis-19052	59	2	last	last	ADJ
bracis-19052	59	3	important	important	ADJ
bracis-19052	59	4	concept	concept	NOUN
bracis-19052	59	5	to	to	ADP
bracis-19052	59	6	gssl	gssl	NOUN
bracis-19052	59	7	is	be	AUX
bracis-19052	59	8	that	that	PRON
bracis-19052	59	9	of	of	ADP
bracis-19052	59	10	the	the	DET
bracis-19052	59	11	graph	graph	NOUN
bracis-19052	59	12	laplacian	laplacian	ADJ
bracis-19052	59	13	operator	operator	NOUN
bracis-19052	59	14	.	.	PUNCT
bracis-19052	60	1	this	this	DET
bracis-19052	60	2	operator	operator	NOUN
bracis-19052	60	3	is	be	AUX
bracis-19052	60	4	analogue	analogue	NOUN
bracis-19052	60	5	to	to	ADP
bracis-19052	60	6	the	the	DET
bracis-19052	60	7	laplace	laplace	NOUN
bracis-19052	60	8	-	-	PUNCT
bracis-19052	60	9	beltrami	beltrami	ADJ
bracis-19052	60	10	operator	operator	NOUN
bracis-19052	60	11	on	on	ADP
bracis-19052	60	12	manifolds	manifold	NOUN
bracis-19052	60	13	.	.	PUNCT
bracis-19052	61	1	there	there	PRON
bracis-19052	61	2	are	be	VERB
bracis-19052	61	3	a	a	DET
bracis-19052	61	4	few	few	ADJ
bracis-19052	61	5	graph	graph	NOUN
bracis-19052	61	6	laplacian	laplacian	ADJ
bracis-19052	61	7	variants	variant	NOUN
bracis-19052	61	8	,	,	PUNCT
bracis-19052	61	9	such	such	ADJ
bracis-19052	61	10	as	as	ADP
bracis-19052	61	11	the	the	DET
bracis-19052	61	12	combinatorial	combinatorial	ADJ
bracis-19052	61	13	laplacian	laplacian	ADJ
bracis-19052	61	14	$	$	SYM
bracis-19052	61	15	$	$	SYM
bracis-19052	61	16	\begin{aligned	\begin{aligne	VERB
bracis-19052	61	17	}	}	PUNCT
bracis-19052	61	18	\mathbf	\mathbf	PROPN
bracis-19052	61	19	{	{	PUNCT
bracis-19052	61	20	l}_{\mathbb	l}_{\mathbb	X
bracis-19052	61	21	{	{	PUNCT
bracis-19052	61	22	c}}=	c}}=	NOUN
bracis-19052	61	23	\mathbf	\mathbf	PROPN
bracis-19052	61	24	{	{	PUNCT
bracis-19052	61	25	d	d	NOUN
bracis-19052	61	26	}	}	PUNCT
bracis-19052	61	27	\mathbf	\mathbf	PROPN
bracis-19052	61	28	{	{	PUNCT
bracis-19052	61	29	w	w	PROPN
bracis-19052	61	30	}	}	PUNCT
bracis-19052	61	31	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	61	32	(	(	PUNCT
bracis-19052	61	33	8)	8)	NUM
bracis-19052	61	34	where	where	SCONJ
bracis-19052	61	35	\	\	PROPN
bracis-19052	61	36	(	(	PUNCT
bracis-19052	61	37	\mathbf	\mathbf	PROPN
bracis-19052	61	38	{	{	PUNCT
bracis-19052	61	39	d}\	d}\	PROPN
bracis-19052	61	40	)	)	PUNCT
bracis-19052	61	41	,	,	PUNCT
bracis-19052	61	42	called	call	VERB
bracis-19052	61	43	the	the	DET
bracis-19052	61	44	degree	degree	NOUN
bracis-19052	61	45	matrix	matrix	NOUN
bracis-19052	61	46	,	,	PUNCT
bracis-19052	61	47	is	be	AUX
bracis-19052	61	48	a	a	DET
bracis-19052	61	49	diagonal	diagonal	ADJ
bracis-19052	61	50	matrix	matrix	NOUN
bracis-19052	61	51	whose	whose	DET
bracis-19052	61	52	entries	entry	NOUN
bracis-19052	61	53	are	be	AUX
bracis-19052	61	54	the	the	DET
bracis-19052	61	55	sum	sum	NOUN
bracis-19052	61	56	of	of	ADP
bracis-19052	61	57	each	each	DET
bracis-19052	61	58	row	row	NOUN
bracis-19052	61	59	of	of	ADP
bracis-19052	61	60	\	\	PROPN
bracis-19052	61	61	(	(	PUNCT
bracis-19052	61	62	\mathbf	\mathbf	PROPN
bracis-19052	61	63	{	{	PUNCT
bracis-19052	61	64	w}\	w}\	PROPN
bracis-19052	61	65	)	)	PUNCT
bracis-19052	61	66	.	.	PUNCT
bracis-19052	62	1	there	there	PRON
bracis-19052	62	2	is	be	VERB
bracis-19052	62	3	also	also	ADV
bracis-19052	62	4	the	the	DET
bracis-19052	62	5	normalized	normalize	VERB
bracis-19052	62	6	laplacian	laplacian	NOUN
bracis-19052	62	7	,	,	PUNCT
bracis-19052	62	8	whose	whose	DET
bracis-19052	62	9	diagonal	diagonal	NOUN
bracis-19052	62	10	is	be	AUX
bracis-19052	62	11	the	the	DET
bracis-19052	62	12	identity	identity	NOUN
bracis-19052	62	13	matrix	matrix	NOUN
bracis-19052	62	14	\(\mathbf	\(\mathbf	X
bracis-19052	62	15	{	{	PUNCT
bracis-19052	62	16	i}\	i}\	NUM
bracis-19052	62	17	):	):	PUNCT
bracis-19052	62	18	$	$	SYM
bracis-19052	62	19	$	$	SYM
bracis-19052	62	20	\begin{aligned	\begin{aligne	VERB
bracis-19052	62	21	}	}	PUNCT
bracis-19052	62	22	{	{	PUNCT
bracis-19052	62	23	\mathbf	\mathbf	PROPN
bracis-19052	62	24	{	{	PUNCT
bracis-19052	62	25	l}_{\mathbb	l}_{\mathbb	PROPN
bracis-19052	62	26	{	{	PUNCT
bracis-19052	62	27	n}}=	n}}=	ADV
bracis-19052	62	28	\mathbf	\mathbf	PROPN
bracis-19052	62	29	{	{	PUNCT
bracis-19052	62	30	i	i	NOUN
bracis-19052	62	31	}	}	PUNCT
bracis-19052	62	32	\mathbf	\mathbf	PROPN
bracis-19052	62	33	{	{	PUNCT
bracis-19052	62	34	d}^{-\frac{1}{2	d}^{-\frac{1}{2	PROPN
bracis-19052	62	35	}	}	PUNCT
bracis-19052	62	36	}	}	PUNCT
bracis-19052	62	37	\mathbf	\mathbf	PROPN
bracis-19052	62	38	{	{	PUNCT
bracis-19052	62	39	w	w	NOUN
bracis-19052	62	40	}	}	PUNCT
bracis-19052	62	41	\mathbf	\mathbf	PROPN
bracis-19052	62	42	{	{	PUNCT
bracis-19052	62	43	d}^{-\frac{1}{2	d}^{-\frac{1}{2	PROPN
bracis-19052	62	44	}	}	PUNCT
bracis-19052	62	45	}	}	PUNCT
bracis-19052	62	46	=	=	SYM
bracis-19052	62	47	\mathbf	\mathbf	PROPN
bracis-19052	62	48	{	{	PUNCT
bracis-19052	62	49	d}^{-\frac{1}{2	d}^{-\frac{1}{2	PROPN
bracis-19052	62	50	}	}	PUNCT
bracis-19052	62	51	}	}	PUNCT
bracis-19052	62	52	\mathbf	\mathbf	PROPN
bracis-19052	62	53	{	{	PUNCT
bracis-19052	62	54	l}_{\mathbb	l}_{\mathbb	PROPN
bracis-19052	62	55	{	{	PUNCT
bracis-19052	62	56	c	c	NOUN
bracis-19052	62	57	}	}	PUNCT
bracis-19052	62	58	}	}	PUNCT
bracis-19052	62	59	\mathbf	\mathbf	PROPN
bracis-19052	62	60	{	{	PUNCT
bracis-19052	62	61	d}^{-\frac{1}{2	d}^{-\frac{1}{2	PROPN
bracis-19052	62	62	}	}	PUNCT
bracis-19052	62	63	}	}	PUNCT
bracis-19052	62	64	}	}	PUNCT
bracis-19052	62	65	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	62	66	(	(	PUNCT
bracis-19052	62	67	9	9	NUM
bracis-19052	62	68	)	)	PUNCT
bracis-19052	62	69	each	each	DET
bracis-19052	62	70	graph	graph	NOUN
bracis-19052	62	71	laplacian	laplacian	ADJ
bracis-19052	62	72	\	\	PROPN
bracis-19052	62	73	(	(	PUNCT
bracis-19052	62	74	\mathbf	\mathbf	PROPN
bracis-19052	62	75	{	{	PUNCT
bracis-19052	62	76	l}\	l}\	PROPN
bracis-19052	62	77	)	)	PUNCT
bracis-19052	62	78	induces	induce	VERB
bracis-19052	62	79	a	a	DET
bracis-19052	62	80	measure	measure	NOUN
bracis-19052	62	81	of	of	ADP
bracis-19052	62	82	smoothness	smoothness	NOUN
bracis-19052	62	83	with	with	ADP
bracis-19052	62	84	respect	respect	NOUN
bracis-19052	62	85	to	to	ADP
bracis-19052	62	86	the	the	DET
bracis-19052	62	87	graph	graph	NOUN
bracis-19052	62	88	on	on	ADP
bracis-19052	62	89	a	a	DET
bracis-19052	62	90	given	give	VERB
bracis-19052	62	91	classification	classification	NOUN
bracis-19052	62	92	matrix	matrix	NOUN
bracis-19052	62	93	\	\	PROPN
bracis-19052	62	94	(	(	PUNCT
bracis-19052	62	95	\mathbf	\mathbf	PROPN
bracis-19052	62	96	{	{	PUNCT
bracis-19052	62	97	f}\	f}\	NOUN
bracis-19052	62	98	)	)	PUNCT
bracis-19052	62	99	,	,	PUNCT
bracis-19052	62	100	namely	namely	ADV
bracis-19052	62	101	$	$	SYM
bracis-19052	62	102	$	$	SYM
bracis-19052	62	103	\begin{aligned	\begin{aligne	VERB
bracis-19052	62	104	}	}	PUNCT
bracis-19052	62	105	{	{	PUNCT
bracis-19052	62	106	\widetilde{s	\widetilde{	NOUN
bracis-19052	62	107	}	}	PUNCT
bracis-19052	62	108	_	_	PUNCT
bracis-19052	63	1	\mathbf	\mathbf	PROPN
bracis-19052	63	2	{	{	PUNCT
bracis-19052	63	3	l	l	NOUN
bracis-19052	63	4	}	}	PUNCT
bracis-19052	63	5	}	}	PUNCT
bracis-19052	63	6	(	(	PUNCT
bracis-19052	63	7	\mathbf	\mathbf	PROPN
bracis-19052	63	8	{	{	PUNCT
bracis-19052	63	9	f	f	NOUN
bracis-19052	63	10	}	}	PUNCT
bracis-19052	63	11	)	)	PUNCT
bracis-19052	63	12	=	=	PUNCT
bracis-19052	63	13	\frac{1}{2	\frac{1}{2	VERB
bracis-19052	63	14	}	}	PUNCT
bracis-19052	63	15	\sum	\sum	NOUN
bracis-19052	63	16	_	_	PUNCT
bracis-19052	63	17	{	{	PUNCT
bracis-19052	63	18	k=1}^{c	k=1}^{c	PROPN
bracis-19052	63	19	}	}	PUNCT
bracis-19052	63	20	(	(	PUNCT
bracis-19052	63	21	\mathbf	\mathbf	PROPN
bracis-19052	63	22	{	{	PUNCT
bracis-19052	63	23	f}_{[:,k]})^{\top	f}_{[:,k]})^{\top	NOUN
bracis-19052	63	24	}	}	PUNCT
bracis-19052	63	25	\mathbf	\mathbf	PROPN
bracis-19052	63	26	{	{	PUNCT
bracis-19052	63	27	l	l	NOUN
bracis-19052	63	28	}	}	PUNCT
bracis-19052	63	29	(	(	PUNCT
bracis-19052	63	30	\mathbf	\mathbf	PROPN
bracis-19052	63	31	{	{	PUNCT
bracis-19052	63	32	f}_{[:,k	f}_{[:,k	NOUN
bracis-19052	63	33	]	]	PUNCT
bracis-19052	63	34	}	}	PUNCT
bracis-19052	63	35	)	)	PUNCT
bracis-19052	63	36	=	=	SYM
bracis-19052	63	37	\frac{1}{2	\frac{1}{2	NOUN
bracis-19052	63	38	}	}	PUNCT
bracis-19052	63	39	tr	tr	VERB
bracis-19052	63	40	(	(	PUNCT
bracis-19052	63	41	\mathbf	\mathbf	PROPN
bracis-19052	63	42	{	{	PUNCT
bracis-19052	63	43	f}^{\top	f}^{\top	PROPN
bracis-19052	63	44	}	}	PUNCT
bracis-19052	63	45	\mathbf	\mathbf	PROPN
bracis-19052	63	46	{	{	PUNCT
bracis-19052	63	47	l	l	NOUN
bracis-19052	63	48	}	}	PUNCT
bracis-19052	63	49	\mathbf	\mathbf	PROPN
bracis-19052	63	50	{	{	PUNCT
bracis-19052	63	51	f	f	NOUN
bracis-19052	63	52	}	}	PUNCT
bracis-19052	63	53	)	)	PUNCT
bracis-19052	63	54	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-19052	63	55	(	(	PUNCT
bracis-19052	63	56	10	10	NUM
bracis-19052	63	57	)	)	PUNCT
bracis-19052	63	58	where	where	SCONJ
bracis-19052	63	59	tr	tr	PRON
bracis-19052	63	60	is	be	AUX
bracis-19052	63	61	the	the	DET
bracis-19052	63	62	trace	trace	NOUN
bracis-19052	63	63	of	of	ADP
bracis-19052	63	64	the	the	DET
bracis-19052	63	65	matrix	matrix	NOUN
bracis-19052	63	66	and	and	CCONJ
bracis-19052	63	67	c	c	X
bracis-19052	63	68	the	the	DET
bracis-19052	63	69	number	number	NOUN
bracis-19052	63	70	of	of	ADP
bracis-19052	63	71	classes	class	NOUN
bracis-19052	63	72	.	.	PUNCT
bracis-19052	64	1	if	if	SCONJ
bracis-19052	64	2	we	we	PRON
bracis-19052	64	3	consider	consider	VERB
bracis-19052	64	4	each	each	DET
bracis-19052	64	5	column	column	NOUN
bracis-19052	64	6	\	\	PROPN
bracis-19052	64	7	(	(	PUNCT
bracis-19052	64	8	\mathbf	\mathbf	PROPN
bracis-19052	64	9	{	{	PUNCT
bracis-19052	64	10	f}\	f}\	NOUN
bracis-19052	64	11	)	)	PUNCT
bracis-19052	64	12	of	of	ADP
bracis-19052	64	13	\	\	PROPN
bracis-19052	64	14	(	(	PUNCT
bracis-19052	64	15	\mathbf	\mathbf	PROPN
bracis-19052	64	16	{	{	PUNCT
bracis-19052	64	17	f}\	f}\	NOUN
bracis-19052	64	18	)	)	PUNCT
bracis-19052	64	19	individually	individually	ADV
bracis-19052	64	20	,	,	PUNCT
bracis-19052	64	21	then	then	ADV
bracis-19052	64	22	we	we	PRON
bracis-19052	64	23	can	can	AUX
bracis-19052	64	24	express	express	VERB
bracis-19052	64	25	graph	graph	NOUN
bracis-19052	64	26	smoothness	smoothness	ADJ
bracis-19052	64	27	of	of	ADP
bracis-19052	64	28	each	each	DET
bracis-19052	64	29	graph	graph	NOUN
bracis-19052	64	30	laplacian	laplacian	ADJ
bracis-19052	64	31	as	as	ADP
bracis-19052	64	32	$	$	SYM
bracis-19052	64	33	$	$	SYM
bracis-19052	64	34	\begin{aligned	\begin{aligne	VERB
bracis-19052	64	35	}	}	PUNCT
bracis-19052	64	36	\mathbf	\mathbf	PROPN
bracis-19052	64	37	{	{	PUNCT
bracis-19052	64	38	f}^{\top	f}^{\top	PROPN
bracis-19052	64	39	}	}	PUNCT
bracis-19052	64	40	\mathbf	\mathbf	PROPN
bracis-19052	64	41	{	{	PUNCT
bracis-19052	64	42	l}_{\mathbb	l}_{\mathbb	PROPN
bracis-19052	64	43	{	{	PUNCT
bracis-19052	64	44	c	c	NOUN
bracis-19052	64	45	}	}	PUNCT
bracis-19052	64	46	}	}	PUNCT
bracis-19052	64	47	\mathbf	\mathbf	PROPN
bracis-19052	64	48	{	{	PUNCT
bracis-19052	64	49	f}&=	f}&=	PROPN
bracis-19052	64	50	\sum	\sum	NOUN
bracis-19052	64	51	_	_	PUNCT
bracis-19052	64	52	{	{	PUNCT
bracis-19052	64	53	1	1	NUM
bracis-19052	64	54	\le	\le	PROPN
bracis-19052	64	55	i	i	NOUN
bracis-19052	64	56	,	,	PUNCT
bracis-19052	64	57	j	j	PROPN
bracis-19052	64	58	\le	\le	PROPN
bracis-19052	64	59	n	n	CCONJ
bracis-19052	64	60	}	}	PUNCT
bracis-19052	64	61	\mathbf	\mathbf	PROPN
bracis-19052	64	62	{	{	PUNCT
bracis-19052	64	63	w}_{ij	w}_{ij	NOUN
bracis-19052	64	64	}	}	PUNCT
bracis-19052	64	65	(	(	PUNCT
bracis-19052	64	66	\mathbf	\mathbf	PROPN
bracis-19052	64	67	{	{	PUNCT
bracis-19052	64	68	f}_i	f}_i	NUM
bracis-19052	64	69	\mathbf	\mathbf	PROPN
bracis-19052	64	70	{	{	PUNCT
bracis-19052	64	71	f}_j)^2	f}_j)^2	PROPN
bracis-19052	64	72	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	64	73	(	(	PUNCT
bracis-19052	64	74	11	11	NUM
bracis-19052	64	75	)	)	PUNCT
bracis-19052	64	76	$	$	SYM
bracis-19052	64	77	$	$	SYM
bracis-19052	64	78	\begin{aligned	\begin{aligne	VERB
bracis-19052	64	79	}	}	PUNCT
bracis-19052	64	80	\mathbf	\mathbf	PROPN
bracis-19052	64	81	{	{	PUNCT
bracis-19052	64	82	f}^{\top	f}^{\top	PROPN
bracis-19052	64	83	}	}	PUNCT
bracis-19052	64	84	\mathbf	\mathbf	PROPN
bracis-19052	64	85	{	{	PUNCT
bracis-19052	64	86	l}_{\mathbb	l}_{\mathbb	X
bracis-19052	64	87	{	{	PUNCT
bracis-19052	64	88	n	n	CCONJ
bracis-19052	64	89	}	}	PUNCT
bracis-19052	64	90	}	}	PUNCT
bracis-19052	64	91	\mathbf	\mathbf	PROPN
bracis-19052	64	92	{	{	PUNCT
bracis-19052	64	93	f}&=	f}&=	PROPN
bracis-19052	64	94	\sum	\sum	NOUN
bracis-19052	64	95	_	_	PUNCT
bracis-19052	64	96	{	{	PUNCT
bracis-19052	64	97	1	1	NUM
bracis-19052	64	98	\le	\le	PROPN
bracis-19052	64	99	i	i	NOUN
bracis-19052	64	100	,	,	PUNCT
bracis-19052	64	101	j	j	PROPN
bracis-19052	64	102	\le	\le	PROPN
bracis-19052	64	103	n	n	CCONJ
bracis-19052	64	104	}	}	PUNCT
bracis-19052	64	105	\left	\left	PROPN
bracis-19052	64	106	(	(	PUNCT
bracis-19052	64	107	\frac	\frac	PROPN
bracis-19052	64	108	{	{	PUNCT
bracis-19052	64	109	\mathbf	\mathbf	PROPN
bracis-19052	64	110	{	{	PUNCT
bracis-19052	64	111	w}_{ij}}{\sqrt	w}_{ij}}{\sqrt	NOUN
bracis-19052	64	112	{	{	PUNCT
bracis-19052	64	113	\mathbf	\mathbf	PROPN
bracis-19052	64	114	{	{	PUNCT
bracis-19052	64	115	d}_{ii	d}_{ii	PROPN
bracis-19052	64	116	}	}	PUNCT
bracis-19052	64	117	}	}	PUNCT
bracis-19052	64	118	}	}	PUNCT
bracis-19052	64	119	\mathbf	\mathbf	PROPN
bracis-19052	64	120	{	{	PUNCT
bracis-19052	64	121	f}_i	f}_i	NUM
bracis-19052	64	122	\frac	\frac	PROPN
bracis-19052	64	123	{	{	PUNCT
bracis-19052	64	124	\mathbf	\mathbf	PROPN
bracis-19052	64	125	{	{	PUNCT
bracis-19052	64	126	w}_{ij}}{\sqrt	w}_{ij}}{\sqrt	NOUN
bracis-19052	64	127	{	{	PUNCT
bracis-19052	64	128	\mathbf	\mathbf	PROPN
bracis-19052	64	129	{	{	PUNCT
bracis-19052	64	130	d}_{jj	d}_{jj	PROPN
bracis-19052	64	131	}	}	PUNCT
bracis-19052	64	132	}	}	PUNCT
bracis-19052	64	133	}	}	PUNCT
bracis-19052	64	134	\mathbf	\mathbf	PROPN
bracis-19052	64	135	{	{	PUNCT
bracis-19052	64	136	f}_j\right	f}_j\right	NUM
bracis-19052	64	137	)	)	PUNCT
bracis-19052	64	138	^2	^2	PUNCT
bracis-19052	64	139	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	64	140	(	(	PUNCT
bracis-19052	64	141	12	12	NUM
bracis-19052	64	142	)	)	PUNCT
bracis-19052	64	143	each	each	DET
bracis-19052	64	144	graph	graph	NOUN
bracis-19052	64	145	laplacian	laplacian	PROPN
bracis-19052	64	146	also	also	ADV
bracis-19052	64	147	has	have	VERB
bracis-19052	64	148	an	an	DET
bracis-19052	64	149	eigendecomposition	eigendecomposition	NOUN
bracis-19052	64	150	:	:	PUNCT
bracis-19052	64	151	$	$	SYM
bracis-19052	64	152	$	$	SYM
bracis-19052	64	153	\begin{aligned	\begin{aligne	VERB
bracis-19052	64	154	}	}	PUNCT
bracis-19052	64	155	\mathbf	\mathbf	PROPN
bracis-19052	64	156	{	{	PUNCT
bracis-19052	64	157	l	l	NOUN
bracis-19052	64	158	}	}	PUNCT
bracis-19052	64	159	=	=	SYM
bracis-19052	64	160	\mathbf	\mathbf	PROPN
bracis-19052	64	161	{	{	PUNCT
bracis-19052	64	162	u	u	NOUN
bracis-19052	64	163	}	}	PUNCT
bracis-19052	64	164	\mathbf	\mathbf	PROPN
bracis-19052	64	165	{	{	PUNCT
bracis-19052	64	166	\lambda	\lambda	PROPN
bracis-19052	64	167	}	}	PUNCT
bracis-19052	64	168	\mathbf	\mathbf	PROPN
bracis-19052	64	169	{	{	PUNCT
bracis-19052	64	170	u}^\top	u}^\top	ADV
bracis-19052	64	171	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	64	172	(	(	PUNCT
bracis-19052	64	173	13	13	NUM
bracis-19052	64	174	)	)	PUNCT
bracis-19052	64	175	where	where	SCONJ
bracis-19052	64	176	the	the	DET
bracis-19052	64	177	set	set	NOUN
bracis-19052	64	178	of	of	ADP
bracis-19052	64	179	columns	column	NOUN
bracis-19052	64	180	of	of	ADP
bracis-19052	64	181	\	\	PROPN
bracis-19052	64	182	(	(	PUNCT
bracis-19052	64	183	\mathbf	\mathbf	PROPN
bracis-19052	64	184	{	{	PUNCT
bracis-19052	64	185	u}\	u}\	PROPN
bracis-19052	64	186	)	)	PUNCT
bracis-19052	64	187	is	be	AUX
bracis-19052	64	188	an	an	DET
bracis-19052	64	189	orthonormal	orthonormal	ADJ
bracis-19052	64	190	basis	basis	NOUN
bracis-19052	64	191	of	of	ADP
bracis-19052	64	192	eigenfunctions	eigenfunction	NOUN
bracis-19052	64	193	,	,	PUNCT
bracis-19052	64	194	with	with	ADP
bracis-19052	64	195	\	\	PROPN
bracis-19052	64	196	(	(	PUNCT
bracis-19052	64	197	\mathbf	\mathbf	PROPN
bracis-19052	64	198	{	{	PUNCT
bracis-19052	64	199	\lambda	\lambda	PROPN
bracis-19052	64	200	}	}	PUNCT
bracis-19052	64	201	\	\	NOUN
bracis-19052	64	202	)	)	PUNCT
bracis-19052	64	203	a	a	DET
bracis-19052	64	204	diagonal	diagonal	ADJ
bracis-19052	64	205	matrix	matrix	NOUN
bracis-19052	64	206	with	with	ADP
bracis-19052	64	207	the	the	DET
bracis-19052	64	208	eigenvalues	eigenvalue	NOUN
bracis-19052	64	209	.	.	PUNCT
bracis-19052	65	1	as	as	ADP
bracis-19052	65	2	\	\	PROPN
bracis-19052	65	3	(	(	PUNCT
bracis-19052	65	4	\mathbf	\mathbf	PROPN
bracis-19052	65	5	{	{	PUNCT
bracis-19052	65	6	u}\	u}\	PROPN
bracis-19052	65	7	)	)	PUNCT
bracis-19052	65	8	is	be	AUX
bracis-19052	65	9	a	a	DET
bracis-19052	65	10	unitary	unitary	ADJ
bracis-19052	65	11	matrix	matrix	NOUN
bracis-19052	65	12	,	,	PUNCT
bracis-19052	65	13	any	any	DET
bracis-19052	65	14	real	real	ADV
bracis-19052	65	15	-	-	PUNCT
bracis-19052	65	16	valued	value	VERB
bracis-19052	65	17	function	function	NOUN
bracis-19052	65	18	on	on	ADP
bracis-19052	65	19	the	the	DET
bracis-19052	65	20	graph	graph	NOUN
bracis-19052	65	21	may	may	AUX
bracis-19052	65	22	be	be	AUX
bracis-19052	65	23	expressed	express	VERB
bracis-19052	65	24	as	as	ADP
bracis-19052	65	25	a	a	DET
bracis-19052	65	26	linear	linear	ADJ
bracis-19052	65	27	combination	combination	NOUN
bracis-19052	65	28	of	of	ADP
bracis-19052	65	29	eigenfunctions	eigenfunction	NOUN
bracis-19052	65	30	.	.	PUNCT
bracis-19052	66	1	we	we	PRON
bracis-19052	66	2	map	map	VERB
bracis-19052	66	3	a	a	DET
bracis-19052	66	4	function	function	NOUN
bracis-19052	66	5	to	to	ADP
bracis-19052	66	6	the	the	DET
bracis-19052	66	7	spectral	spectral	ADJ
bracis-19052	66	8	domain	domain	NOUN
bracis-19052	66	9	by	by	ADP
bracis-19052	66	10	pre	pre	VERB
bracis-19052	66	11	-	-	VERB
bracis-19052	66	12	multiplying	multiply	VERB
bracis-19052	66	13	it	it	PRON
bracis-19052	66	14	by	by	ADP
bracis-19052	66	15	\	\	PROPN
bracis-19052	66	16	(	(	PUNCT
bracis-19052	66	17	\mathbf	\mathbf	PROPN
bracis-19052	66	18	{	{	PUNCT
bracis-19052	66	19	u}^\top	u}^\top	PROPN
bracis-19052	66	20	\	\	NOUN
bracis-19052	66	21	)	)	PUNCT
bracis-19052	66	22	(	(	PUNCT
bracis-19052	66	23	also	also	ADV
bracis-19052	66	24	called	call	VERB
bracis-19052	66	25	graph	graph	NOUN
bracis-19052	66	26	fourier	fourier	NOUN
bracis-19052	66	27	transform	transform	NOUN
bracis-19052	66	28	,	,	PUNCT
bracis-19052	66	29	also	also	ADV
bracis-19052	66	30	known	know	VERB
bracis-19052	66	31	as	as	ADP
bracis-19052	66	32	gft	gft	PROPN
bracis-19052	66	33	)	)	PUNCT
bracis-19052	66	34	.	.	PUNCT
bracis-19052	67	1	additionally	additionally	ADV
bracis-19052	67	2	,	,	PUNCT
bracis-19052	67	3	pre	pre	ADJ
bracis-19052	67	4	-	-	VERB
bracis-19052	67	5	multiplying	multiply	VERB
bracis-19052	67	6	by	by	ADP
bracis-19052	67	7	\	\	PROPN
bracis-19052	67	8	(	(	PUNCT
bracis-19052	67	9	\mathbf	\mathbf	PROPN
bracis-19052	67	10	{	{	PUNCT
bracis-19052	67	11	u}\	u}\	PROPN
bracis-19052	67	12	)	)	PUNCT
bracis-19052	67	13	gives	give	VERB
bracis-19052	67	14	us	we	PRON
bracis-19052	67	15	the	the	DET
bracis-19052	67	16	inverse	inverse	NOUN
bracis-19052	67	17	transform	transform	NOUN
bracis-19052	67	18	.	.	PUNCT
bracis-19052	68	1	this	this	DET
bracis-19052	68	2	spectral	spectral	ADJ
bracis-19052	68	3	representation	representation	NOUN
bracis-19052	68	4	is	be	AUX
bracis-19052	68	5	very	very	ADV
bracis-19052	68	6	useful	useful	ADJ
bracis-19052	68	7	,	,	PUNCT
bracis-19052	68	8	as	as	SCONJ
bracis-19052	68	9	eigenfunctions	eigenfunction	NOUN
bracis-19052	68	10	that	that	PRON
bracis-19052	68	11	are	be	AUX
bracis-19052	68	12	smooth	smooth	ADJ
bracis-19052	68	13	with	with	ADP
bracis-19052	68	14	respect	respect	NOUN
bracis-19052	68	15	to	to	ADP
bracis-19052	68	16	the	the	DET
bracis-19052	68	17	graph	graph	NOUN
bracis-19052	68	18	have	have	VERB
bracis-19052	68	19	smaller	small	ADJ
bracis-19052	68	20	eigenvalues	eigenvalue	NOUN
bracis-19052	68	21	.	.	PUNCT
bracis-19052	69	1	outright	outright	ADV
bracis-19052	69	2	restricting	restrict	VERB
bracis-19052	69	3	the	the	DET
bracis-19052	69	4	amount	amount	NOUN
bracis-19052	69	5	of	of	ADP
bracis-19052	69	6	eigenfunctions	eigenfunction	NOUN
bracis-19052	69	7	is	be	AUX
bracis-19052	69	8	known	know	VERB
bracis-19052	69	9	as	as	ADP
bracis-19052	69	10	smooth	smooth	ADJ
bracis-19052	69	11	eigenbasis	eigenbasis	NOUN
bracis-19052	69	12	pursuit	pursuit	NOUN
bracis-19052	69	13	[	[	X
bracis-19052	69	14	6	6	NUM
bracis-19052	69	15	]	]	PUNCT
bracis-19052	69	16	,	,	PUNCT
bracis-19052	69	17	a	a	DET
bracis-19052	69	18	valid	valid	ADJ
bracis-19052	69	19	strategy	strategy	NOUN
bracis-19052	69	20	for	for	ADP
bracis-19052	69	21	semi	semi	ADJ
bracis-19052	69	22	-	-	ADJ
bracis-19052	69	23	supervised	supervised	ADJ
bracis-19052	69	24	regularization	regularization	NOUN
bracis-19052	69	25	.	.	PUNCT
bracis-19052	70	1	in	in	ADP
bracis-19052	70	2	this	this	DET
bracis-19052	70	3	work	work	NOUN
bracis-19052	70	4	,	,	PUNCT
bracis-19052	70	5	we	we	PRON
bracis-19052	70	6	explore	explore	VERB
bracis-19052	70	7	the	the	DET
bracis-19052	70	8	problem	problem	NOUN
bracis-19052	70	9	of	of	ADP
bracis-19052	70	10	parameter	parameter	NOUN
bracis-19052	70	11	selection	selection	NOUN
bracis-19052	70	12	for	for	ADP
bracis-19052	70	13	the	the	DET
bracis-19052	70	14	local	local	ADJ
bracis-19052	70	15	and	and	CCONJ
bracis-19052	70	16	global	global	ADJ
bracis-19052	70	17	consistency	consistency	NOUN
bracis-19052	70	18	model	model	NOUN
bracis-19052	70	19	.	.	PUNCT
bracis-19052	71	1	this	this	DET
bracis-19052	71	2	model	model	NOUN
bracis-19052	71	3	yields	yield	VERB
bracis-19052	71	4	a	a	DET
bracis-19052	71	5	propagation	propagation	NOUN
bracis-19052	71	6	matrix	matrix	NOUN
bracis-19052	71	7	,	,	PUNCT
bracis-19052	71	8	which	which	PRON
bracis-19052	71	9	itself	itself	PRON
bracis-19052	71	10	depends	depend	VERB
bracis-19052	71	11	on	on	ADP
bracis-19052	71	12	a	a	DET
bracis-19052	71	13	fixed	fix	VERB
bracis-19052	71	14	parameter	parameter	NOUN
bracis-19052	71	15	\(\alpha	\(\alpha	PROPN
bracis-19052	71	16	\	\	NOUN
bracis-19052	71	17	)	)	PUNCT
bracis-19052	71	18	determining	determine	VERB
bracis-19052	71	19	the	the	DET
bracis-19052	71	20	diffusion	diffusion	NOUN
bracis-19052	71	21	rate	rate	NOUN
bracis-19052	71	22	.	.	PUNCT
bracis-19052	72	1	we	we	PRON
bracis-19052	72	2	show	show	VERB
bracis-19052	72	3	that	that	SCONJ
bracis-19052	72	4	,	,	PUNCT
bracis-19052	72	5	by	by	ADP
bracis-19052	72	6	removing	remove	VERB
bracis-19052	72	7	the	the	DET
bracis-19052	72	8	diagonal	diagonal	ADJ
bracis-19052	72	9	in	in	ADP
bracis-19052	72	10	the	the	DET
bracis-19052	72	11	propagation	propagation	NOUN
bracis-19052	72	12	matrix	matrix	NOUN
bracis-19052	72	13	used	use	VERB
bracis-19052	72	14	by	by	ADP
bracis-19052	72	15	our	our	PRON
bracis-19052	72	16	baseline	baseline	NOUN
bracis-19052	72	17	,	,	PUNCT
bracis-19052	72	18	a	a	DET
bracis-19052	72	19	leave	leave	VERB
bracis-19052	72	20	-	-	PUNCT
bracis-19052	72	21	one	one	NUM
bracis-19052	72	22	-	-	PUNCT
bracis-19052	72	23	out	out	ADP
bracis-19052	72	24	criterion	criterion	NOUN
bracis-19052	72	25	can	can	AUX
bracis-19052	72	26	be	be	AUX
bracis-19052	72	27	easily	easily	ADV
bracis-19052	72	28	computed	compute	VERB
bracis-19052	72	29	.	.	PUNCT
bracis-19052	73	1	our	our	PRON
bracis-19052	73	2	first	first	ADJ
bracis-19052	73	3	proposed	propose	VERB
bracis-19052	73	4	algorithm	algorithm	NOUN
bracis-19052	73	5	attempts	attempt	VERB
bracis-19052	73	6	to	to	PART
bracis-19052	73	7	calculate	calculate	VERB
bracis-19052	73	8	label	label	NOUN
bracis-19052	73	9	reliability	reliability	NOUN
bracis-19052	73	10	by	by	ADP
bracis-19052	73	11	optimizing	optimize	VERB
bracis-19052	73	12	the	the	DET
bracis-19052	73	13	label	label	NOUN
bracis-19052	73	14	matrix	matrix	NOUN
bracis-19052	73	15	,	,	PUNCT
bracis-19052	73	16	subject	subject	ADJ
bracis-19052	73	17	to	to	ADP
bracis-19052	73	18	constraints	constraint	NOUN
bracis-19052	73	19	.	.	PUNCT
bracis-19052	74	1	this	this	DET
bracis-19052	74	2	approach	approach	NOUN
bracis-19052	74	3	is	be	AUX
bracis-19052	74	4	shown	show	VERB
bracis-19052	74	5	to	to	PART
bracis-19052	74	6	be	be	AUX
bracis-19052	74	7	competitive	competitive	ADJ
bracis-19052	74	8	with	with	ADP
bracis-19052	74	9	robust	robust	ADJ
bracis-19052	74	10	\(\ell	\(\ell	NOUN
bracis-19052	75	1	_	_	PUNCT
bracis-19052	76	1	1\)-norm	1\)-norm	NOUN
bracis-19052	76	2	classifiers	classifier	NOUN
bracis-19052	76	3	.	.	PUNCT
bracis-19052	77	1	then	then	ADV
bracis-19052	77	2	,	,	PUNCT
bracis-19052	77	3	we	we	PRON
bracis-19052	77	4	consider	consider	VERB
bracis-19052	77	5	the	the	DET
bracis-19052	77	6	problem	problem	NOUN
bracis-19052	77	7	of	of	ADP
bracis-19052	77	8	optimizing	optimize	VERB
bracis-19052	77	9	the	the	DET
bracis-19052	77	10	diffusion	diffusion	NOUN
bracis-19052	77	11	rate	rate	NOUN
bracis-19052	77	12	.	.	PUNCT
bracis-19052	78	1	doing	do	VERB
bracis-19052	78	2	this	this	PRON
bracis-19052	78	3	in	in	ADP
bracis-19052	78	4	the	the	DET
bracis-19052	78	5	usual	usual	ADJ
bracis-19052	78	6	formulation	formulation	NOUN
bracis-19052	78	7	of	of	ADP
bracis-19052	78	8	lgc	lgc	NOUN
bracis-19052	78	9	is	be	AUX
bracis-19052	78	10	impractically	impractically	ADV
bracis-19052	78	11	expensive	expensive	ADJ
bracis-19052	78	12	.	.	PUNCT
bracis-19052	79	1	however	however	ADV
bracis-19052	79	2	,	,	PUNCT
bracis-19052	79	3	we	we	PRON
bracis-19052	79	4	show	show	VERB
bracis-19052	79	5	that	that	SCONJ
bracis-19052	79	6	the	the	DET
bracis-19052	79	7	spectral	spectral	ADJ
bracis-19052	79	8	representation	representation	NOUN
bracis-19052	79	9	of	of	ADP
bracis-19052	79	10	the	the	DET
bracis-19052	79	11	problem	problem	NOUN
bracis-19052	79	12	can	can	AUX
bracis-19052	79	13	be	be	AUX
bracis-19052	79	14	exploited	exploit	VERB
bracis-19052	79	15	to	to	PART
bracis-19052	79	16	easily	easily	ADV
bracis-19052	79	17	solve	solve	VERB
bracis-19052	79	18	an	an	DET
bracis-19052	79	19	approximate	approximate	ADJ
bracis-19052	79	20	version	version	NOUN
bracis-19052	79	21	of	of	ADP
bracis-19052	79	22	the	the	DET
bracis-19052	79	23	problem	problem	NOUN
bracis-19052	79	24	.	.	PUNCT
bracis-19052	80	1	experimental	experimental	ADJ
bracis-19052	80	2	results	result	NOUN
bracis-19052	80	3	show	show	VERB
bracis-19052	80	4	that	that	SCONJ
bracis-19052	80	5	minimizing	minimize	VERB
bracis-19052	80	6	leave	leave	VERB
bracis-19052	80	7	-	-	PUNCT
bracis-19052	80	8	one	one	NUM
bracis-19052	80	9	-	-	PUNCT
bracis-19052	80	10	out	out	NOUN
bracis-19052	80	11	error	error	NOUN
bracis-19052	80	12	leads	lead	VERB
bracis-19052	80	13	to	to	ADP
bracis-19052	80	14	good	good	ADJ
bracis-19052	80	15	generalization	generalization	NOUN
bracis-19052	80	16	.	.	PUNCT
bracis-19052	81	1	the	the	DET
bracis-19052	81	2	remaining	remain	VERB
bracis-19052	81	3	of	of	ADP
bracis-19052	81	4	this	this	DET
bracis-19052	81	5	paper	paper	NOUN
bracis-19052	81	6	is	be	AUX
bracis-19052	81	7	organized	organize	VERB
bracis-19052	81	8	as	as	SCONJ
bracis-19052	81	9	follows	follow	VERB
bracis-19052	81	10	.	.	PUNCT
bracis-19052	82	1	section	section	NOUN
bracis-19052	82	2	 	 	SPACE
bracis-19052	82	3	2	2	NUM
bracis-19052	82	4	summarizes	summarize	NOUN
bracis-19052	82	5	the	the	DET
bracis-19052	82	6	key	key	ADJ
bracis-19052	82	7	ideas	idea	NOUN
bracis-19052	82	8	and	and	CCONJ
bracis-19052	82	9	concepts	concept	NOUN
bracis-19052	82	10	that	that	PRON
bracis-19052	82	11	are	be	AUX
bracis-19052	82	12	related	relate	VERB
bracis-19052	82	13	to	to	ADP
bracis-19052	82	14	our	our	PRON
bracis-19052	82	15	work	work	NOUN
bracis-19052	82	16	.	.	PUNCT
bracis-19052	83	1	section	section	NOUN
bracis-19052	83	2	 	 	SPACE
bracis-19052	83	3	3	3	NUM
bracis-19052	83	4	presents	present	VERB
bracis-19052	83	5	our	our	PRON
bracis-19052	83	6	two	two	NUM
bracis-19052	83	7	proposed	propose	VERB
bracis-19052	83	8	algorithms	algorithm	NOUN
bracis-19052	83	9	:	:	PUNCT
bracis-19052	83	10	\(\texttt	\(\texttt	NOUN
bracis-19052	83	11	{	{	PUNCT
bracis-19052	83	12	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	83	13	{	{	PUNCT
bracis-19052	83	14	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	83	15	{	{	PUNCT
bracis-19052	83	16	autol}\	autol}\	PROPN
bracis-19052	83	17	)	)	PUNCT
bracis-19052	83	18	for	for	ADP
bracis-19052	83	19	determining	determine	VERB
bracis-19052	83	20	label	label	NOUN
bracis-19052	83	21	reliability	reliability	NOUN
bracis-19052	83	22	,	,	PUNCT
bracis-19052	83	23	and	and	CCONJ
bracis-19052	83	24	\(\texttt	\(\texttt	NOUN
bracis-19052	83	25	{	{	PUNCT
bracis-19052	83	26	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	83	27	{	{	PUNCT
bracis-19052	83	28	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	83	29	{	{	PUNCT
bracis-19052	83	30	autod}\	autod}\	PROPN
bracis-19052	83	31	)	)	PUNCT
bracis-19052	83	32	for	for	ADP
bracis-19052	83	33	determining	determine	VERB
bracis-19052	83	34	the	the	DET
bracis-19052	83	35	optimal	optimal	ADJ
bracis-19052	83	36	diffusion	diffusion	NOUN
bracis-19052	83	37	rate	rate	NOUN
bracis-19052	83	38	parameter	parameter	NOUN
bracis-19052	83	39	.	.	PUNCT
bracis-19052	84	1	our	our	PRON
bracis-19052	84	2	methodology	methodology	NOUN
bracis-19052	84	3	is	be	AUX
bracis-19052	84	4	detailed	detail	VERB
bracis-19052	84	5	in	in	ADP
bracis-19052	84	6	sect	sect	NOUN
bracis-19052	84	7	.	.	PUNCT
bracis-19052	84	8	 	 	SPACE
bracis-19052	85	1	4	4	NUM
bracis-19052	85	2	,	,	PUNCT
bracis-19052	85	3	going	go	VERB
bracis-19052	85	4	over	over	ADP
bracis-19052	85	5	the	the	DET
bracis-19052	85	6	basic	basic	ADJ
bracis-19052	85	7	framework	framework	NOUN
bracis-19052	85	8	and	and	CCONJ
bracis-19052	85	9	baselines	baseline	NOUN
bracis-19052	85	10	.	.	PUNCT
bracis-19052	86	1	the	the	DET
bracis-19052	86	2	results	result	NOUN
bracis-19052	86	3	are	be	AUX
bracis-19052	86	4	presented	present	VERB
bracis-19052	86	5	in	in	ADP
bracis-19052	86	6	sect	sect	NOUN
bracis-19052	86	7	.	.	PUNCT
bracis-19052	86	8	 	 	SPACE
bracis-19052	87	1	5	5	NUM
bracis-19052	87	2	.	.	PUNCT
bracis-19052	87	3	lastly	lastly	ADV
bracis-19052	87	4	,	,	PUNCT
bracis-19052	87	5	concluding	conclude	VERB
bracis-19052	87	6	remarks	remark	NOUN
bracis-19052	87	7	are	be	AUX
bracis-19052	87	8	found	find	VERB
bracis-19052	87	9	in	in	ADP
bracis-19052	87	10	sect	sect	NOUN
bracis-19052	87	11	.	.	PUNCT
bracis-19052	87	12	 	 	SPACE
bracis-19052	88	1	6	6	NUM
bracis-19052	88	2	.	.	SYM
bracis-19052	88	3	2	2	NUM
bracis-19052	88	4	related	relate	VERB
bracis-19052	88	5	work	work	NOUN
bracis-19052	88	6	in	in	ADP
bracis-19052	88	7	this	this	DET
bracis-19052	88	8	section	section	NOUN
bracis-19052	88	9	,	,	PUNCT
bracis-19052	88	10	we	we	PRON
bracis-19052	88	11	present	present	VERB
bracis-19052	88	12	some	some	PRON
bracis-19052	88	13	of	of	ADP
bracis-19052	88	14	the	the	DET
bracis-19052	88	15	algorithms	algorithm	NOUN
bracis-19052	88	16	and	and	CCONJ
bracis-19052	88	17	concepts	concept	NOUN
bracis-19052	88	18	that	that	PRON
bracis-19052	88	19	are	be	AUX
bracis-19052	88	20	central	central	ADJ
bracis-19052	88	21	to	to	ADP
bracis-19052	88	22	our	our	PRON
bracis-19052	88	23	approach	approach	NOUN
bracis-19052	88	24	.	.	PUNCT
bracis-19052	89	1	we	we	PRON
bracis-19052	89	2	describe	describe	VERB
bracis-19052	89	3	the	the	DET
bracis-19052	89	4	inner	inner	ADJ
bracis-19052	89	5	workings	working	NOUN
bracis-19052	89	6	of	of	ADP
bracis-19052	89	7	our	our	PRON
bracis-19052	89	8	baseline	baseline	NOUN
bracis-19052	89	9	algorithm	algorithm	NOUN
bracis-19052	89	10	,	,	PUNCT
bracis-19052	89	11	and	and	CCONJ
bracis-19052	89	12	how	how	SCONJ
bracis-19052	89	13	eliminating	eliminate	VERB
bracis-19052	89	14	diagonal	diagonal	ADJ
bracis-19052	89	15	entries	entry	NOUN
bracis-19052	89	16	of	of	ADP
bracis-19052	89	17	its	its	PRON
bracis-19052	89	18	propagation	propagation	NOUN
bracis-19052	89	19	matrix	matrix	NOUN
bracis-19052	89	20	may	may	AUX
bracis-19052	89	21	lead	lead	VERB
bracis-19052	89	22	to	to	ADP
bracis-19052	89	23	better	well	ADJ
bracis-19052	89	24	generalization	generalization	NOUN
bracis-19052	89	25	.	.	PUNCT
bracis-19052	90	1	2.1	2.1	NUM
bracis-19052	90	2	local	local	ADJ
bracis-19052	90	3	and	and	CCONJ
bracis-19052	90	4	 	 	SPACE
bracis-19052	90	5	global	global	ADJ
bracis-19052	90	6	consistency	consistency	NOUN
bracis-19052	90	7	the	the	DET
bracis-19052	90	8	local	local	ADJ
bracis-19052	90	9	and	and	CCONJ
bracis-19052	90	10	global	global	ADJ
bracis-19052	90	11	consistency	consistency	NOUN
bracis-19052	90	12	(	(	PUNCT
bracis-19052	90	13	lgc	lgc	NOUN
bracis-19052	90	14	)	)	PUNCT
bracis-19052	91	1	[	[	X
bracis-19052	91	2	17	17	NUM
bracis-19052	91	3	]	]	PUNCT
bracis-19052	91	4	algorithm	algorithm	NOUN
bracis-19052	91	5	is	be	AUX
bracis-19052	91	6	one	one	NUM
bracis-19052	91	7	of	of	ADP
bracis-19052	91	8	the	the	DET
bracis-19052	91	9	most	most	ADV
bracis-19052	91	10	widely	widely	ADV
bracis-19052	91	11	known	know	VERB
bracis-19052	91	12	graph	graph	NOUN
bracis-19052	91	13	-	-	PUNCT
bracis-19052	91	14	based	base	VERB
bracis-19052	91	15	semi	semi	ADJ
bracis-19052	91	16	-	-	ADJ
bracis-19052	91	17	supervised	supervised	ADJ
bracis-19052	91	18	algorithms	algorithm	NOUN
bracis-19052	91	19	.	.	PUNCT
bracis-19052	92	1	it	it	PRON
bracis-19052	92	2	minimizes	minimize	VERB
bracis-19052	92	3	the	the	DET
bracis-19052	92	4	following	follow	VERB
bracis-19052	92	5	cost	cost	NOUN
bracis-19052	92	6	:	:	PUNCT
bracis-19052	92	7	$	$	SYM
bracis-19052	92	8	$	$	SYM
bracis-19052	92	9	\begin{aligned	\begin{aligne	VERB
bracis-19052	92	10	}	}	PUNCT
bracis-19052	92	11	\mathcal	\mathcal	ADJ
bracis-19052	92	12	{	{	PUNCT
bracis-19052	92	13	q	q	NOUN
bracis-19052	92	14	}	}	PUNCT
bracis-19052	92	15	(	(	PUNCT
bracis-19052	92	16	\mathbf	\mathbf	PROPN
bracis-19052	92	17	{	{	PUNCT
bracis-19052	92	18	f	f	NOUN
bracis-19052	92	19	}	}	PUNCT
bracis-19052	92	20	)	)	PUNCT
bracis-19052	92	21	=	=	PUNCT
bracis-19052	92	22	\frac{1}{2	\frac{1}{2	PROPN
bracis-19052	92	23	}	}	PUNCT
bracis-19052	92	24	\left	\left	PROPN
bracis-19052	92	25	(	(	PUNCT
bracis-19052	92	26	tr	tr	VERB
bracis-19052	92	27	(	(	PUNCT
bracis-19052	92	28	\mathbf	\mathbf	PROPN
bracis-19052	92	29	{	{	PUNCT
bracis-19052	92	30	f}^{\top	f}^{\top	PROPN
bracis-19052	92	31	}	}	PUNCT
bracis-19052	92	32	\mathbf	\mathbf	PROPN
bracis-19052	92	33	{	{	PUNCT
bracis-19052	92	34	l}_{\mathbb	l}_{\mathbb	X
bracis-19052	92	35	{	{	PUNCT
bracis-19052	92	36	n	n	CCONJ
bracis-19052	92	37	}	}	PUNCT
bracis-19052	92	38	}	}	PUNCT
bracis-19052	92	39	\mathbf	\mathbf	PROPN
bracis-19052	92	40	{	{	PUNCT
bracis-19052	92	41	f	f	NOUN
bracis-19052	92	42	}	}	PUNCT
bracis-19052	92	43	)	)	PUNCT
bracis-19052	93	1	+	+	CCONJ
bracis-19052	93	2	\mu	\mu	PROPN
bracis-19052	93	3	\big	\big	PROPN
bracis-19052	93	4	\vert	\vert	PROPN
bracis-19052	93	5	\mathbf	\mathbf	PROPN
bracis-19052	93	6	{	{	PUNCT
bracis-19052	93	7	f	f	NOUN
bracis-19052	93	8	}	}	PUNCT
bracis-19052	93	9	\mathbf	\mathbf	PROPN
bracis-19052	93	10	{	{	PUNCT
bracis-19052	93	11	y}\big	y}\big	NOUN
bracis-19052	93	12	\vert	\vert	PROPN
bracis-19052	93	13	^2	^2	PUNCT
bracis-19052	93	14	\right	\right	PROPN
bracis-19052	93	15	)	)	PUNCT
bracis-19052	93	16	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	93	17	(	(	PUNCT
bracis-19052	93	18	14	14	NUM
bracis-19052	93	19	)	)	PUNCT
bracis-19052	93	20	lgc	lgc	ADJ
bracis-19052	93	21	addresses	address	NOUN
bracis-19052	93	22	the	the	DET
bracis-19052	93	23	issue	issue	NOUN
bracis-19052	93	24	of	of	ADP
bracis-19052	93	25	label	label	NOUN
bracis-19052	93	26	reliability	reliability	NOUN
bracis-19052	93	27	by	by	ADP
bracis-19052	93	28	introducing	introduce	VERB
bracis-19052	93	29	the	the	DET
bracis-19052	93	30	parameter	parameter	NOUN
bracis-19052	93	31	\(\mu	\(\mu	PROPN
bracis-19052	93	32	\in	\in	PROPN
bracis-19052	93	33	(	(	PUNCT
bracis-19052	93	34	0	0	NUM
bracis-19052	93	35	,	,	PUNCT
bracis-19052	93	36	\infty	\infty	NOUN
bracis-19052	93	37	)	)	PUNCT
bracis-19052	93	38	\	\	PROPN
bracis-19052	93	39	)	)	PUNCT
bracis-19052	93	40	.	.	PUNCT
bracis-19052	94	1	this	this	DET
bracis-19052	94	2	parameter	parameter	NOUN
bracis-19052	94	3	controls	control	VERB
bracis-19052	94	4	the	the	DET
bracis-19052	94	5	trade	trade	NOUN
bracis-19052	94	6	-	-	PUNCT
bracis-19052	94	7	off	off	NOUN
bracis-19052	94	8	between	between	ADP
bracis-19052	94	9	fitting	fitting	ADJ
bracis-19052	94	10	labels	label	NOUN
bracis-19052	94	11	,	,	PUNCT
bracis-19052	94	12	and	and	CCONJ
bracis-19052	94	13	achieving	achieve	VERB
bracis-19052	94	14	high	high	ADJ
bracis-19052	94	15	graph	graph	NOUN
bracis-19052	94	16	smoothness	smoothness	ADJ
bracis-19052	94	17	.	.	PUNCT
bracis-19052	95	1	lgc	lgc	PROPN
bracis-19052	95	2	has	have	VERB
bracis-19052	95	3	an	an	DET
bracis-19052	95	4	analytic	analytic	ADJ
bracis-19052	95	5	solution	solution	NOUN
bracis-19052	95	6	.	.	PUNCT
bracis-19052	96	1	to	to	PART
bracis-19052	96	2	see	see	VERB
bracis-19052	96	3	this	this	PRON
bracis-19052	96	4	,	,	PUNCT
bracis-19052	96	5	we	we	PRON
bracis-19052	96	6	take	take	VERB
bracis-19052	96	7	the	the	DET
bracis-19052	96	8	partial	partial	ADJ
bracis-19052	96	9	derivative	derivative	NOUN
bracis-19052	96	10	of	of	ADP
bracis-19052	96	11	the	the	DET
bracis-19052	96	12	cost	cost	NOUN
bracis-19052	96	13	with	with	ADP
bracis-19052	96	14	respect	respect	NOUN
bracis-19052	96	15	to	to	ADP
bracis-19052	96	16	\	\	PROPN
bracis-19052	96	17	(	(	PUNCT
bracis-19052	96	18	\mathbf	\mathbf	PROPN
bracis-19052	96	19	{	{	PUNCT
bracis-19052	96	20	f}\	f}\	NOUN
bracis-19052	96	21	):	):	PUNCT
bracis-19052	96	22	$	$	SYM
bracis-19052	96	23	$	$	SYM
bracis-19052	96	24	\begin{aligned	\begin{aligne	VERB
bracis-19052	96	25	}	}	PUNCT
bracis-19052	96	26	\frac{\partial	\frac{\partial	NOUN
bracis-19052	96	27	^	^	PUNCT
bracis-19052	96	28	{	{	PUNCT
bracis-19052	96	29	}	}	PUNCT
bracis-19052	96	30	\mathcal	\mathcal	ADJ
bracis-19052	96	31	{	{	PUNCT
bracis-19052	96	32	q}}{\partial	q}}{\partial	ADJ
bracis-19052	96	33	\mathbf	\mathbf	PROPN
bracis-19052	96	34	{	{	PUNCT
bracis-19052	96	35	f}}&=	f}}&=	PROPN
bracis-19052	96	36	\frac{1}{2	\frac{1}{2	PROPN
bracis-19052	96	37	}	}	PUNCT
bracis-19052	96	38	\frac{\partial	\frac{\partial	NOUN
bracis-19052	96	39	^	^	PUNCT
bracis-19052	96	40	{	{	PUNCT
bracis-19052	96	41	}	}	PUNCT
bracis-19052	96	42	tr	tr	VERB
bracis-19052	96	43	(	(	PUNCT
bracis-19052	96	44	\mathbf	\mathbf	PROPN
bracis-19052	96	45	{	{	PUNCT
bracis-19052	96	46	f}^{\top	f}^{\top	PROPN
bracis-19052	96	47	}	}	PUNCT
bracis-19052	96	48	\mathbf	\mathbf	PROPN
bracis-19052	96	49	{	{	PUNCT
bracis-19052	96	50	l}_{\mathbb	l}_{\mathbb	X
bracis-19052	96	51	{	{	PUNCT
bracis-19052	96	52	n	n	CCONJ
bracis-19052	96	53	}	}	PUNCT
bracis-19052	96	54	}	}	PUNCT
bracis-19052	96	55	\mathbf	\mathbf	PROPN
bracis-19052	96	56	{	{	PUNCT
bracis-19052	96	57	f})}{\partial	f})}{\partial	ADJ
bracis-19052	96	58	\mathbf	\mathbf	PROPN
bracis-19052	96	59	{	{	PUNCT
bracis-19052	96	60	f	f	NOUN
bracis-19052	96	61	}	}	PUNCT
bracis-19052	96	62	}	}	PUNCT
bracis-19052	96	63	+	+	CCONJ
bracis-19052	96	64	\frac{1}{2	\frac{1}{2	NOUN
bracis-19052	96	65	}	}	PUNCT
bracis-19052	96	66	\mu	\mu	PROPN
bracis-19052	96	67	\frac{\partial	\frac{\partial	NOUN
bracis-19052	96	68	^	^	PUNCT
bracis-19052	96	69	{	{	PUNCT
bracis-19052	96	70	}	}	PUNCT
bracis-19052	96	71	\big	\big	PROPN
bracis-19052	96	72	\vert	\vert	PROPN
bracis-19052	96	73	\mathbf	\mathbf	PROPN
bracis-19052	96	74	{	{	PUNCT
bracis-19052	96	75	f	f	NOUN
bracis-19052	96	76	}	}	PUNCT
bracis-19052	96	77	\mathbf	\mathbf	PROPN
bracis-19052	96	78	{	{	PUNCT
bracis-19052	96	79	y}\big	y}\big	ADJ
bracis-19052	96	80	\vert	\vert	PROPN
bracis-19052	96	81	^2}{\partial	^2}{\partial	ADJ
bracis-19052	96	82	\mathbf	\mathbf	PROPN
bracis-19052	96	83	{	{	PUNCT
bracis-19052	96	84	f}}\end{aligned}$$	f}}\end{aligned}$$	PROPN
bracis-19052	96	85	(	(	PUNCT
bracis-19052	96	86	15	15	NUM
bracis-19052	96	87	)	)	PUNCT
bracis-19052	96	88	$	$	SYM
bracis-19052	96	89	$	$	SYM
bracis-19052	96	90	\begin{aligned}&=	\begin{aligned}&=	NOUN
bracis-19052	96	91	(	(	PUNCT
bracis-19052	96	92	(	(	PUNCT
bracis-19052	96	93	1+\mu	1+\mu	NUM
bracis-19052	96	94	)	)	PUNCT
bracis-19052	96	95	\mathbf	\mathbf	PROPN
bracis-19052	96	96	{	{	PUNCT
bracis-19052	96	97	i	i	NOUN
bracis-19052	96	98	}	}	PUNCT
bracis-19052	96	99	\mathbf	\mathbf	PROPN
bracis-19052	96	100	{	{	PUNCT
bracis-19052	96	101	s	s	NOUN
bracis-19052	96	102	}	}	PUNCT
bracis-19052	96	103	)	)	PUNCT
bracis-19052	97	1	\mathbf	\mathbf	PROPN
bracis-19052	97	2	{	{	PUNCT
bracis-19052	97	3	f	f	X
bracis-19052	97	4	}	}	PUNCT
bracis-19052	97	5	\mu	\mu	PROPN
bracis-19052	97	6	\mathbf	\mathbf	PROPN
bracis-19052	97	7	{	{	PUNCT
bracis-19052	97	8	y	y	PROPN
bracis-19052	97	9	}	}	PUNCT
bracis-19052	97	10	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	97	11	(	(	PUNCT
bracis-19052	97	12	16	16	NUM
bracis-19052	97	13	)	)	PUNCT
bracis-19052	97	14	where	where	SCONJ
bracis-19052	97	15	\	\	PROPN
bracis-19052	97	16	(	(	PUNCT
bracis-19052	97	17	\mathbf	\mathbf	PROPN
bracis-19052	97	18	{	{	PUNCT
bracis-19052	97	19	s	s	NOUN
bracis-19052	97	20	}	}	PUNCT
bracis-19052	97	21	=	=	SYM
bracis-19052	97	22	\mathbf	\mathbf	NOUN
bracis-19052	97	23	{	{	PUNCT
bracis-19052	97	24	d}^{-\frac{1}{2	d}^{-\frac{1}{2	PROPN
bracis-19052	97	25	}	}	PUNCT
bracis-19052	97	26	}	}	PUNCT
bracis-19052	97	27	\mathbf	\mathbf	PROPN
bracis-19052	97	28	{	{	PUNCT
bracis-19052	97	29	w	w	NOUN
bracis-19052	97	30	}	}	PUNCT
bracis-19052	97	31	\mathbf	\mathbf	PROPN
bracis-19052	97	32	{	{	PUNCT
bracis-19052	97	33	d}^{-\frac{1}{2	d}^{-\frac{1}{2	PROPN
bracis-19052	97	34	}	}	PUNCT
bracis-19052	97	35	}	}	PUNCT
bracis-19052	97	36	=	=	SYM
bracis-19052	97	37	\mathbf	\mathbf	PROPN
bracis-19052	97	38	{	{	PUNCT
bracis-19052	97	39	i	i	NOUN
bracis-19052	97	40	}	}	PUNCT
bracis-19052	97	41	\mathbf	\mathbf	PROPN
bracis-19052	97	42	{	{	PUNCT
bracis-19052	97	43	l}_{\mathbb	l}_{\mathbb	PROPN
bracis-19052	97	44	{	{	PUNCT
bracis-19052	97	45	n}}\	n}}\	INTJ
bracis-19052	97	46	)	)	PUNCT
bracis-19052	97	47	.	.	PUNCT
bracis-19052	98	1	by	by	ADP
bracis-19052	98	2	dividing	divide	VERB
bracis-19052	98	3	the	the	DET
bracis-19052	98	4	above	above	ADJ
bracis-19052	98	5	by	by	ADP
bracis-19052	98	6	(	(	PUNCT
bracis-19052	98	7	\(1	\(1	PROPN
bracis-19052	98	8	+	+	X
bracis-19052	98	9	\mu	\mu	PROPN
bracis-19052	98	10	\	\	NOUN
bracis-19052	98	11	)	)	PUNCT
bracis-19052	98	12	)	)	PUNCT
bracis-19052	98	13	,	,	PUNCT
bracis-19052	98	14	we	we	PRON
bracis-19052	98	15	observe	observe	VERB
bracis-19052	98	16	that	that	SCONJ
bracis-19052	98	17	this	this	DET
bracis-19052	98	18	derivative	derivative	NOUN
bracis-19052	98	19	is	be	AUX
bracis-19052	98	20	zero	zero	NUM
bracis-19052	98	21	exactly	exactly	ADV
bracis-19052	98	22	when	when	SCONJ
bracis-19052	98	23	$	$	SYM
bracis-19052	98	24	$	$	SYM
bracis-19052	98	25	\begin{aligned	\begin{aligne	VERB
bracis-19052	98	26	}	}	PUNCT
bracis-19052	98	27	(	(	PUNCT
bracis-19052	98	28	i	i	PRON
bracis-19052	98	29	\alpha	\alpha	ADP
bracis-19052	98	30	\mathbf	\mathbf	PROPN
bracis-19052	98	31	{	{	PUNCT
bracis-19052	98	32	s	s	PROPN
bracis-19052	98	33	}	}	PUNCT
bracis-19052	98	34	)	)	PUNCT
bracis-19052	99	1	\mathbf	\mathbf	PROPN
bracis-19052	99	2	{	{	PUNCT
bracis-19052	99	3	f	f	X
bracis-19052	99	4	}	}	PUNCT
bracis-19052	99	5	=	=	PUNCT
bracis-19052	99	6	\beta	\beta	PROPN
bracis-19052	99	7	\mathbf	\mathbf	PROPN
bracis-19052	99	8	{	{	PUNCT
bracis-19052	99	9	y	y	PROPN
bracis-19052	99	10	}	}	PUNCT
bracis-19052	99	11	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	99	12	(	(	PUNCT
bracis-19052	99	13	17	17	NUM
bracis-19052	99	14	)	)	PUNCT
bracis-19052	99	15	with	with	ADP
bracis-19052	99	16	$	$	SYM
bracis-19052	99	17	$	$	SYM
bracis-19052	99	18	\begin{aligned	\begin{aligne	VERB
bracis-19052	99	19	}	}	PUNCT
bracis-19052	99	20	\alpha	\alpha	ADJ
bracis-19052	99	21	=	=	PUNCT
bracis-19052	99	22	\frac{1}{1+\mu	\frac{1}{1+\mu	NOUN
bracis-19052	99	23	}	}	PUNCT
bracis-19052	99	24	\in	\in	PROPN
bracis-19052	99	25	(	(	PUNCT
bracis-19052	99	26	0,1	0,1	NUM
bracis-19052	99	27	)	)	PUNCT
bracis-19052	99	28	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	99	29	(	(	PUNCT
bracis-19052	99	30	18	18	NUM
bracis-19052	99	31	)	)	PUNCT
bracis-19052	99	32	and	and	CCONJ
bracis-19052	99	33	$	$	SYM
bracis-19052	99	34	$	$	SYM
bracis-19052	99	35	\begin{aligned	\begin{aligne	VERB
bracis-19052	99	36	}	}	PUNCT
bracis-19052	99	37	\beta	\beta	NOUN
bracis-19052	99	38	=	=	SYM
bracis-19052	99	39	1	1	NUM
bracis-19052	99	40	\alpha	\alpha	NOUN
bracis-19052	99	41	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	99	42	(	(	PUNCT
bracis-19052	99	43	19	19	NUM
bracis-19052	99	44	)	)	PUNCT
bracis-19052	99	45	the	the	DET
bracis-19052	99	46	matrix	matrix	NOUN
bracis-19052	99	47	\	\	PROPN
bracis-19052	99	48	(	(	PUNCT
bracis-19052	99	49	(	(	PUNCT
bracis-19052	99	50	\mathbf	\mathbf	PROPN
bracis-19052	99	51	{	{	PUNCT
bracis-19052	99	52	i	i	NOUN
bracis-19052	99	53	}	}	PUNCT
bracis-19052	99	54	\alpha	\alpha	ADP
bracis-19052	99	55	\mathbf	\mathbf	PROPN
bracis-19052	99	56	{	{	PUNCT
bracis-19052	99	57	s})\	s})\	X
bracis-19052	99	58	)	)	PUNCT
bracis-19052	99	59	can	can	AUX
bracis-19052	99	60	be	be	AUX
bracis-19052	99	61	shown	show	VERB
bracis-19052	99	62	to	to	PART
bracis-19052	99	63	be	be	AUX
bracis-19052	99	64	positive	positive	ADJ
bracis-19052	99	65	-	-	PUNCT
bracis-19052	99	66	definite	definite	ADJ
bracis-19052	99	67	and	and	CCONJ
bracis-19052	99	68	therefore	therefore	ADV
bracis-19052	99	69	invertible	invertible	ADJ
bracis-19052	99	70	,	,	PUNCT
bracis-19052	99	71	so	so	CCONJ
bracis-19052	99	72	the	the	DET
bracis-19052	99	73	optimal	optimal	ADJ
bracis-19052	99	74	\	\	NOUN
bracis-19052	99	75	(	(	PUNCT
bracis-19052	99	76	\mathbf	\mathbf	PROPN
bracis-19052	99	77	{	{	PUNCT
bracis-19052	99	78	f}\	f}\	NOUN
bracis-19052	99	79	)	)	PUNCT
bracis-19052	99	80	can	can	AUX
bracis-19052	99	81	be	be	AUX
bracis-19052	99	82	obtained	obtain	VERB
bracis-19052	99	83	as	as	ADP
bracis-19052	99	84	$	$	SYM
bracis-19052	99	85	$	$	SYM
bracis-19052	99	86	\begin{aligned	\begin{aligne	VERB
bracis-19052	99	87	}	}	PUNCT
bracis-19052	99	88	\mathbf	\mathbf	PROPN
bracis-19052	99	89	{	{	PUNCT
bracis-19052	99	90	f	f	NOUN
bracis-19052	99	91	}	}	PUNCT
bracis-19052	99	92	=	=	SYM
bracis-19052	99	93	\beta	\beta	PROPN
bracis-19052	99	94	(	(	PUNCT
bracis-19052	99	95	i	i	PRON
bracis-19052	99	96	\alpha	\alpha	ADP
bracis-19052	99	97	\mathbf	\mathbf	PROPN
bracis-19052	99	98	{	{	PUNCT
bracis-19052	99	99	s})^{-1	s})^{-1	PROPN
bracis-19052	99	100	}	}	PUNCT
bracis-19052	99	101	\mathbf	\mathbf	PROPN
bracis-19052	99	102	{	{	PUNCT
bracis-19052	99	103	y	y	PROPN
bracis-19052	99	104	}	}	PUNCT
bracis-19052	99	105	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	99	106	(	(	PUNCT
bracis-19052	99	107	20	20	NUM
bracis-19052	99	108	)	)	PUNCT
bracis-19052	99	109	we	we	PRON
bracis-19052	99	110	hereafter	hereafter	ADV
bracis-19052	99	111	refer	refer	VERB
bracis-19052	99	112	to	to	ADP
bracis-19052	99	113	\((i	\((i	ADV
bracis-19052	99	114	\alpha	\alpha	ADJ
bracis-19052	99	115	s)^{-1}\	s)^{-1}\	NOUN
bracis-19052	99	116	)	)	PUNCT
bracis-19052	99	117	as	as	ADP
bracis-19052	99	118	the	the	DET
bracis-19052	99	119	propagation	propagation	NOUN
bracis-19052	99	120	matrix	matrix	NOUN
bracis-19052	99	121	\	\	PROPN
bracis-19052	99	122	(	(	PUNCT
bracis-19052	99	123	\mathbf	\mathbf	PROPN
bracis-19052	99	124	{	{	PUNCT
bracis-19052	99	125	p}\	p}\	NUM
bracis-19052	99	126	)	)	PUNCT
bracis-19052	99	127	.	.	PUNCT
bracis-19052	100	1	each	each	DET
bracis-19052	100	2	entry	entry	NOUN
bracis-19052	100	3	\	\	PROPN
bracis-19052	100	4	(	(	PUNCT
bracis-19052	100	5	\mathbf	\mathbf	PROPN
bracis-19052	100	6	{	{	PUNCT
bracis-19052	100	7	p}_{ij}\	p}_{ij}\	PROPN
bracis-19052	100	8	)	)	PUNCT
bracis-19052	100	9	represents	represent	VERB
bracis-19052	100	10	the	the	DET
bracis-19052	100	11	amount	amount	NOUN
bracis-19052	100	12	of	of	ADP
bracis-19052	100	13	label	label	NOUN
bracis-19052	100	14	information	information	NOUN
bracis-19052	100	15	from	from	ADP
bracis-19052	100	16	\(x_j\	\(x_j\	PROPN
bracis-19052	100	17	)	)	PUNCT
bracis-19052	100	18	that	that	PRON
bracis-19052	100	19	\(x_i\	\(x_i\	VERB
bracis-19052	100	20	)	)	PUNCT
bracis-19052	100	21	inherits	inherit	VERB
bracis-19052	100	22	.	.	PUNCT
bracis-19052	101	1	it	it	PRON
bracis-19052	101	2	can	can	AUX
bracis-19052	101	3	be	be	AUX
bracis-19052	101	4	shown	show	VERB
bracis-19052	101	5	that	that	SCONJ
bracis-19052	101	6	the	the	DET
bracis-19052	101	7	inverse	inverse	NOUN
bracis-19052	101	8	is	be	AUX
bracis-19052	101	9	a	a	DET
bracis-19052	101	10	result	result	NOUN
bracis-19052	101	11	of	of	ADP
bracis-19052	101	12	a	a	DET
bracis-19052	101	13	diffusion	diffusion	NOUN
bracis-19052	101	14	process	process	NOUN
bracis-19052	101	15	,	,	PUNCT
bracis-19052	101	16	which	which	PRON
bracis-19052	101	17	is	be	AUX
bracis-19052	101	18	calculated	calculate	VERB
bracis-19052	101	19	via	via	ADP
bracis-19052	101	20	iteration	iteration	NOUN
bracis-19052	101	21	:	:	PUNCT
bracis-19052	101	22	$	$	SYM
bracis-19052	101	23	$	$	SYM
bracis-19052	101	24	\begin{aligned}&f(0	\begin{aligned}&f(0	NOUN
bracis-19052	101	25	)	)	PUNCT
bracis-19052	102	1	=	=	SYM
bracis-19052	102	2	\mathbf	\mathbf	PROPN
bracis-19052	102	3	{	{	PUNCT
bracis-19052	102	4	y}\end{aligned}$$	y}\end{aligned}$$	PROPN
bracis-19052	102	5	(	(	PUNCT
bracis-19052	102	6	21	21	NUM
bracis-19052	102	7	)	)	PUNCT
bracis-19052	102	8	$	$	SYM
bracis-19052	102	9	$	$	SYM
bracis-19052	102	10	\begin{aligned}&f(t\!+\!1	\begin{aligned}&f(t\!+\!1	NUM
bracis-19052	102	11	)	)	PUNCT
bracis-19052	102	12	=	=	SYM
bracis-19052	102	13	\alpha	\alpha	ADP
bracis-19052	102	14	\mathbf	\mathbf	PROPN
bracis-19052	102	15	{	{	PUNCT
bracis-19052	102	16	s	s	PROPN
bracis-19052	102	17	}	}	PUNCT
bracis-19052	102	18	f(t	f(t	NOUN
bracis-19052	102	19	)	)	PUNCT
bracis-19052	103	1	+	+	CCONJ
bracis-19052	103	2	(	(	PUNCT
bracis-19052	103	3	1\!-\!\alpha	1\!-\!\alpha	NUM
bracis-19052	103	4	)	)	PUNCT
bracis-19052	103	5	\mathbf	\mathbf	PROPN
bracis-19052	103	6	{	{	PUNCT
bracis-19052	103	7	y	y	PROPN
bracis-19052	103	8	}	}	PUNCT
bracis-19052	103	9	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	103	10	(	(	PUNCT
bracis-19052	103	11	22	22	NUM
bracis-19052	103	12	)	)	PUNCT
bracis-19052	103	13	moreover	moreover	ADV
bracis-19052	103	14	,	,	PUNCT
bracis-19052	103	15	it	it	PRON
bracis-19052	103	16	can	can	AUX
bracis-19052	103	17	be	be	AUX
bracis-19052	103	18	shown	show	VERB
bracis-19052	103	19	that	that	SCONJ
bracis-19052	103	20	the	the	DET
bracis-19052	103	21	closed	closed	ADJ
bracis-19052	103	22	expression	expression	NOUN
bracis-19052	103	23	for	for	ADP
bracis-19052	103	24	f	f	PROPN
bracis-19052	103	25	at	at	ADP
bracis-19052	103	26	any	any	DET
bracis-19052	103	27	iteration	iteration	NOUN
bracis-19052	103	28	is	be	AUX
bracis-19052	103	29	$	$	SYM
bracis-19052	103	30	$	$	SYM
bracis-19052	103	31	\begin{aligned	\begin{aligne	VERB
bracis-19052	103	32	}	}	PUNCT
bracis-19052	103	33	f(t	f(t	NOUN
bracis-19052	103	34	)	)	PUNCT
bracis-19052	104	1	=	=	SYM
bracis-19052	104	2	(	(	PUNCT
bracis-19052	104	3	\alpha	\alpha	ADP
bracis-19052	104	4	\mathbf	\mathbf	PROPN
bracis-19052	104	5	{	{	PUNCT
bracis-19052	104	6	s})^{t-1	s})^{t-1	PROPN
bracis-19052	104	7	}	}	PUNCT
bracis-19052	104	8	\mathbf	\mathbf	PROPN
bracis-19052	104	9	{	{	PUNCT
bracis-19052	104	10	y	y	NOUN
bracis-19052	104	11	}	}	PUNCT
bracis-19052	104	12	+	+	CCONJ
bracis-19052	104	13	(	(	PUNCT
bracis-19052	104	14	1-\alpha	1-\alpha	ADJ
bracis-19052	104	15	)	)	PUNCT
bracis-19052	104	16	\sum	\sum	NOUN
bracis-19052	104	17	_	_	PUNCT
bracis-19052	104	18	{	{	PUNCT
bracis-19052	104	19	i=0}^{t-1}(\alpha	i=0}^{t-1}(\alpha	PROPN
bracis-19052	104	20	\mathbf	\mathbf	PROPN
bracis-19052	104	21	{	{	PUNCT
bracis-19052	104	22	s})^{i	s})^{i	PROPN
bracis-19052	104	23	}	}	PUNCT
bracis-19052	104	24	\mathbf	\mathbf	PROPN
bracis-19052	104	25	{	{	PUNCT
bracis-19052	104	26	y	y	PROPN
bracis-19052	104	27	}	}	PUNCT
bracis-19052	104	28	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	104	29	(	(	PUNCT
bracis-19052	104	30	23	23	NUM
bracis-19052	104	31	)	)	PUNCT
bracis-19052	105	1	s	s	VERB
bracis-19052	105	2	is	be	AUX
bracis-19052	105	3	similar	similar	ADJ
bracis-19052	105	4	to	to	ADP
bracis-19052	105	5	\(d^{-1}w\	\(d^{-1}w\	ADJ
bracis-19052	105	6	)	)	PUNCT
bracis-19052	105	7	,	,	PUNCT
bracis-19052	105	8	whose	whose	DET
bracis-19052	105	9	eigenvalues	eigenvalue	NOUN
bracis-19052	105	10	are	be	AUX
bracis-19052	105	11	always	always	ADV
bracis-19052	105	12	in	in	ADP
bracis-19052	105	13	the	the	DET
bracis-19052	105	14	range	range	NOUN
bracis-19052	105	15	\([-1,1]\	\([-1,1]\	NUM
bracis-19052	105	16	)	)	PUNCT
bracis-19052	106	1	[	[	X
bracis-19052	106	2	17	17	NUM
bracis-19052	106	3	]	]	PUNCT
bracis-19052	106	4	.	.	PUNCT
bracis-19052	107	1	this	this	PRON
bracis-19052	107	2	ensures	ensure	VERB
bracis-19052	107	3	the	the	DET
bracis-19052	107	4	first	first	ADJ
bracis-19052	107	5	term	term	NOUN
bracis-19052	107	6	vanishes	vanish	VERB
bracis-19052	107	7	as	as	SCONJ
bracis-19052	107	8	t	t	PROPN
bracis-19052	107	9	grows	grow	VERB
bracis-19052	107	10	larger	large	ADJ
bracis-19052	107	11	,	,	PUNCT
bracis-19052	107	12	whereas	whereas	SCONJ
bracis-19052	107	13	the	the	DET
bracis-19052	107	14	second	second	ADJ
bracis-19052	107	15	term	term	NOUN
bracis-19052	107	16	converges	converge	VERB
bracis-19052	107	17	to	to	ADP
bracis-19052	107	18	\	\	PROPN
bracis-19052	107	19	(	(	PUNCT
bracis-19052	107	20	\mathbf	\mathbf	PROPN
bracis-19052	107	21	{	{	PUNCT
bracis-19052	107	22	p}y\	p}y\	PROPN
bracis-19052	107	23	)	)	PUNCT
bracis-19052	107	24	.	.	PUNCT
bracis-19052	108	1	consequently	consequently	ADV
bracis-19052	108	2	,	,	PUNCT
bracis-19052	108	3	\	\	PROPN
bracis-19052	108	4	(	(	PUNCT
bracis-19052	108	5	\mathbf	\mathbf	PROPN
bracis-19052	108	6	{	{	PUNCT
bracis-19052	108	7	p}\	p}\	NOUN
bracis-19052	108	8	)	)	PUNCT
bracis-19052	108	9	can	can	AUX
bracis-19052	108	10	be	be	AUX
bracis-19052	108	11	characterized	characterize	VERB
bracis-19052	108	12	as	as	ADP
bracis-19052	108	13	$	$	SYM
bracis-19052	108	14	$	$	SYM
bracis-19052	108	15	\begin{aligned	\begin{aligne	VERB
bracis-19052	108	16	}	}	PUNCT
bracis-19052	108	17	\mathbf	\mathbf	PROPN
bracis-19052	108	18	{	{	PUNCT
bracis-19052	108	19	p}&=	p}&=	X
bracis-19052	108	20	(	(	PUNCT
bracis-19052	108	21	1-\alpha	1-\alpha	NUM
bracis-19052	108	22	)	)	PUNCT
bracis-19052	108	23	\lim	\lim	NOUN
bracis-19052	108	24	_	_	NOUN
bracis-19052	108	25	{	{	PUNCT
bracis-19052	109	1	t	t	NOUN
bracis-19052	109	2	\rightarrow	\rightarrow	PROPN
bracis-19052	109	3	\infty	\infty	PROPN
bracis-19052	109	4	}	}	PUNCT
bracis-19052	109	5	\sum	\sum	NOUN
bracis-19052	109	6	_	_	NOUN
bracis-19052	109	7	{	{	PUNCT
bracis-19052	109	8	i=0}^{t}(\alpha	i=0}^{t}(\alpha	PROPN
bracis-19052	109	9	\mathbf	\mathbf	PROPN
bracis-19052	109	10	{	{	PUNCT
bracis-19052	109	11	s})^{i}\end{aligned}$$	s})^{i}\end{aligned}$$	PROPN
bracis-19052	109	12	(	(	PUNCT
bracis-19052	109	13	24	24	NUM
bracis-19052	109	14	)	)	PUNCT
bracis-19052	109	15	$	$	SYM
bracis-19052	109	16	$	$	SYM
bracis-19052	109	17	\begin{aligned}&=	\begin{aligned}&=	NOUN
bracis-19052	109	18	(	(	PUNCT
bracis-19052	109	19	1-\alpha	1-\alpha	NUM
bracis-19052	109	20	)	)	PUNCT
bracis-19052	109	21	\lim	\lim	NOUN
bracis-19052	109	22	_	_	NOUN
bracis-19052	109	23	{	{	PUNCT
bracis-19052	109	24	t	t	NOUN
bracis-19052	109	25	\rightarrow	\rightarrow	PROPN
bracis-19052	109	26	\infty	\infty	PROPN
bracis-19052	109	27	}	}	PUNCT
bracis-19052	109	28	\sum	\sum	NOUN
bracis-19052	109	29	_	_	PUNCT
bracis-19052	109	30	{	{	PUNCT
bracis-19052	109	31	i=0}^{t	i=0}^{t	NOUN
bracis-19052	109	32	}	}	PUNCT
bracis-19052	109	33	\alpha	\alpha	ADP
bracis-19052	109	34	^i	^i	VERB
bracis-19052	109	35	\mathbf	\mathbf	PROPN
bracis-19052	109	36	{	{	PUNCT
bracis-19052	109	37	d}^{\frac{1}{2	d}^{\frac{1}{2	NOUN
bracis-19052	109	38	}	}	PUNCT
bracis-19052	109	39	}	}	PUNCT
bracis-19052	109	40	(	(	PUNCT
bracis-19052	109	41	\mathbf	\mathbf	PROPN
bracis-19052	109	42	{	{	PUNCT
bracis-19052	109	43	d}^{-1	d}^{-1	PROPN
bracis-19052	109	44	}	}	PUNCT
bracis-19052	109	45	\mathbf	\mathbf	PROPN
bracis-19052	109	46	{	{	PUNCT
bracis-19052	109	47	w})^{i	w})^{i	PROPN
bracis-19052	109	48	}	}	PUNCT
bracis-19052	109	49	\mathbf	\mathbf	PROPN
bracis-19052	109	50	{	{	PUNCT
bracis-19052	109	51	d}^{-\frac{1}{2	d}^{-\frac{1}{2	PROPN
bracis-19052	109	52	}	}	PUNCT
bracis-19052	109	53	}	}	PUNCT
bracis-19052	109	54	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	109	55	(	(	PUNCT
bracis-19052	109	56	25	25	NUM
bracis-19052	109	57	)	)	PUNCT
bracis-19052	109	58	the	the	DET
bracis-19052	109	59	transition	transition	NOUN
bracis-19052	109	60	probability	probability	NOUN
bracis-19052	109	61	matrix	matrix	NOUN
bracis-19052	109	62	\(\widetilde{w	\(\widetilde{w	PROPN
bracis-19052	109	63	}	}	PUNCT
bracis-19052	109	64	=	=	SYM
bracis-19052	109	65	\mathbf	\mathbf	PROPN
bracis-19052	109	66	{	{	PUNCT
bracis-19052	109	67	d^{-1}w}\	d^{-1}w}\	PROPN
bracis-19052	109	68	)	)	PUNCT
bracis-19052	109	69	makes	make	VERB
bracis-19052	109	70	it	it	PRON
bracis-19052	109	71	so	so	ADV
bracis-19052	109	72	we	we	PRON
bracis-19052	109	73	can	can	AUX
bracis-19052	109	74	interpret	interpret	VERB
bracis-19052	109	75	the	the	DET
bracis-19052	109	76	process	process	NOUN
bracis-19052	109	77	as	as	ADP
bracis-19052	109	78	a	a	DET
bracis-19052	109	79	random	random	ADJ
bracis-19052	109	80	walk	walk	NOUN
bracis-19052	109	81	.	.	PUNCT
bracis-19052	110	1	let	let	VERB
bracis-19052	110	2	us	we	PRON
bracis-19052	110	3	imagine	imagine	VERB
bracis-19052	110	4	a	a	DET
bracis-19052	110	5	particle	particle	NOUN
bracis-19052	110	6	walking	walk	VERB
bracis-19052	110	7	through	through	ADP
bracis-19052	110	8	the	the	DET
bracis-19052	110	9	graph	graph	NOUN
bracis-19052	110	10	according	accord	VERB
bracis-19052	110	11	to	to	ADP
bracis-19052	110	12	the	the	DET
bracis-19052	110	13	transition	transition	NOUN
bracis-19052	110	14	matrix	matrix	NOUN
bracis-19052	110	15	.	.	PUNCT
bracis-19052	111	1	assume	assume	VERB
bracis-19052	111	2	it	it	PRON
bracis-19052	111	3	began	begin	VERB
bracis-19052	111	4	at	at	ADP
bracis-19052	111	5	a	a	DET
bracis-19052	111	6	labeled	label	VERB
bracis-19052	111	7	vertex	vertex	NOUN
bracis-19052	111	8	\(v_a\	\(v_a\	NOUN
bracis-19052	111	9	)	)	PUNCT
bracis-19052	111	10	,	,	PUNCT
bracis-19052	111	11	and	and	CCONJ
bracis-19052	111	12	at	at	ADP
bracis-19052	111	13	step	step	NOUN
bracis-19052	111	14	i	i	PRON
bracis-19052	111	15	it	it	PRON
bracis-19052	111	16	reaches	reach	VERB
bracis-19052	111	17	a	a	DET
bracis-19052	111	18	labeled	label	VERB
bracis-19052	111	19	vertex	vertex	NOUN
bracis-19052	111	20	\(v_b\	\(v_b\	NOUN
bracis-19052	111	21	)	)	PUNCT
bracis-19052	111	22	,	,	PUNCT
bracis-19052	111	23	initially	initially	ADV
bracis-19052	111	24	labeled	label	VERB
bracis-19052	111	25	with	with	ADP
bracis-19052	111	26	class	class	PROPN
bracis-19052	111	27	\(c_b\	\(c_b\	PROPN
bracis-19052	111	28	)	)	PUNCT
bracis-19052	111	29	.	.	PUNCT
bracis-19052	112	1	when	when	SCONJ
bracis-19052	112	2	this	this	PRON
bracis-19052	112	3	happens	happen	VERB
bracis-19052	112	4	,	,	PUNCT
bracis-19052	112	5	\(v_a\	\(v_a\	NOUN
bracis-19052	112	6	)	)	PUNCT
bracis-19052	112	7	receives	receive	VERB
bracis-19052	112	8	a	a	DET
bracis-19052	112	9	confidence	confidence	NOUN
bracis-19052	112	10	boost	boost	NOUN
bracis-19052	112	11	to	to	ADP
bracis-19052	112	12	class	class	PROPN
bracis-19052	112	13	\(c_b\	\(c_b\	PROPN
bracis-19052	112	14	)	)	PUNCT
bracis-19052	112	15	.	.	PUNCT
bracis-19052	113	1	alternatively	alternatively	ADV
bracis-19052	113	2	,	,	PUNCT
bracis-19052	113	3	one	one	PRON
bracis-19052	113	4	can	can	AUX
bracis-19052	113	5	say	say	VERB
bracis-19052	113	6	that	that	SCONJ
bracis-19052	113	7	this	this	DET
bracis-19052	113	8	boost	boost	NOUN
bracis-19052	113	9	goes	go	VERB
bracis-19052	113	10	to	to	ADP
bracis-19052	113	11	the	the	DET
bracis-19052	113	12	entry	entry	NOUN
bracis-19052	113	13	which	which	PRON
bracis-19052	113	14	corresponds	correspond	VERB
bracis-19052	113	15	to	to	ADP
bracis-19052	113	16	the	the	DET
bracis-19052	113	17	contribution	contribution	NOUN
bracis-19052	113	18	from	from	ADP
bracis-19052	113	19	\(v_b\	\(v_b\	NOUN
bracis-19052	113	20	)	)	PUNCT
bracis-19052	113	21	to	to	PART
bracis-19052	113	22	\(v_a\	\(v_a\	VERB
bracis-19052	113	23	)	)	PUNCT
bracis-19052	113	24	,	,	PUNCT
bracis-19052	113	25	i.e.	i.e.	X
bracis-19052	113	26	\	\	PROPN
bracis-19052	113	27	(	(	PUNCT
bracis-19052	113	28	\mathbf	\mathbf	PROPN
bracis-19052	113	29	{	{	PUNCT
bracis-19052	113	30	p}_{ab}\	p}_{ab}\	NOUN
bracis-19052	113	31	)	)	PUNCT
bracis-19052	113	32	.	.	PUNCT
bracis-19052	114	1	this	this	DET
bracis-19052	114	2	boost	boost	NOUN
bracis-19052	114	3	is	be	AUX
bracis-19052	114	4	proportional	proportional	ADJ
bracis-19052	114	5	to	to	ADP
bracis-19052	114	6	\(\alpha	\(\alpha	NOUN
bracis-19052	114	7	^i\	^i\	NOUN
bracis-19052	114	8	)	)	PUNCT
bracis-19052	114	9	.	.	PUNCT
bracis-19052	115	1	this	this	PRON
bracis-19052	115	2	gives	give	VERB
bracis-19052	115	3	us	we	PRON
bracis-19052	115	4	a	a	DET
bracis-19052	115	5	good	good	ADJ
bracis-19052	115	6	intuition	intuition	NOUN
bracis-19052	115	7	as	as	ADP
bracis-19052	115	8	to	to	ADP
bracis-19052	115	9	the	the	DET
bracis-19052	115	10	role	role	NOUN
bracis-19052	115	11	of	of	ADP
bracis-19052	115	12	\(\alpha	\(\alpha	NOUN
bracis-19052	115	13	\	\	NOUN
bracis-19052	115	14	)	)	PUNCT
bracis-19052	115	15	.	.	PUNCT
bracis-19052	116	1	more	more	ADV
bracis-19052	116	2	precisely	precisely	ADV
bracis-19052	116	3	,	,	PUNCT
bracis-19052	116	4	the	the	DET
bracis-19052	116	5	contribution	contribution	NOUN
bracis-19052	116	6	of	of	ADP
bracis-19052	116	7	vertices	vertex	NOUN
bracis-19052	116	8	found	find	VERB
bracis-19052	116	9	later	later	ADV
bracis-19052	116	10	in	in	ADP
bracis-19052	116	11	the	the	DET
bracis-19052	116	12	random	random	ADJ
bracis-19052	116	13	walk	walk	NOUN
bracis-19052	116	14	decays	decay	NOUN
bracis-19052	116	15	exponentially	exponentially	ADV
bracis-19052	116	16	according	accord	VERB
bracis-19052	116	17	to	to	ADP
bracis-19052	116	18	\(\alpha	\(\alpha	NOUN
bracis-19052	116	19	^i\	^i\	NOUN
bracis-19052	116	20	)	)	PUNCT
bracis-19052	116	21	.	.	PUNCT
bracis-19052	117	1	2.2	2.2	NUM
bracis-19052	117	2	self	self	NOUN
bracis-19052	117	3	-	-	PUNCT
bracis-19052	117	4	influence	influence	NOUN
bracis-19052	117	5	and	and	CCONJ
bracis-19052	117	6	 	 	SPACE
bracis-19052	117	7	leave	leave	VERB
bracis-19052	117	8	-	-	PUNCT
bracis-19052	117	9	one	one	NUM
bracis-19052	117	10	-	-	PUNCT
bracis-19052	117	11	out	out	NOUN
bracis-19052	117	12	-	-	PUNCT
bracis-19052	117	13	error	error	NOUN
bracis-19052	117	14	there	there	PRON
bracis-19052	117	15	is	be	VERB
bracis-19052	117	16	one	one	NUM
bracis-19052	117	17	major	major	ADJ
bracis-19052	117	18	problem	problem	NOUN
bracis-19052	117	19	with	with	ADP
bracis-19052	117	20	lgc	lgc	PROPN
bracis-19052	117	21	’s	’s	PART
bracis-19052	117	22	solution	solution	NOUN
bracis-19052	117	23	:	:	PUNCT
bracis-19052	117	24	the	the	DET
bracis-19052	117	25	diagonal	diagonal	NOUN
bracis-19052	117	26	of	of	ADP
bracis-19052	117	27	\	\	PROPN
bracis-19052	117	28	(	(	PUNCT
bracis-19052	117	29	\mathbf	\mathbf	PROPN
bracis-19052	117	30	{	{	PUNCT
bracis-19052	117	31	p}\	p}\	NUM
bracis-19052	117	32	)	)	PUNCT
bracis-19052	117	33	.	.	PUNCT
bracis-19052	118	1	at	at	ADP
bracis-19052	118	2	first	first	ADJ
bracis-19052	118	3	glance	glance	NOUN
bracis-19052	118	4	,	,	PUNCT
bracis-19052	118	5	we	we	PRON
bracis-19052	118	6	would	would	AUX
bracis-19052	118	7	think	think	VERB
bracis-19052	118	8	that	that	SCONJ
bracis-19052	118	9	“	"	PUNCT
bracis-19052	118	10	fitting	fit	VERB
bracis-19052	118	11	the	the	DET
bracis-19052	118	12	labels	label	NOUN
bracis-19052	118	13	”	"	PUNCT
bracis-19052	118	14	means	mean	VERB
bracis-19052	118	15	looking	look	VERB
bracis-19052	118	16	for	for	ADP
bracis-19052	118	17	a	a	DET
bracis-19052	118	18	model	model	NOUN
bracis-19052	118	19	that	that	PRON
bracis-19052	118	20	explains	explain	VERB
bracis-19052	118	21	our	our	PRON
bracis-19052	118	22	data	datum	NOUN
bracis-19052	118	23	very	very	ADV
bracis-19052	118	24	well	well	ADV
bracis-19052	118	25	.	.	PUNCT
bracis-19052	119	1	in	in	ADP
bracis-19052	119	2	reality	reality	NOUN
bracis-19052	119	3	,	,	PUNCT
bracis-19052	119	4	this	this	PRON
bracis-19052	119	5	translates	translate	VERB
bracis-19052	119	6	to	to	ADP
bracis-19052	119	7	memorizing	memorize	VERB
bracis-19052	119	8	the	the	DET
bracis-19052	119	9	labeled	label	VERB
bracis-19052	119	10	set	set	NOUN
bracis-19052	119	11	.	.	PUNCT
bracis-19052	120	1	the	the	DET
bracis-19052	120	2	main	main	ADJ
bracis-19052	120	3	problem	problem	NOUN
bracis-19052	120	4	resides	reside	VERB
bracis-19052	120	5	within	within	ADP
bracis-19052	120	6	the	the	DET
bracis-19052	120	7	diagonal	diagonal	NOUN
bracis-19052	120	8	of	of	ADP
bracis-19052	120	9	the	the	DET
bracis-19052	120	10	propagation	propagation	NOUN
bracis-19052	120	11	matrix	matrix	NOUN
bracis-19052	120	12	.	.	PUNCT
bracis-19052	121	1	any	any	DET
bracis-19052	121	2	entry	entry	NOUN
bracis-19052	121	3	\	\	PROPN
bracis-19052	121	4	(	(	PUNCT
bracis-19052	121	5	\mathbf	\mathbf	PROPN
bracis-19052	121	6	{	{	PUNCT
bracis-19052	121	7	p}_{ii}\	p}_{ii}\	PROPN
bracis-19052	121	8	)	)	PUNCT
bracis-19052	121	9	stores	store	VERB
bracis-19052	121	10	the	the	DET
bracis-19052	121	11	self	self	NOUN
bracis-19052	121	12	-	-	PUNCT
bracis-19052	121	13	influence	influence	NOUN
bracis-19052	121	14	of	of	ADP
bracis-19052	121	15	a	a	DET
bracis-19052	121	16	vertex	vertex	NOUN
bracis-19052	121	17	,	,	PUNCT
bracis-19052	121	18	which	which	PRON
bracis-19052	121	19	is	be	AUX
bracis-19052	121	20	calculated	calculate	VERB
bracis-19052	121	21	according	accord	VERB
bracis-19052	121	22	to	to	ADP
bracis-19052	121	23	the	the	DET
bracis-19052	121	24	expected	expect	VERB
bracis-19052	121	25	reward	reward	NOUN
bracis-19052	121	26	obtained	obtain	VERB
bracis-19052	121	27	by	by	ADP
bracis-19052	121	28	looping	loop	VERB
bracis-19052	121	29	around	around	ADV
bracis-19052	121	30	and	and	CCONJ
bracis-19052	121	31	visiting	visit	VERB
bracis-19052	121	32	itself	itself	PRON
bracis-19052	121	33	.	.	PUNCT
bracis-19052	122	1	the	the	DET
bracis-19052	122	2	optimal	optimal	ADJ
bracis-19052	122	3	solution	solution	NOUN
bracis-19052	122	4	w.r.t	w.r.t	NOUN
bracis-19052	122	5	.	.	PUNCT
bracis-19052	123	1	label	label	NOUN
bracis-19052	123	2	fitting	fitting	ADJ
bracis-19052	123	3	occurs	occur	VERB
bracis-19052	123	4	when	when	SCONJ
bracis-19052	123	5	\(\alpha	\(\alpha	X
bracis-19052	123	6	\	\	NOUN
bracis-19052	123	7	)	)	PUNCT
bracis-19052	123	8	tends	tend	VERB
bracis-19052	123	9	to	to	ADP
bracis-19052	123	10	zero	zero	NUM
bracis-19052	123	11	.	.	PUNCT
bracis-19052	124	1	for	for	ADP
bracis-19052	124	2	labeled	label	VERB
bracis-19052	124	3	instances	instance	NOUN
bracis-19052	124	4	,	,	PUNCT
bracis-19052	124	5	an	an	DET
bracis-19052	124	6	initial	initial	ADJ
bracis-19052	124	7	reward	reward	NOUN
bracis-19052	124	8	is	be	AUX
bracis-19052	124	9	given	give	VERB
bracis-19052	124	10	for	for	ADP
bracis-19052	124	11	the	the	DET
bracis-19052	124	12	starting	start	VERB
bracis-19052	124	13	vertex	vertex	NOUN
bracis-19052	124	14	itself	itself	PRON
bracis-19052	124	15	,	,	PUNCT
bracis-19052	124	16	and	and	CCONJ
bracis-19052	124	17	the	the	DET
bracis-19052	124	18	remaining	remain	VERB
bracis-19052	124	19	are	be	AUX
bracis-19052	124	20	essentially	essentially	ADV
bracis-19052	124	21	ignored	ignore	VERB
bracis-19052	124	22	.	.	PUNCT
bracis-19052	125	1	we	we	PRON
bracis-19052	125	2	argue	argue	VERB
bracis-19052	125	3	that	that	SCONJ
bracis-19052	125	4	the	the	DET
bracis-19052	125	5	diagonal	diagonal	NOUN
bracis-19052	125	6	is	be	AUX
bracis-19052	125	7	directly	directly	ADV
bracis-19052	125	8	related	relate	VERB
bracis-19052	125	9	to	to	ADP
bracis-19052	125	10	overfitting	overfitte	VERB
bracis-19052	125	11	.	.	PUNCT
bracis-19052	126	1	it	it	PRON
bracis-19052	126	2	essentially	essentially	ADV
bracis-19052	126	3	tells	tell	VERB
bracis-19052	126	4	the	the	DET
bracis-19052	126	5	model	model	NOUN
bracis-19052	126	6	to	to	PART
bracis-19052	126	7	rely	rely	VERB
bracis-19052	126	8	on	on	ADP
bracis-19052	126	9	the	the	DET
bracis-19052	126	10	label	label	NOUN
bracis-19052	126	11	information	information	NOUN
bracis-19052	126	12	it	it	PRON
bracis-19052	126	13	knows	know	VERB
bracis-19052	126	14	.	.	PUNCT
bracis-19052	127	1	there	there	PRON
bracis-19052	127	2	are	be	VERB
bracis-19052	127	3	a	a	DET
bracis-19052	127	4	few	few	ADJ
bracis-19052	127	5	analogies	analogy	NOUN
bracis-19052	127	6	to	to	PART
bracis-19052	127	7	be	be	AUX
bracis-19052	127	8	made	make	VERB
bracis-19052	127	9	:	:	PUNCT
bracis-19052	127	10	say	say	VERB
bracis-19052	127	11	that	that	SCONJ
bracis-19052	127	12	we	we	PRON
bracis-19052	127	13	are	be	AUX
bracis-19052	127	14	optimizing	optimize	VERB
bracis-19052	127	15	the	the	DET
bracis-19052	127	16	number	number	NOUN
bracis-19052	127	17	of	of	ADP
bracis-19052	127	18	neighbors	neighbor	NOUN
bracis-19052	127	19	k	k	PROPN
bracis-19052	127	20	for	for	ADP
bracis-19052	127	21	a	a	DET
bracis-19052	127	22	knn	knn	NOUN
bracis-19052	127	23	classifier	classifier	NOUN
bracis-19052	127	24	.	.	PUNCT
bracis-19052	128	1	the	the	DET
bracis-19052	128	2	analog	analog	NOUN
bracis-19052	128	3	of	of	ADP
bracis-19052	128	4	“	"	PUNCT
bracis-19052	128	5	lgc	lgc	ADJ
bracis-19052	128	6	-	-	PUNCT
bracis-19052	128	7	style	style	NOUN
bracis-19052	128	8	optimal	optimal	ADJ
bracis-19052	128	9	label	label	NOUN
bracis-19052	128	10	fitting	fitting	ADJ
bracis-19052	128	11	”	"	PUNCT
bracis-19052	128	12	would	would	AUX
bracis-19052	128	13	be	be	AUX
bracis-19052	128	14	to	to	PART
bracis-19052	128	15	include	include	VERB
bracis-19052	128	16	each	each	DET
bracis-19052	128	17	labeled	label	VERB
bracis-19052	128	18	instance	instance	NOUN
bracis-19052	128	19	as	as	ADP
bracis-19052	128	20	a	a	DET
bracis-19052	128	21	neighbor	neighbor	NOUN
bracis-19052	128	22	to	to	ADP
bracis-19052	128	23	itself	itself	PRON
bracis-19052	128	24	,	,	PUNCT
bracis-19052	128	25	and	and	CCONJ
bracis-19052	128	26	set	set	VERB
bracis-19052	128	27	\(k	\(k	NOUN
bracis-19052	128	28	=	=	SYM
bracis-19052	128	29	1\	1\	NUM
bracis-19052	128	30	)	)	PUNCT
bracis-19052	128	31	.	.	PUNCT
bracis-19052	129	1	this	this	PRON
bracis-19052	129	2	is	be	AUX
bracis-19052	129	3	obviously	obviously	ADV
bracis-19052	129	4	not	not	PART
bracis-19052	129	5	a	a	DET
bracis-19052	129	6	good	good	ADJ
bracis-19052	129	7	criterion	criterion	NOUN
bracis-19052	129	8	.	.	PUNCT
bracis-19052	130	1	the	the	DET
bracis-19052	130	2	answer	answer	NOUN
bracis-19052	130	3	that	that	PRON
bracis-19052	130	4	maximizes	maximize	VERB
bracis-19052	130	5	a	a	DET
bracis-19052	130	6	proper	proper	ADJ
bracis-19052	130	7	“	"	PUNCT
bracis-19052	130	8	label	label	NOUN
bracis-19052	130	9	fitting	fitting	ADJ
bracis-19052	130	10	”	"	PUNCT
bracis-19052	130	11	criteria	criterion	NOUN
bracis-19052	130	12	,	,	PUNCT
bracis-19052	130	13	in	in	ADP
bracis-19052	130	14	this	this	DET
bracis-19052	130	15	case	case	NOUN
bracis-19052	130	16	,	,	PUNCT
bracis-19052	130	17	is	be	AUX
bracis-19052	130	18	selecting	select	VERB
bracis-19052	130	19	k	k	NOUN
bracis-19052	130	20	that	that	PRON
bracis-19052	130	21	minimizes	minimize	VERB
bracis-19052	130	22	classification	classification	NOUN
bracis-19052	130	23	error	error	NOUN
bracis-19052	130	24	with	with	ADP
bracis-19052	130	25	the	the	DET
bracis-19052	130	26	extremely	extremely	ADV
bracis-19052	130	27	important	important	ADJ
bracis-19052	130	28	caveat	caveat	NOUN
bracis-19052	130	29	:	:	PUNCT
bracis-19052	130	30	directly	directly	ADV
bracis-19052	130	31	using	use	VERB
bracis-19052	130	32	each	each	DET
bracis-19052	130	33	instance	instance	NOUN
bracis-19052	130	34	’s	’s	PART
bracis-19052	130	35	own	own	ADJ
bracis-19052	130	36	label	label	NOUN
bracis-19052	130	37	is	be	AUX
bracis-19052	130	38	prohibited	prohibit	VERB
bracis-19052	130	39	.	.	PUNCT
bracis-19052	131	1	in	in	ADP
bracis-19052	131	2	spite	spite	NOUN
bracis-19052	131	3	of	of	ADP
bracis-19052	131	4	the	the	DET
bracis-19052	131	5	problems	problem	NOUN
bracis-19052	131	6	we	we	PRON
bracis-19052	131	7	have	have	AUX
bracis-19052	131	8	presented	present	VERB
bracis-19052	131	9	,	,	PUNCT
bracis-19052	131	10	the	the	DET
bracis-19052	131	11	family	family	NOUN
bracis-19052	131	12	of	of	ADP
bracis-19052	131	13	lgc	lgc	ADJ
bracis-19052	131	14	solutions	solution	NOUN
bracis-19052	131	15	remains	remain	VERB
bracis-19052	131	16	very	very	ADV
bracis-19052	131	17	interesting	interesting	ADJ
bracis-19052	131	18	to	to	PART
bracis-19052	131	19	consider	consider	VERB
bracis-19052	131	20	.	.	PUNCT
bracis-19052	132	1	we	we	PRON
bracis-19052	132	2	will	will	AUX
bracis-19052	132	3	have	have	VERB
bracis-19052	132	4	to	to	PART
bracis-19052	132	5	eliminate	eliminate	VERB
bracis-19052	132	6	diagonals	diagonal	NOUN
bracis-19052	132	7	,	,	PUNCT
bracis-19052	132	8	however	however	ADV
bracis-19052	132	9	.	.	PUNCT
bracis-19052	133	1	let	let	VERB
bracis-19052	133	2	$	$	SYM
bracis-19052	133	3	$	$	SYM
bracis-19052	133	4	\begin{aligned	\begin{aligne	VERB
bracis-19052	133	5	}	}	PUNCT
bracis-19052	133	6	\mathbf	\mathbf	PROPN
bracis-19052	133	7	{	{	PUNCT
bracis-19052	133	8	h}(\alpha	h}(\alpha	NOUN
bracis-19052	133	9	)	)	PUNCT
bracis-19052	134	1	:	:	PUNCT
bracis-19052	134	2	=	=	SYM
bracis-19052	134	3	\left	\left	PROPN
bracis-19052	134	4	(	(	PUNCT
bracis-19052	134	5	\mathbf	\mathbf	PROPN
bracis-19052	134	6	{	{	PUNCT
bracis-19052	134	7	(	(	PUNCT
bracis-19052	134	8	\mathbf	\mathbf	PROPN
bracis-19052	134	9	{	{	PUNCT
bracis-19052	134	10	i}-\alpha	i}-\alpha	ADJ
bracis-19052	134	11	\mathbf	\mathbf	PROPN
bracis-19052	134	12	{	{	PUNCT
bracis-19052	134	13	s})^{-1	s})^{-1	NOUN
bracis-19052	134	14	}	}	PUNCT
bracis-19052	134	15	}	}	PUNCT
bracis-19052	134	16	diag	diag	NOUN
bracis-19052	134	17	(	(	PUNCT
bracis-19052	134	18	(	(	PUNCT
bracis-19052	134	19	\mathbf	\mathbf	PROPN
bracis-19052	134	20	{	{	PUNCT
bracis-19052	134	21	i}-\alpha	i}-\alpha	ADJ
bracis-19052	134	22	\mathbf	\mathbf	PROPN
bracis-19052	134	23	{	{	PUNCT
bracis-19052	134	24	s})^{-1})\right	s})^{-1})\right	NUM
bracis-19052	134	25	)	)	PUNCT
bracis-19052	134	26	_	_	PUNCT
bracis-19052	134	27	\mathcal	\mathcal	ADJ
bracis-19052	134	28	{	{	PUNCT
bracis-19052	134	29	l	l	NOUN
bracis-19052	134	30	}	}	PUNCT
bracis-19052	134	31	\mathbf	\mathbf	PROPN
bracis-19052	134	32	{	{	PUNCT
bracis-19052	134	33	y}_\mathcal	y}_\mathcal	PROPN
bracis-19052	134	34	{	{	PUNCT
bracis-19052	134	35	l}\end{aligned}$$	l}\end{aligned}$$	PROPN
bracis-19052	134	36	(	(	PUNCT
bracis-19052	134	37	26	26	NUM
bracis-19052	134	38	)	)	PUNCT
bracis-19052	134	39	by	by	ADP
bracis-19052	134	40	eliminating	eliminate	VERB
bracis-19052	134	41	the	the	DET
bracis-19052	134	42	diagonal	diagonal	ADJ
bracis-19052	134	43	,	,	PUNCT
bracis-19052	134	44	we	we	PRON
bracis-19052	134	45	obtain	obtain	VERB
bracis-19052	134	46	,	,	PUNCT
bracis-19052	134	47	for	for	ADP
bracis-19052	134	48	each	each	DET
bracis-19052	134	49	label	label	NOUN
bracis-19052	134	50	,	,	PUNCT
bracis-19052	134	51	its	its	PRON
bracis-19052	134	52	classification	classification	NOUN
bracis-19052	134	53	if	if	SCONJ
bracis-19052	134	54	it	it	PRON
bracis-19052	134	55	were	be	AUX
bracis-19052	134	56	not	not	PART
bracis-19052	134	57	included	include	VERB
bracis-19052	134	58	in	in	ADP
bracis-19052	134	59	the	the	DET
bracis-19052	134	60	label	label	NOUN
bracis-19052	134	61	propagation	propagation	NOUN
bracis-19052	134	62	process	process	NOUN
bracis-19052	134	63	.	.	PUNCT
bracis-19052	135	1	as	as	ADP
bracis-19052	135	2	such	such	ADJ
bracis-19052	135	3	,	,	PUNCT
bracis-19052	135	4	it	it	PRON
bracis-19052	135	5	can	can	AUX
bracis-19052	135	6	be	be	AUX
bracis-19052	135	7	argued	argue	VERB
bracis-19052	135	8	that	that	SCONJ
bracis-19052	135	9	minimizing	minimize	VERB
bracis-19052	135	10	$	$	SYM
bracis-19052	135	11	$	$	SYM
bracis-19052	135	12	\begin{aligned	\begin{aligne	VERB
bracis-19052	135	13	}	}	PUNCT
bracis-19052	135	14	\big	\big	PROPN
bracis-19052	135	15	\vert	\vert	PROPN
bracis-19052	135	16	\mathbf	\mathbf	PROPN
bracis-19052	135	17	{	{	PUNCT
bracis-19052	135	18	h}(\alpha	h}(\alpha	NOUN
bracis-19052	135	19	)	)	PUNCT
bracis-19052	135	20	\mathbf	\mathbf	PROPN
bracis-19052	135	21	{	{	PUNCT
bracis-19052	135	22	y}_\mathcal	y}_\mathcal	PROPN
bracis-19052	135	23	{	{	PUNCT
bracis-19052	135	24	l}\big	l}\big	NOUN
bracis-19052	135	25	\vert	\vert	PROPN
bracis-19052	135	26	^2	^2	PROPN
bracis-19052	135	27	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	135	28	(	(	PUNCT
bracis-19052	135	29	27	27	NUM
bracis-19052	135	30	)	)	PUNCT
bracis-19052	135	31	also	also	ADV
bracis-19052	135	32	minimizes	minimize	VERB
bracis-19052	135	33	the	the	DET
bracis-19052	135	34	leave	leave	VERB
bracis-19052	135	35	-	-	PUNCT
bracis-19052	135	36	one	one	NUM
bracis-19052	135	37	-	-	PUNCT
bracis-19052	135	38	out	out	NOUN
bracis-19052	135	39	(	(	PUNCT
bracis-19052	135	40	loo	loo	NOUN
bracis-19052	135	41	)	)	PUNCT
bracis-19052	135	42	error	error	NOUN
bracis-19052	135	43	.	.	PUNCT
bracis-19052	136	1	there	there	PRON
bracis-19052	136	2	is	be	VERB
bracis-19052	136	3	an	an	DET
bracis-19052	136	4	asterisk	asterisk	NOUN
bracis-19052	136	5	:	:	PUNCT
bracis-19052	136	6	each	each	DET
bracis-19052	136	7	instance	instance	NOUN
bracis-19052	136	8	is	be	AUX
bracis-19052	136	9	still	still	ADV
bracis-19052	136	10	used	use	VERB
bracis-19052	136	11	as	as	ADP
bracis-19052	136	12	unlabeled	unlabeled	ADJ
bracis-19052	136	13	data	datum	NOUN
bracis-19052	136	14	,	,	PUNCT
bracis-19052	136	15	but	but	CCONJ
bracis-19052	136	16	this	this	DET
bracis-19052	136	17	effect	effect	NOUN
bracis-19052	136	18	should	should	AUX
bracis-19052	136	19	be	be	AUX
bracis-19052	136	20	insignificant	insignificant	ADJ
bracis-19052	136	21	.	.	PUNCT
bracis-19052	137	1	it	it	PRON
bracis-19052	137	2	is	be	AUX
bracis-19052	137	3	also	also	ADV
bracis-19052	137	4	interesting	interesting	ADJ
bracis-19052	137	5	to	to	PART
bracis-19052	137	6	row	row	VERB
bracis-19052	137	7	-	-	PUNCT
bracis-19052	137	8	normalize	normalize	VERB
bracis-19052	137	9	(	(	PUNCT
bracis-19052	137	10	a	a	DET
bracis-19052	137	11	small	small	ADJ
bracis-19052	137	12	constant	constant	ADJ
bracis-19052	137	13	\(\epsilon	\(\epsilon	NOUN
bracis-19052	137	14	\	\	NOUN
bracis-19052	137	15	)	)	PUNCT
bracis-19052	137	16	may	may	AUX
bracis-19052	137	17	be	be	AUX
bracis-19052	137	18	added	add	VERB
bracis-19052	137	19	for	for	ADP
bracis-19052	137	20	stabilization	stabilization	NOUN
bracis-19052	137	21	)	)	PUNCT
bracis-19052	137	22	the	the	DET
bracis-19052	137	23	rows	row	NOUN
bracis-19052	137	24	,	,	PUNCT
bracis-19052	137	25	so	so	SCONJ
bracis-19052	137	26	that	that	SCONJ
bracis-19052	137	27	we	we	PRON
bracis-19052	137	28	end	end	VERB
bracis-19052	137	29	up	up	ADP
bracis-19052	137	30	with	with	ADP
bracis-19052	137	31	classification	classification	NOUN
bracis-19052	137	32	probabilities	probability	NOUN
bracis-19052	137	33	.	.	PUNCT
bracis-19052	138	1	previously	previously	ADV
bracis-19052	138	2	,	,	PUNCT
bracis-19052	138	3	we	we	PRON
bracis-19052	138	4	developed	develop	VERB
bracis-19052	138	5	a	a	DET
bracis-19052	138	6	semi	semi	ADJ
bracis-19052	138	7	-	-	ADJ
bracis-19052	138	8	supervised	supervised	ADJ
bracis-19052	138	9	leave	leave	VERB
bracis-19052	138	10	-	-	PUNCT
bracis-19052	138	11	one	one	NUM
bracis-19052	138	12	-	-	PUNCT
bracis-19052	138	13	out	out	ADP
bracis-19052	138	14	filter	filter	NOUN
bracis-19052	138	15	[	[	X
bracis-19052	138	16	2	2	NUM
bracis-19052	138	17	,	,	PUNCT
bracis-19052	138	18	4	4	NUM
bracis-19052	138	19	]	]	PUNCT
bracis-19052	138	20	.	.	PUNCT
bracis-19052	139	1	we	we	PRON
bracis-19052	139	2	also	also	ADV
bracis-19052	139	3	managed	manage	VERB
bracis-19052	139	4	to	to	PART
bracis-19052	139	5	reduce	reduce	VERB
bracis-19052	139	6	the	the	DET
bracis-19052	139	7	amount	amount	NOUN
bracis-19052	139	8	of	of	ADP
bracis-19052	139	9	storage	storage	NOUN
bracis-19052	139	10	used	use	VERB
bracis-19052	139	11	by	by	ADP
bracis-19052	139	12	only	only	ADV
bracis-19052	139	13	calculating	calculate	VERB
bracis-19052	139	14	a	a	DET
bracis-19052	139	15	propagation	propagation	NOUN
bracis-19052	139	16	submatrix	submatrix	NOUN
bracis-19052	139	17	.	.	PUNCT
bracis-19052	140	1	the	the	DET
bracis-19052	140	2	loo	loo	NOUN
bracis-19052	140	3	-	-	PUNCT
bracis-19052	140	4	inspired	inspire	VERB
bracis-19052	140	5	criterion	criterion	NOUN
bracis-19052	140	6	encourages	encourage	VERB
bracis-19052	140	7	label	label	NOUN
bracis-19052	140	8	information	information	NOUN
bracis-19052	140	9	to	to	PART
bracis-19052	140	10	be	be	AUX
bracis-19052	140	11	redundant	redundant	ADJ
bracis-19052	140	12	,	,	PUNCT
bracis-19052	140	13	so	so	ADV
bracis-19052	140	14	labels	label	NOUN
bracis-19052	140	15	that	that	PRON
bracis-19052	140	16	are	be	AUX
bracis-19052	140	17	incoherent	incoherent	ADJ
bracis-19052	140	18	with	with	ADP
bracis-19052	140	19	the	the	DET
bracis-19052	140	20	implicit	implicit	ADJ
bracis-19052	140	21	model	model	NOUN
bracis-19052	140	22	are	be	AUX
bracis-19052	140	23	removed	remove	VERB
bracis-19052	140	24	.	.	PUNCT
bracis-19052	141	1	the	the	DET
bracis-19052	141	2	major	major	ADJ
bracis-19052	141	3	drawback	drawback	NOUN
bracis-19052	141	4	of	of	ADP
bracis-19052	141	5	our	our	PRON
bracis-19052	141	6	proposal	proposal	NOUN
bracis-19052	141	7	is	be	AUX
bracis-19052	141	8	that	that	SCONJ
bracis-19052	141	9	it	it	PRON
bracis-19052	141	10	needs	need	VERB
bracis-19052	141	11	an	an	DET
bracis-19052	141	12	extra	extra	ADJ
bracis-19052	141	13	parameter	parameter	NOUN
bracis-19052	141	14	r	r	NOUN
bracis-19052	141	15	,	,	PUNCT
bracis-19052	141	16	which	which	PRON
bracis-19052	141	17	is	be	AUX
bracis-19052	141	18	the	the	DET
bracis-19052	141	19	number	number	NOUN
bracis-19052	141	20	of	of	ADP
bracis-19052	141	21	labels	label	NOUN
bracis-19052	141	22	to	to	PART
bracis-19052	141	23	remove	remove	VERB
bracis-19052	141	24	.	.	PUNCT
bracis-19052	142	1	the	the	DET
bracis-19052	142	2	optimal	optimal	ADJ
bracis-19052	142	3	r	r	NOUN
bracis-19052	142	4	is	be	AUX
bracis-19052	142	5	usually	usually	ADV
bracis-19052	142	6	around	around	ADP
bracis-19052	142	7	the	the	DET
bracis-19052	142	8	number	number	NOUN
bracis-19052	142	9	of	of	ADP
bracis-19052	142	10	noisy	noisy	ADJ
bracis-19052	142	11	labels	label	NOUN
bracis-19052	142	12	,	,	PUNCT
bracis-19052	142	13	which	which	PRON
bracis-19052	142	14	is	be	AUX
bracis-19052	142	15	unknown	unknown	ADJ
bracis-19052	142	16	to	to	ADP
bracis-19052	142	17	us	we	PRON
bracis-19052	142	18	.	.	PUNCT
bracis-19052	143	1	this	this	PRON
bracis-19052	143	2	was	be	AUX
bracis-19052	143	3	somewhat	somewhat	ADV
bracis-19052	143	4	addressed	address	VERB
bracis-19052	143	5	in	in	ADP
bracis-19052	143	6	[	[	X
bracis-19052	143	7	4	4	NUM
bracis-19052	143	8	]	]	PUNCT
bracis-19052	143	9	:	:	PUNCT
bracis-19052	143	10	we	we	PRON
bracis-19052	143	11	can	can	AUX
bracis-19052	143	12	instead	instead	ADV
bracis-19052	143	13	use	use	VERB
bracis-19052	143	14	a	a	DET
bracis-19052	143	15	threshold	threshold	NOUN
bracis-19052	143	16	,	,	PUNCT
bracis-19052	143	17	which	which	PRON
bracis-19052	143	18	tells	tell	VERB
bracis-19052	143	19	us	we	PRON
bracis-19052	143	20	how	how	SCONJ
bracis-19052	143	21	much	much	ADJ
bracis-19052	143	22	labels	label	NOUN
bracis-19052	143	23	can	can	AUX
bracis-19052	143	24	deviate	deviate	VERB
bracis-19052	143	25	from	from	ADP
bracis-19052	143	26	the	the	DET
bracis-19052	143	27	original	original	ADJ
bracis-19052	143	28	model	model	NOUN
bracis-19052	143	29	.	.	PUNCT
bracis-19052	144	1	nonetheless	nonetheless	ADV
bracis-19052	144	2	,	,	PUNCT
bracis-19052	144	3	it	it	PRON
bracis-19052	144	4	is	be	AUX
bracis-19052	144	5	desirable	desirable	ADJ
bracis-19052	144	6	to	to	PART
bracis-19052	144	7	solve	solve	VERB
bracis-19052	144	8	this	this	DET
bracis-19052	144	9	problem	problem	NOUN
bracis-19052	144	10	in	in	ADP
bracis-19052	144	11	a	a	DET
bracis-19052	144	12	way	way	NOUN
bracis-19052	144	13	that	that	PRON
bracis-19052	144	14	removes	remove	VERB
bracis-19052	144	15	such	such	DET
bracis-19052	144	16	a	a	DET
bracis-19052	144	17	parameter	parameter	NOUN
bracis-19052	144	18	.	.	PUNCT
bracis-19052	145	1	we	we	PRON
bracis-19052	145	2	will	will	AUX
bracis-19052	145	3	do	do	VERB
bracis-19052	145	4	this	this	PRON
bracis-19052	145	5	by	by	ADP
bracis-19052	145	6	introducing	introduce	VERB
bracis-19052	145	7	a	a	DET
bracis-19052	145	8	new	new	ADJ
bracis-19052	145	9	optimization	optimization	NOUN
bracis-19052	145	10	problem	problem	NOUN
bracis-19052	145	11	.	.	PUNCT
bracis-19052	146	1	3	3	NUM
bracis-19052	146	2	proposal	proposal	NOUN
bracis-19052	146	3	in	in	ADP
bracis-19052	146	4	this	this	DET
bracis-19052	146	5	work	work	NOUN
bracis-19052	146	6	,	,	PUNCT
bracis-19052	146	7	we	we	PRON
bracis-19052	146	8	consider	consider	VERB
bracis-19052	146	9	the	the	DET
bracis-19052	146	10	optimal	optimal	ADJ
bracis-19052	146	11	value	value	NOUN
bracis-19052	146	12	of	of	ADP
bracis-19052	146	13	\({\alpha	\({\alpha	PROPN
bracis-19052	146	14	}	}	PUNCT
bracis-19052	146	15	\	\	NOUN
bracis-19052	146	16	)	)	PUNCT
bracis-19052	146	17	for	for	ADP
bracis-19052	146	18	our	our	PRON
bracis-19052	146	19	loo	loo	NOUN
bracis-19052	146	20	-	-	PUNCT
bracis-19052	146	21	inspired	inspire	VERB
bracis-19052	146	22	loss	loss	NOUN
bracis-19052	146	23	[	[	X
bracis-19052	146	24	4	4	NUM
bracis-19052	146	25	]	]	PUNCT
bracis-19052	146	26	.	.	PUNCT
bracis-19052	147	1	the	the	DET
bracis-19052	147	2	objective	objective	NOUN
bracis-19052	147	3	is	be	AUX
bracis-19052	147	4	to	to	PART
bracis-19052	147	5	develop	develop	VERB
bracis-19052	147	6	a	a	DET
bracis-19052	147	7	method	method	NOUN
bracis-19052	147	8	to	to	PART
bracis-19052	147	9	minimize	minimize	VERB
bracis-19052	147	10	surrogate	surrogate	ADJ
bracis-19052	147	11	losses	loss	NOUN
bracis-19052	147	12	based	base	VERB
bracis-19052	147	13	on	on	ADP
bracis-19052	147	14	loo	loo	NOUN
bracis-19052	147	15	error	error	NOUN
bracis-19052	147	16	for	for	ADP
bracis-19052	147	17	the	the	DET
bracis-19052	147	18	lgc	lgc	ADJ
bracis-19052	147	19	gssl	gssl	NOUN
bracis-19052	147	20	classifier	classifier	NOUN
bracis-19052	147	21	and	and	CCONJ
bracis-19052	147	22	evaluate	evaluate	VERB
bracis-19052	147	23	the	the	DET
bracis-19052	147	24	generalization	generalization	NOUN
bracis-19052	147	25	of	of	ADP
bracis-19052	147	26	its	its	PRON
bracis-19052	147	27	solutions	solution	NOUN
bracis-19052	147	28	.	.	PUNCT
bracis-19052	148	1	we	we	PRON
bracis-19052	148	2	use	use	VERB
bracis-19052	148	3	the	the	DET
bracis-19052	148	4	term	term	NOUN
bracis-19052	148	5	“	"	PUNCT
bracis-19052	148	6	surrogate	surrogate	ADJ
bracis-19052	148	7	loss	loss	NOUN
bracis-19052	148	8	”	"	PUNCT
bracis-19052	148	9	[	[	X
bracis-19052	148	10	9	9	NUM
bracis-19052	148	11	]	]	PUNCT
bracis-19052	148	12	to	to	PART
bracis-19052	148	13	denote	denote	VERB
bracis-19052	148	14	losses	loss	NOUN
bracis-19052	148	15	such	such	ADJ
bracis-19052	148	16	as	as	ADP
bracis-19052	148	17	squared	square	VERB
bracis-19052	148	18	error	error	NOUN
bracis-19052	148	19	,	,	PUNCT
bracis-19052	148	20	cross	cross	NOUN
bracis-19052	148	21	-	-	NOUN
bracis-19052	148	22	entropy	entropy	NOUN
bracis-19052	148	23	and	and	CCONJ
bracis-19052	148	24	so	so	ADV
bracis-19052	148	25	on	on	ADV
bracis-19052	148	26	.	.	PUNCT
bracis-19052	149	1	we	we	PRON
bracis-19052	149	2	use	use	VERB
bracis-19052	149	3	this	this	DET
bracis-19052	149	4	term	term	NOUN
bracis-19052	149	5	to	to	PART
bracis-19052	149	6	purposefully	purposefully	ADV
bracis-19052	149	7	remind	remind	VERB
bracis-19052	149	8	that	that	SCONJ
bracis-19052	149	9	the	the	DET
bracis-19052	149	10	solution	solution	NOUN
bracis-19052	149	11	\	\	PROPN
bracis-19052	149	12	(	(	PUNCT
bracis-19052	149	13	\mathbf	\mathbf	PROPN
bracis-19052	149	14	{	{	PUNCT
bracis-19052	149	15	h}(\alpha	h}(\alpha	NOUN
bracis-19052	149	16	)	)	PUNCT
bracis-19052	149	17	\	\	NOUN
bracis-19052	149	18	)	)	PUNCT
bracis-19052	149	19	that	that	PRON
bracis-19052	149	20	minimizes	minimize	VERB
bracis-19052	149	21	the	the	DET
bracis-19052	149	22	loss	loss	NOUN
bracis-19052	149	23	on	on	ADP
bracis-19052	149	24	the	the	DET
bracis-19052	149	25	test	test	NOUN
bracis-19052	149	26	set	set	NOUN
bracis-19052	149	27	does	do	AUX
bracis-19052	149	28	not	not	PART
bracis-19052	149	29	also	also	ADV
bracis-19052	149	30	necessarily	necessarily	ADV
bracis-19052	149	31	be	be	AUX
bracis-19052	149	32	the	the	DET
bracis-19052	149	33	one	one	NOUN
bracis-19052	149	34	that	that	PRON
bracis-19052	149	35	maximizes	maximize	VERB
bracis-19052	149	36	accuracy	accuracy	NOUN
bracis-19052	149	37	.	.	PUNCT
bracis-19052	150	1	we	we	PRON
bracis-19052	150	2	use	use	VERB
bracis-19052	150	3	automatic	automatic	ADJ
bracis-19052	150	4	differentiation	differentiation	NOUN
bracis-19052	150	5	as	as	ADP
bracis-19052	150	6	our	our	PRON
bracis-19052	150	7	optimization	optimization	NOUN
bracis-19052	150	8	procedure	procedure	NOUN
bracis-19052	150	9	.	.	PUNCT
bracis-19052	151	1	as	as	ADP
bracis-19052	151	2	such	such	ADJ
bracis-19052	151	3	,	,	PUNCT
bracis-19052	151	4	we	we	PRON
bracis-19052	151	5	call	call	VERB
bracis-19052	151	6	our	our	PRON
bracis-19052	151	7	approach	approach	NOUN
bracis-19052	151	8	\(\texttt	\(\texttt	NOUN
bracis-19052	151	9	{	{	PUNCT
bracis-19052	151	10	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	151	11	{	{	PUNCT
bracis-19052	151	12	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	151	13	{	{	PUNCT
bracis-19052	151	14	autol}\	autol}\	PROPN
bracis-19052	151	15	)	)	PUNCT
bracis-19052	151	16	and	and	CCONJ
bracis-19052	151	17	\(\texttt	\(\texttt	NOUN
bracis-19052	151	18	{	{	PUNCT
bracis-19052	151	19	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	151	20	{	{	PUNCT
bracis-19052	151	21	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	151	22	{	{	PUNCT
bracis-19052	151	23	autod}\	autod}\	PROPN
bracis-19052	151	24	)	)	PUNCT
bracis-19052	151	25	when	when	SCONJ
bracis-19052	151	26	learning	learn	VERB
bracis-19052	151	27	label	label	NOUN
bracis-19052	151	28	reliability	reliability	NOUN
bracis-19052	151	29	and	and	CCONJ
bracis-19052	151	30	diffusion	diffusion	NOUN
bracis-19052	151	31	rate	rate	NOUN
bracis-19052	151	32	,	,	PUNCT
bracis-19052	151	33	respectively	respectively	ADV
bracis-19052	151	34	.	.	PUNCT
bracis-19052	152	1	we	we	PRON
bracis-19052	152	2	exploit	exploit	VERB
bracis-19052	152	3	the	the	DET
bracis-19052	152	4	fact	fact	NOUN
bracis-19052	152	5	that	that	SCONJ
bracis-19052	152	6	we	we	PRON
bracis-19052	152	7	can	can	AUX
bracis-19052	152	8	compute	compute	VERB
bracis-19052	152	9	the	the	DET
bracis-19052	152	10	gradients	gradient	NOUN
bracis-19052	152	11	of	of	ADP
bracis-19052	152	12	our	our	PRON
bracis-19052	152	13	loss	loss	NOUN
bracis-19052	152	14	.	.	PUNCT
bracis-19052	153	1	3.1	3.1	NUM
bracis-19052	153	2	\(\texttt	\(\texttt	NOUN
bracis-19052	153	3	{	{	PUNCT
bracis-19052	153	4	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	153	5	{	{	PUNCT
bracis-19052	153	6	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	153	7	{	{	PUNCT
bracis-19052	153	8	autol}\	autol}\	PROPN
bracis-19052	153	9	):	):	PUNCT
bracis-19052	153	10	automatic	automatic	ADJ
bracis-19052	153	11	correction	correction	NOUN
bracis-19052	153	12	of	of	ADP
bracis-19052	153	13	 	 	SPACE
bracis-19052	153	14	noisy	noisy	ADJ
bracis-19052	153	15	labels	label	NOUN
bracis-19052	153	16	let	let	VERB
bracis-19052	153	17	\	\	PROPN
bracis-19052	153	18	(	(	PUNCT
bracis-19052	153	19	\mathbf	\mathbf	PROPN
bracis-19052	153	20	{	{	PUNCT
bracis-19052	153	21	p}\	p}\	NOUN
bracis-19052	153	22	)	)	PUNCT
bracis-19052	153	23	be	be	AUX
bracis-19052	153	24	the	the	DET
bracis-19052	153	25	propagation	propagation	NOUN
bracis-19052	153	26	matrix	matrix	NOUN
bracis-19052	153	27	,	,	PUNCT
bracis-19052	153	28	whose	whose	DET
bracis-19052	153	29	submatrix	submatrix	NOUN
bracis-19052	153	30	\	\	PROPN
bracis-19052	153	31	(	(	PUNCT
bracis-19052	153	32	\mathbf	\mathbf	PROPN
bracis-19052	153	33	{	{	PUNCT
bracis-19052	153	34	p}_{\mathcal	p}_{\mathcal	ADJ
bracis-19052	153	35	{	{	PUNCT
bracis-19052	153	36	l}\mathcal	l}\mathcal	ADJ
bracis-19052	153	37	{	{	PUNCT
bracis-19052	153	38	l}}\	l}}\	NOUN
bracis-19052	153	39	)	)	PUNCT
bracis-19052	153	40	corresponds	correspond	NOUN
bracis-19052	153	41	to	to	ADP
bracis-19052	153	42	kernel	kernel	PROPN
bracis-19052	153	43	values	value	NOUN
bracis-19052	153	44	between	between	ADP
bracis-19052	153	45	labeled	label	VERB
bracis-19052	153	46	data	datum	NOUN
bracis-19052	153	47	only	only	ADV
bracis-19052	153	48	.	.	PUNCT
bracis-19052	154	1	then	then	ADV
bracis-19052	154	2	,	,	PUNCT
bracis-19052	154	3	the	the	DET
bracis-19052	154	4	modified	modify	VERB
bracis-19052	154	5	lgc	lgc	ADJ
bracis-19052	154	6	solution	solution	NOUN
bracis-19052	154	7	is	be	AUX
bracis-19052	154	8	given	give	VERB
bracis-19052	154	9	by	by	ADP
bracis-19052	154	10	\(\widetilde	\(\widetilde	ADJ
bracis-19052	154	11	{	{	PUNCT
bracis-19052	154	12	\mathbf	\mathbf	PROPN
bracis-19052	154	13	{	{	PUNCT
bracis-19052	154	14	p	p	NOUN
bracis-19052	154	15	}	}	PUNCT
bracis-19052	154	16	}	}	PUNCT
bracis-19052	154	17	\mathbf	\mathbf	PROPN
bracis-19052	154	18	{	{	PUNCT
bracis-19052	154	19	y}_\mathcal	y}_\mathcal	X
bracis-19052	154	20	{	{	PUNCT
bracis-19052	154	21	l}\	l}\	PROPN
bracis-19052	154	22	)	)	PUNCT
bracis-19052	154	23	,	,	PUNCT
bracis-19052	154	24	where	where	SCONJ
bracis-19052	154	25	$	$	SYM
bracis-19052	154	26	$	$	SYM
bracis-19052	154	27	\begin{aligned	\begin{aligne	VERB
bracis-19052	154	28	}	}	PUNCT
bracis-19052	154	29	\widetilde	\widetilde	NOUN
bracis-19052	154	30	{	{	PUNCT
bracis-19052	154	31	\mathbf	\mathbf	PROPN
bracis-19052	154	32	{	{	PUNCT
bracis-19052	154	33	p	p	NOUN
bracis-19052	154	34	}	}	PUNCT
bracis-19052	154	35	}	}	PUNCT
bracis-19052	154	36	:	:	PUNCT
bracis-19052	154	37	=	=	SYM
bracis-19052	154	38	(	(	PUNCT
bracis-19052	154	39	\mathbf	\mathbf	PROPN
bracis-19052	154	40	{	{	PUNCT
bracis-19052	154	41	p}_{\mathcal	p}_{\mathcal	ADJ
bracis-19052	154	42	{	{	PUNCT
bracis-19052	154	43	l}\mathcal	l}\mathcal	ADJ
bracis-19052	154	44	{	{	PUNCT
bracis-19052	154	45	l	l	NOUN
bracis-19052	154	46	}	}	PUNCT
bracis-19052	154	47	}	}	PUNCT
bracis-19052	154	48	-diag	-diag	PROPN
bracis-19052	154	49	(	(	PUNCT
bracis-19052	154	50	\mathbf	\mathbf	PROPN
bracis-19052	154	51	{	{	PUNCT
bracis-19052	154	52	p}_{\mathcal	p}_{\mathcal	ADJ
bracis-19052	154	53	{	{	PUNCT
bracis-19052	154	54	l}\mathcal	l}\mathcal	ADJ
bracis-19052	154	55	{	{	PUNCT
bracis-19052	154	56	l	l	NOUN
bracis-19052	154	57	}	}	PUNCT
bracis-19052	154	58	}	}	PUNCT
bracis-19052	154	59	)	)	PUNCT
bracis-19052	154	60	)	)	PUNCT
bracis-19052	154	61	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-19052	154	62	(	(	PUNCT
bracis-19052	154	63	28	28	NUM
bracis-19052	154	64	)	)	PUNCT
bracis-19052	154	65	our	our	PRON
bracis-19052	154	66	optimization	optimization	NOUN
bracis-19052	154	67	problem	problem	NOUN
bracis-19052	154	68	is	be	AUX
bracis-19052	154	69	to	to	PART
bracis-19052	154	70	optimize	optimize	VERB
bracis-19052	154	71	a	a	DET
bracis-19052	154	72	diagonal	diagonal	ADJ
bracis-19052	154	73	matrix	matrix	NOUN
bracis-19052	154	74	\	\	PROPN
bracis-19052	154	75	(	(	PUNCT
bracis-19052	154	76	\mathbf	\mathbf	PROPN
bracis-19052	154	77	{	{	PUNCT
bracis-19052	154	78	\omega	\omega	PROPN
bracis-19052	154	79	}	}	PUNCT
bracis-19052	154	80	\	\	NOUN
bracis-19052	154	81	)	)	PUNCT
bracis-19052	154	82	indicating	indicate	VERB
bracis-19052	154	83	the	the	DET
bracis-19052	154	84	updated	update	VERB
bracis-19052	154	85	reliability	reliability	NOUN
bracis-19052	154	86	of	of	ADP
bracis-19052	154	87	each	each	DET
bracis-19052	154	88	label	label	NOUN
bracis-19052	154	89	:	:	PUNCT
bracis-19052	154	90	$	$	SYM
bracis-19052	154	91	$	$	SYM
bracis-19052	154	92	\begin{aligned	\begin{aligne	VERB
bracis-19052	154	93	}	}	PUNCT
bracis-19052	154	94	\min	\min	NOUN
bracis-19052	154	95	_	_	PUNCT
bracis-19052	154	96	{	{	PUNCT
bracis-19052	154	97	\mathbf	\mathbf	PROPN
bracis-19052	154	98	{	{	PUNCT
bracis-19052	154	99	\omega	\omega	PROPN
bracis-19052	154	100	}	}	PUNCT
bracis-19052	154	101	}	}	PUNCT
bracis-19052	154	102	\texttt	\texttt	PROPN
bracis-19052	154	103	{	{	PUNCT
bracis-19052	154	104	loss	loss	NOUN
bracis-19052	154	105	}	}	PUNCT
bracis-19052	154	106	(	(	PUNCT
bracis-19052	154	107	{	{	PUNCT
bracis-19052	154	108	deg(\widetilde	deg(\widetilde	ADJ
bracis-19052	154	109	{	{	PUNCT
bracis-19052	154	110	\mathbf	\mathbf	PROPN
bracis-19052	154	111	{	{	PUNCT
bracis-19052	154	112	p	p	NOUN
bracis-19052	154	113	}	}	PUNCT
bracis-19052	154	114	}	}	PUNCT
bracis-19052	154	115	\mathbf	\mathbf	PROPN
bracis-19052	154	116	{	{	PUNCT
bracis-19052	154	117	\omega	\omega	PROPN
bracis-19052	154	118	}	}	PUNCT
bracis-19052	154	119	\mathbf	\mathbf	PROPN
bracis-19052	154	120	{	{	PUNCT
bracis-19052	154	121	y}_\mathcal	y}_\mathcal	X
bracis-19052	154	122	{	{	PUNCT
bracis-19052	154	123	l})^{-1	l})^{-1	NOUN
bracis-19052	154	124	}	}	PUNCT
bracis-19052	154	125	\widetilde	\widetilde	PROPN
bracis-19052	154	126	{	{	PUNCT
bracis-19052	154	127	\mathbf	\mathbf	PROPN
bracis-19052	154	128	{	{	PUNCT
bracis-19052	154	129	p	p	NOUN
bracis-19052	154	130	}	}	PUNCT
bracis-19052	154	131	}	}	PUNCT
bracis-19052	154	132	\mathbf	\mathbf	PROPN
bracis-19052	154	133	{	{	PUNCT
bracis-19052	154	134	\omega	\omega	PROPN
bracis-19052	154	135	}	}	PUNCT
bracis-19052	154	136	\mathbf	\mathbf	PROPN
bracis-19052	154	137	{	{	PUNCT
bracis-19052	154	138	y}_\mathcal	y}_\mathcal	X
bracis-19052	154	139	{	{	PUNCT
bracis-19052	154	140	l},\;\	l},\;\	PROPN
bracis-19052	154	141	;	;	PUNCT
bracis-19052	154	142	\mathbf	\mathbf	PROPN
bracis-19052	154	143	{	{	PUNCT
bracis-19052	154	144	y}_\mathcal	y}_\mathcal	X
bracis-19052	154	145	{	{	PUNCT
bracis-19052	154	146	l	l	NOUN
bracis-19052	154	147	}	}	PUNCT
bracis-19052	154	148	}	}	PUNCT
bracis-19052	154	149	)	)	PUNCT
bracis-19052	155	1	\;\;\;\;\;\;\	\;\;\;\;\;\;\	NOUN
bracis-19052	155	2	;	;	PUNCT
bracis-19052	155	3	\text	\text	PROPN
bracis-19052	155	4	{	{	PUNCT
bracis-19052	155	5	such	such	ADJ
bracis-19052	155	6	that	that	SCONJ
bracis-19052	155	7	}	}	PUNCT
bracis-19052	155	8	\;\	\;\	NOUN
bracis-19052	155	9	;	;	PUNCT
bracis-19052	155	10	\forall	\forall	PRON
bracis-19052	155	11	i	i	PRON
bracis-19052	155	12	:	:	PUNCT
bracis-19052	155	13	\mathbf	\mathbf	PROPN
bracis-19052	155	14	{	{	PUNCT
bracis-19052	155	15	\omega	\omega	PROPN
bracis-19052	155	16	}	}	PUNCT
bracis-19052	155	17	_	_	PUNCT
bracis-19052	155	18	{	{	PUNCT
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bracis-19052	155	20	}	}	PUNCT
bracis-19052	155	21	\ge	\ge	PROPN
bracis-19052	155	22	0	0	NUM
bracis-19052	155	23	\end{aligned}$$	\end{aligned}$$	NOUN
bracis-19052	155	24	(	(	PUNCT
bracis-19052	155	25	29	29	NUM
bracis-19052	155	26	)	)	PUNCT
bracis-19052	155	27	where	where	SCONJ
bracis-19052	155	28	\(\texttt	\(\texttt	NOUN
bracis-19052	155	29	{	{	PUNCT
bracis-19052	155	30	loss}\	loss}\	PROPN
bracis-19052	155	31	)	)	PUNCT
bracis-19052	155	32	denotes	denote	VERB
bracis-19052	155	33	some	some	DET
bracis-19052	155	34	loss	loss	NOUN
bracis-19052	155	35	function	function	NOUN
bracis-19052	155	36	such	such	ADJ
bracis-19052	155	37	as	as	ADP
bracis-19052	155	38	squared	square	VERB
bracis-19052	155	39	error	error	NOUN
bracis-19052	155	40	or	or	CCONJ
bracis-19052	155	41	cross	cross	NOUN
bracis-19052	155	42	-	-	NOUN
bracis-19052	155	43	entropy	entropy	ADJ
bracis-19052	155	44	.	.	PUNCT
bracis-19052	155	45	3.2	3.2	NUM
bracis-19052	155	46	\(\texttt	\(\texttt	NOUN
bracis-19052	155	47	{	{	PUNCT
bracis-19052	155	48	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	155	49	{	{	PUNCT
bracis-19052	155	50	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	155	51	{	{	PUNCT
bracis-19052	155	52	autod}\	autod}\	PROPN
bracis-19052	155	53	):	):	PUNCT
bracis-19052	155	54	automatic	automatic	ADJ
bracis-19052	155	55	choice	choice	NOUN
bracis-19052	155	56	of	of	ADP
bracis-19052	155	57	 	 	SPACE
bracis-19052	155	58	diffusion	diffusion	NOUN
bracis-19052	155	59	rate	rate	NOUN
bracis-19052	155	60	in	in	ADP
bracis-19052	155	61	[	[	X
bracis-19052	155	62	4	4	NUM
bracis-19052	155	63	]	]	PUNCT
bracis-19052	155	64	,	,	PUNCT
bracis-19052	155	65	we	we	PRON
bracis-19052	155	66	use	use	VERB
bracis-19052	155	67	a	a	DET
bracis-19052	155	68	modified	modify	VERB
bracis-19052	155	69	version	version	NOUN
bracis-19052	155	70	of	of	ADP
bracis-19052	155	71	the	the	DET
bracis-19052	155	72	power	power	NOUN
bracis-19052	155	73	method	method	NOUN
bracis-19052	155	74	to	to	PART
bracis-19052	155	75	calculate	calculate	VERB
bracis-19052	155	76	the	the	DET
bracis-19052	155	77	submatrix	submatrix	NOUN
bracis-19052	155	78	\	\	PROPN
bracis-19052	155	79	(	(	PUNCT
bracis-19052	155	80	\mathbf	\mathbf	PROPN
bracis-19052	155	81	{	{	PUNCT
bracis-19052	155	82	p}_\mathcal	p}_\mathcal	ADJ
bracis-19052	155	83	{	{	PUNCT
bracis-19052	155	84	l}\	l}\	PROPN
bracis-19052	155	85	)	)	PUNCT
bracis-19052	155	86	.	.	PUNCT
bracis-19052	156	1	this	this	PRON
bracis-19052	156	2	is	be	AUX
bracis-19052	156	3	enough	enough	ADJ
bracis-19052	156	4	to	to	PART
bracis-19052	156	5	give	give	VERB
bracis-19052	156	6	us	we	PRON
bracis-19052	156	7	the	the	DET
bracis-19052	156	8	answer	answer	NOUN
bracis-19052	156	9	in	in	ADP
bracis-19052	156	10	a	a	DET
bracis-19052	156	11	few	few	ADJ
bracis-19052	156	12	seconds	second	NOUN
bracis-19052	156	13	for	for	ADP
bracis-19052	156	14	a	a	DET
bracis-19052	156	15	fixed	fix	VERB
bracis-19052	156	16	\(\alpha	\(\alpha	X
bracis-19052	156	17	\	\	NOUN
bracis-19052	156	18	)	)	PUNCT
bracis-19052	156	19	,	,	PUNCT
bracis-19052	156	20	but	but	CCONJ
bracis-19052	156	21	would	would	AUX
bracis-19052	156	22	quickly	quickly	ADV
bracis-19052	156	23	turn	turn	VERB
bracis-19052	156	24	into	into	ADP
bracis-19052	156	25	a	a	DET
bracis-19052	156	26	huge	huge	ADJ
bracis-19052	156	27	bottleneck	bottleneck	NOUN
bracis-19052	156	28	if	if	SCONJ
bracis-19052	156	29	we	we	PRON
bracis-19052	156	30	were	be	AUX
bracis-19052	156	31	to	to	PART
bracis-19052	156	32	constantly	constantly	ADV
bracis-19052	156	33	update	update	VERB
bracis-19052	156	34	\(\alpha	\(\alpha	NOUN
bracis-19052	156	35	\	\	NOUN
bracis-19052	156	36	)	)	PUNCT
bracis-19052	156	37	.	.	PUNCT
bracis-19052	157	1	our	our	PRON
bracis-19052	157	2	new	new	ADJ
bracis-19052	157	3	approach	approach	NOUN
bracis-19052	157	4	uses	use	VERB
bracis-19052	157	5	the	the	DET
bracis-19052	157	6	graph	graph	NOUN
bracis-19052	157	7	fourier	fourier	NOUN
bracis-19052	157	8	transform	transform	NOUN
bracis-19052	157	9	.	.	PUNCT
bracis-19052	158	1	in	in	ADP
bracis-19052	158	2	other	other	ADJ
bracis-19052	158	3	words	word	NOUN
bracis-19052	158	4	,	,	PUNCT
bracis-19052	158	5	we	we	PRON
bracis-19052	158	6	adapt	adapt	VERB
bracis-19052	158	7	the	the	DET
bracis-19052	158	8	idea	idea	NOUN
bracis-19052	158	9	of	of	ADP
bracis-19052	158	10	smooth	smooth	ADJ
bracis-19052	158	11	eigenbasis	eigenbasis	NOUN
bracis-19052	158	12	pursuit	pursuit	NOUN
bracis-19052	158	13	to	to	ADP
bracis-19052	158	14	this	this	DET
bracis-19052	158	15	particular	particular	ADJ
bracis-19052	158	16	problem	problem	NOUN
bracis-19052	158	17	.	.	PUNCT
bracis-19052	159	1	let	let	VERB
bracis-19052	159	2	us	we	PRON
bracis-19052	159	3	write	write	VERB
bracis-19052	159	4	the	the	DET
bracis-19052	159	5	propagation	propagation	NOUN
bracis-19052	159	6	matrix	matrix	NOUN
bracis-19052	159	7	using	use	VERB
bracis-19052	159	8	eigenfunctions	eigenfunction	NOUN
bracis-19052	159	9	:	:	PUNCT
bracis-19052	159	10	$	$	SYM
bracis-19052	159	11	$	$	SYM
bracis-19052	159	12	\begin{aligned	\begin{aligne	VERB
bracis-19052	159	13	}	}	PUNCT
bracis-19052	159	14	\mathbf	\mathbf	PROPN
bracis-19052	159	15	{	{	PUNCT
bracis-19052	159	16	p}&=	p}&=	X
bracis-19052	159	17	\sum	\sum	NOUN
bracis-19052	159	18	_	_	PUNCT
bracis-19052	159	19	{	{	PUNCT
bracis-19052	159	20	t=0}^\infty	t=0}^\infty	NOUN
bracis-19052	159	21	\alpha	\alpha	ADP
bracis-19052	159	22	^t	^t	ADP
bracis-19052	159	23	\mathbf	\mathbf	PROPN
bracis-19052	159	24	{	{	PUNCT
bracis-19052	159	25	s}^t	s}^t	PROPN
bracis-19052	159	26	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	159	27	(	(	PUNCT
bracis-19052	159	28	30	30	NUM
bracis-19052	159	29	)	)	PUNCT
bracis-19052	159	30	$	$	SYM
bracis-19052	159	31	$	$	SYM
bracis-19052	159	32	\begin{aligned}&=	\begin{aligned}&=	VERB
bracis-19052	159	33	\sum	\sum	NOUN
bracis-19052	160	1	_	_	PUNCT
bracis-19052	160	2	{	{	PUNCT
bracis-19052	160	3	t=0}^\infty	t=0}^\infty	NOUN
bracis-19052	160	4	\alpha	\alpha	ADP
bracis-19052	160	5	^t	^t	PROPN
bracis-19052	160	6	(	(	PUNCT
bracis-19052	160	7	\mathbf	\mathbf	PROPN
bracis-19052	160	8	{	{	PUNCT
bracis-19052	160	9	i}\mathbf	i}\mathbf	PROPN
bracis-19052	160	10	{	{	PUNCT
bracis-19052	160	11	\mathbf	\mathbf	PROPN
bracis-19052	160	12	{	{	PUNCT
bracis-19052	160	13	l}_{\mathbb	l}_{\mathbb	PROPN
bracis-19052	160	14	{	{	PUNCT
bracis-19052	160	15	n}}})^t	n}}})^t	X
bracis-19052	160	16	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	160	17	(	(	PUNCT
bracis-19052	160	18	31	31	NUM
bracis-19052	160	19	)	)	PUNCT
bracis-19052	160	20	using	use	VERB
bracis-19052	160	21	the	the	DET
bracis-19052	160	22	graph	graph	NOUN
bracis-19052	160	23	fourier	fourier	NOUN
bracis-19052	160	24	transform	transform	NOUN
bracis-19052	160	25	,	,	PUNCT
bracis-19052	160	26	we	we	PRON
bracis-19052	160	27	have	have	VERB
bracis-19052	160	28	that	that	SCONJ
bracis-19052	160	29	$	$	SYM
bracis-19052	160	30	$	$	SYM
bracis-19052	160	31	\begin{aligned	\begin{aligne	VERB
bracis-19052	160	32	}	}	PUNCT
bracis-19052	160	33	\mathbf	\mathbf	PROPN
bracis-19052	160	34	{	{	PUNCT
bracis-19052	160	35	\mathbf	\mathbf	PROPN
bracis-19052	160	36	{	{	PUNCT
bracis-19052	160	37	l}_{\mathbb	l}_{\mathbb	PROPN
bracis-19052	160	38	{	{	PUNCT
bracis-19052	160	39	n}}}&=	n}}}&=	ADJ
bracis-19052	160	40	\mathbf	\mathbf	PROPN
bracis-19052	160	41	{	{	PUNCT
bracis-19052	160	42	u	u	NOUN
bracis-19052	160	43	}	}	PUNCT
bracis-19052	160	44	\mathbf	\mathbf	PROPN
bracis-19052	160	45	{	{	PUNCT
bracis-19052	160	46	\lambda	\lambda	PROPN
bracis-19052	160	47	}	}	PUNCT
bracis-19052	160	48	\mathbf	\mathbf	PROPN
bracis-19052	160	49	{	{	PUNCT
bracis-19052	160	50	u}^\top	u}^\top	ADJ
bracis-19052	160	51	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	160	52	(	(	PUNCT
bracis-19052	160	53	32	32	NUM
bracis-19052	160	54	)	)	PUNCT
bracis-19052	160	55	$	$	SYM
bracis-19052	160	56	$	$	SYM
bracis-19052	160	57	\begin{aligned	\begin{aligne	VERB
bracis-19052	160	58	}	}	PUNCT
bracis-19052	160	59	\mathbf	\mathbf	PROPN
bracis-19052	160	60	{	{	PUNCT
bracis-19052	160	61	i}&=	i}&=	PROPN
bracis-19052	160	62	\mathbf	\mathbf	PROPN
bracis-19052	160	63	{	{	PUNCT
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bracis-19052	160	66	\mathbf	\mathbf	PROPN
bracis-19052	160	67	{	{	PUNCT
bracis-19052	160	68	i	i	NOUN
bracis-19052	160	69	}	}	PUNCT
bracis-19052	160	70	\mathbf	\mathbf	PROPN
bracis-19052	160	71	{	{	PUNCT
bracis-19052	160	72	u}^\top	u}^\top	ADV
bracis-19052	160	73	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	160	74	(	(	PUNCT
bracis-19052	160	75	33	33	NUM
bracis-19052	160	76	)	)	PUNCT
bracis-19052	160	77	so	so	SCONJ
bracis-19052	160	78	it	it	PRON
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bracis-19052	160	80	that	that	SCONJ
bracis-19052	160	81	$	$	SYM
bracis-19052	160	82	$	$	SYM
bracis-19052	160	83	\begin{aligned	\begin{aligne	VERB
bracis-19052	160	84	}	}	PUNCT
bracis-19052	160	85	\mathbf	\mathbf	PROPN
bracis-19052	160	86	{	{	PUNCT
bracis-19052	160	87	p}&=	p}&=	X
bracis-19052	160	88	\mathbf	\mathbf	PROPN
bracis-19052	160	89	{	{	PUNCT
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bracis-19052	160	92	\widetilde{\varlambda	\widetilde{\varlambda	VERB
bracis-19052	160	93	}	}	PUNCT
bracis-19052	160	94	\mathbf	\mathbf	PROPN
bracis-19052	160	95	{	{	PUNCT
bracis-19052	160	96	u}^\top	u}^\top	ADV
bracis-19052	160	97	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	160	98	(	(	PUNCT
bracis-19052	160	99	34	34	NUM
bracis-19052	160	100	)	)	PUNCT
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bracis-19052	160	102	\(\forall	\(\forall	ADV
bracis-19052	160	103	i	i	PRON
bracis-19052	160	104	\in	\in	VERB
bracis-19052	160	105	\{1	\{1	PROPN
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bracis-19052	160	107	n\}\	n\}\	NOUN
bracis-19052	160	108	):	):	PUNCT
bracis-19052	160	109	$	$	SYM
bracis-19052	160	110	$	$	SYM
bracis-19052	160	111	\begin{aligned	\begin{aligne	VERB
bracis-19052	160	112	}	}	PUNCT
bracis-19052	160	113	\widetilde{\varlambda	\widetilde{\varlambda	NOUN
bracis-19052	160	114	}	}	PUNCT
bracis-19052	160	115	_	_	PUNCT
bracis-19052	160	116	{	{	PUNCT
bracis-19052	160	117	ii}&=	ii}&=	PROPN
bracis-19052	160	118	\sum	\sum	PROPN
bracis-19052	160	119	_	_	PUNCT
bracis-19052	160	120	{	{	PUNCT
bracis-19052	160	121	t=0}^\infty	t=0}^\infty	NOUN
bracis-19052	160	122	(	(	PUNCT
bracis-19052	160	123	\alpha	\alpha	PROPN
bracis-19052	160	124	(	(	PUNCT
bracis-19052	160	125	1-\varlambda	1-\varlambda	NUM
bracis-19052	160	126	_	_	PRON
bracis-19052	160	127	{	{	PUNCT
bracis-19052	160	128	ii	ii	NOUN
bracis-19052	160	129	}	}	PUNCT
bracis-19052	160	130	)	)	PUNCT
bracis-19052	160	131	)	)	PUNCT
bracis-19052	161	1	^t	^t	PROPN
bracis-19052	161	2	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	162	1	(	(	PUNCT
bracis-19052	162	2	35	35	NUM
bracis-19052	162	3	)	)	PUNCT
bracis-19052	162	4	$	$	SYM
bracis-19052	162	5	$	$	SYM
bracis-19052	162	6	\begin{aligned	\begin{aligne	VERB
bracis-19052	162	7	}	}	PUNCT
bracis-19052	162	8	\	\	NOUN
bracis-19052	162	9	{	{	PUNCT
bracis-19052	163	1	\big	\big	PROPN
bracis-19052	163	2	\vert	\vert	PROPN
bracis-19052	163	3	\alpha	\alpha	PROPN
bracis-19052	163	4	(	(	PUNCT
bracis-19052	163	5	1-\varlambda	1-\varlambda	NUM
bracis-19052	163	6	_	_	PRON
bracis-19052	163	7	{	{	PUNCT
bracis-19052	163	8	ii	ii	NOUN
bracis-19052	163	9	}	}	PUNCT
bracis-19052	163	10	)	)	PUNCT
bracis-19052	164	1	\big	\big	PROPN
bracis-19052	164	2	\vert	\vert	PROPN
bracis-19052	164	3	<	<	X
bracis-19052	164	4	1\}&=	1\}&=	PROPN
bracis-19052	164	5	\frac{1}{1(\alpha	\frac{1}{1(\alpha	PROPN
bracis-19052	164	6	(	(	PUNCT
bracis-19052	164	7	1-\varlambda	1-\varlambda	NUM
bracis-19052	164	8	_	_	PRON
bracis-19052	164	9	{	{	PUNCT
bracis-19052	164	10	ii	ii	NOUN
bracis-19052	164	11	}	}	PUNCT
bracis-19052	164	12	)	)	PUNCT
bracis-19052	164	13	)	)	PUNCT
bracis-19052	164	14	}	}	PUNCT
bracis-19052	164	15	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	164	16	(	(	PUNCT
bracis-19052	164	17	36	36	NUM
bracis-19052	164	18	)	)	PUNCT
bracis-19052	164	19	$	$	SYM
bracis-19052	164	20	$	$	SYM
bracis-19052	164	21	\begin{aligned}&=	\begin{aligned}&=	VERB
bracis-19052	164	22	\frac{1}{(1	\frac{1}{(1	PROPN
bracis-19052	164	23	\alpha	\alpha	PROPN
bracis-19052	164	24	)	)	PUNCT
bracis-19052	164	25	\times	\time	VERB
bracis-19052	164	26	1	1	NUM
bracis-19052	164	27	+	+	CCONJ
bracis-19052	164	28	(	(	PUNCT
bracis-19052	164	29	\alpha	\alpha	ADJ
bracis-19052	164	30	)	)	PUNCT
bracis-19052	164	31	\times	\times	ADP
bracis-19052	164	32	\varlambda	\varlambda	PROPN
bracis-19052	164	33	_	_	PUNCT
bracis-19052	164	34	{	{	PUNCT
bracis-19052	164	35	ii	ii	NOUN
bracis-19052	164	36	}	}	PUNCT
bracis-19052	164	37	}	}	PUNCT
bracis-19052	164	38	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-19052	164	39	(	(	PUNCT
bracis-19052	164	40	37	37	NUM
bracis-19052	164	41	)	)	PUNCT
bracis-19052	164	42	in	in	ADP
bracis-19052	164	43	practice	practice	NOUN
bracis-19052	164	44	,	,	PUNCT
bracis-19052	164	45	we	we	PRON
bracis-19052	164	46	can	can	AUX
bracis-19052	164	47	assume	assume	VERB
bracis-19052	164	48	that	that	SCONJ
bracis-19052	164	49	\	\	PROPN
bracis-19052	164	50	(	(	PUNCT
bracis-19052	164	51	\mathbf	\mathbf	PROPN
bracis-19052	164	52	{	{	PUNCT
bracis-19052	164	53	u}\	u}\	PROPN
bracis-19052	164	54	)	)	PUNCT
bracis-19052	164	55	is	be	AUX
bracis-19052	164	56	an	an	DET
bracis-19052	164	57	matrix	matrix	NOUN
bracis-19052	164	58	,	,	PUNCT
bracis-19052	164	59	with	with	ADP
bracis-19052	164	60	l	l	NOUN
bracis-19052	164	61	the	the	DET
bracis-19052	164	62	number	number	NOUN
bracis-19052	164	63	of	of	ADP
bracis-19052	164	64	labeled	label	VERB
bracis-19052	164	65	instances	instance	NOUN
bracis-19052	164	66	and	and	CCONJ
bracis-19052	164	67	p	p	X
bracis-19052	164	68	the	the	DET
bracis-19052	164	69	chosen	choose	VERB
bracis-19052	164	70	amount	amount	NOUN
bracis-19052	164	71	of	of	ADP
bracis-19052	164	72	eigenfunctions	eigenfunction	NOUN
bracis-19052	164	73	.	.	PUNCT
bracis-19052	165	1	the	the	DET
bracis-19052	165	2	diagonal	diagonal	ADJ
bracis-19052	165	3	entries	entry	NOUN
bracis-19052	165	4	are	be	AUX
bracis-19052	165	5	given	give	VERB
bracis-19052	165	6	 	 	SPACE
bracis-19052	165	7	by	by	ADP
bracis-19052	165	8	$	$	SYM
bracis-19052	165	9	$	$	SYM
bracis-19052	165	10	\begin{aligned	\begin{aligne	VERB
bracis-19052	165	11	}	}	PUNCT
bracis-19052	165	12	\mathbf	\mathbf	PROPN
bracis-19052	165	13	{	{	PUNCT
bracis-19052	165	14	p}_{ii}&=	p}_{ii}&=	X
bracis-19052	165	15	(	(	PUNCT
bracis-19052	165	16	\mathbf	\mathbf	PROPN
bracis-19052	165	17	{	{	PUNCT
bracis-19052	165	18	u}\widetilde{\varlambda	u}\widetilde{\varlambda	PROPN
bracis-19052	165	19	}	}	PUNCT
bracis-19052	165	20	\mathbf	\mathbf	PROPN
bracis-19052	165	21	{	{	PUNCT
bracis-19052	165	22	u}^\top	u}^\top	ADP
bracis-19052	165	23	)	)	PUNCT
bracis-19052	165	24	_	_	PRON
bracis-19052	165	25	{	{	PUNCT
bracis-19052	165	26	ii	ii	NOUN
bracis-19052	165	27	}	}	PUNCT
bracis-19052	165	28	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-19052	165	29	(	(	PUNCT
bracis-19052	165	30	38	38	NUM
bracis-19052	165	31	)	)	PUNCT
bracis-19052	165	32	$	$	SYM
bracis-19052	165	33	$	$	SYM
bracis-19052	165	34	\begin{aligned}&=	\begin{aligned}&=	VERB
bracis-19052	165	35	(	(	PUNCT
bracis-19052	165	36	\mathbf	\mathbf	PROPN
bracis-19052	165	37	{	{	PUNCT
bracis-19052	165	38	u}^\top	u}^\top	ADJ
bracis-19052	165	39	)	)	PUNCT
bracis-19052	166	1	_	_	PUNCT
bracis-19052	166	2	{	{	PUNCT
bracis-19052	167	1	[:	[:	X
bracis-19052	167	2	,	,	PUNCT
bracis-19052	167	3	i]}\widetilde{\varlambda	i]}\widetilde{\varlambda	NOUN
bracis-19052	167	4	}	}	PUNCT
bracis-19052	167	5	(	(	PUNCT
bracis-19052	167	6	\mathbf	\mathbf	PROPN
bracis-19052	167	7	{	{	PUNCT
bracis-19052	167	8	u}^\top	u}^\top	ADJ
bracis-19052	167	9	)	)	PUNCT
bracis-19052	168	1	_	_	PUNCT
bracis-19052	168	2	{	{	PUNCT
bracis-19052	169	1	[:	[:	X
bracis-19052	169	2	,	,	PUNCT
bracis-19052	169	3	i	i	PRON
bracis-19052	169	4	]	]	X
bracis-19052	169	5	}	}	PUNCT
bracis-19052	169	6	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	169	7	(	(	PUNCT
bracis-19052	169	8	39	39	NUM
bracis-19052	169	9	)	)	PUNCT
bracis-19052	169	10	$	$	SYM
bracis-19052	169	11	$	$	SYM
bracis-19052	169	12	\begin{aligned}&=	\begin{aligned}&=	VERB
bracis-19052	169	13	\varsigma	\varsigma	PROPN
bracis-19052	169	14	_	_	PRON
bracis-19052	169	15	{	{	PUNCT
bracis-19052	169	16	i=1}^p	i=1}^p	PROPN
bracis-19052	169	17	\mathbf	\mathbf	PROPN
bracis-19052	169	18	{	{	PUNCT
bracis-19052	169	19	u}_{ik}^2	u}_{ik}^2	PROPN
bracis-19052	169	20	\widetilde{\varlambda	\widetilde{\varlambda	NOUN
bracis-19052	169	21	}	}	PUNCT
bracis-19052	169	22	_	_	PUNCT
bracis-19052	169	23	{	{	PUNCT
bracis-19052	169	24	kk	kk	X
bracis-19052	169	25	}	}	PUNCT
bracis-19052	169	26	\end{aligned}$$	\end{aligned}$$	X
bracis-19052	169	27	(	(	PUNCT
bracis-19052	169	28	40	40	NUM
bracis-19052	169	29	)	)	PUNCT
bracis-19052	169	30	$	$	SYM
bracis-19052	169	31	$	$	SYM
bracis-19052	169	32	\begin{aligned}&=	\begin{aligned}&=	VERB
bracis-19052	169	33	(	(	PUNCT
bracis-19052	169	34	\mathbf	\mathbf	PROPN
bracis-19052	169	35	{	{	PUNCT
bracis-19052	169	36	u}_{[i	u}_{[i	PROPN
bracis-19052	169	37	,	,	PUNCT
bracis-19052	169	38	:]	:]	NOUN
bracis-19052	169	39	}	}	PUNCT
bracis-19052	169	40	)	)	PUNCT
bracis-19052	169	41	(	(	PUNCT
bracis-19052	169	42	\mathbf	\mathbf	PROPN
bracis-19052	169	43	{	{	PUNCT
bracis-19052	169	44	u}_{[i	u}_{[i	PROPN
bracis-19052	169	45	,	,	PUNCT
bracis-19052	169	46	:]	:]	NOUN
bracis-19052	169	47	}	}	PUNCT
bracis-19052	169	48	\widetilde{\varlambda	\widetilde{\varlambda	NOUN
bracis-19052	169	49	}	}	PUNCT
bracis-19052	169	50	)	)	PUNCT
bracis-19052	169	51	^\top	^\top	ADP
bracis-19052	169	52	\end{aligned}$$	\end{aligned}$$	ADP
bracis-19052	169	53	(	(	PUNCT
bracis-19052	169	54	41	41	NUM
bracis-19052	169	55	)	)	PUNCT
bracis-19052	169	56	next	next	ADV
bracis-19052	169	57	,	,	PUNCT
bracis-19052	169	58	we	we	PRON
bracis-19052	169	59	’ll	’ll	AUX
bracis-19052	169	60	analyze	analyze	VERB
bracis-19052	169	61	the	the	DET
bracis-19052	169	62	complexity	complexity	NOUN
bracis-19052	169	63	of	of	ADP
bracis-19052	169	64	calculating	calculate	VERB
bracis-19052	169	65	the	the	DET
bracis-19052	169	66	leave	leave	VERB
bracis-19052	169	67	-	-	PUNCT
bracis-19052	169	68	one	one	NUM
bracis-19052	169	69	-	-	PUNCT
bracis-19052	169	70	out	out	NOUN
bracis-19052	169	71	error	error	NOUN
bracis-19052	169	72	for	for	ADP
bracis-19052	169	73	a	a	DET
bracis-19052	169	74	given	give	VERB
bracis-19052	169	75	diffusion	diffusion	NOUN
bracis-19052	169	76	rate	rate	NOUN
bracis-19052	169	77	\(\alpha	\(\alpha	NOUN
bracis-19052	169	78	\	\	NOUN
bracis-19052	169	79	)	)	PUNCT
bracis-19052	169	80	,	,	PUNCT
bracis-19052	169	81	given	give	VERB
bracis-19052	169	82	that	that	SCONJ
bracis-19052	169	83	we	we	PRON
bracis-19052	169	84	have	have	AUX
bracis-19052	169	85	stored	store	VERB
bracis-19052	169	86	the	the	DET
bracis-19052	169	87	first	first	ADJ
bracis-19052	169	88	p	p	ADJ
bracis-19052	169	89	eigenfunctions	eigenfunction	NOUN
bracis-19052	169	90	in	in	ADP
bracis-19052	169	91	the	the	DET
bracis-19052	169	92	matrix	matrix	NOUN
bracis-19052	169	93	\	\	PROPN
bracis-19052	169	94	(	(	PUNCT
bracis-19052	169	95	\mathbf	\mathbf	PROPN
bracis-19052	169	96	{	{	PUNCT
bracis-19052	169	97	u}\	u}\	PROPN
bracis-19052	169	98	)	)	PUNCT
bracis-19052	169	99	.	.	PUNCT
bracis-19052	170	1	let	let	AUX
bracis-19052	170	2	be	be	AUX
bracis-19052	170	3	the	the	DET
bracis-19052	170	4	matrix	matrix	NOUN
bracis-19052	170	5	of	of	ADP
bracis-19052	170	6	eigenfunctions	eigenfunction	NOUN
bracis-19052	170	7	with	with	ADP
bracis-19052	170	8	domain	domain	NOUN
bracis-19052	170	9	restricted	restrict	VERB
bracis-19052	170	10	to	to	ADP
bracis-19052	170	11	labeled	label	VERB
bracis-19052	170	12	instances	instance	NOUN
bracis-19052	170	13	.	.	PUNCT
bracis-19052	171	1	exploiting	exploit	VERB
bracis-19052	171	2	the	the	DET
bracis-19052	171	3	fact	fact	NOUN
bracis-19052	171	4	that	that	SCONJ
bracis-19052	171	5	\	\	PROPN
bracis-19052	171	6	(	(	PUNCT
bracis-19052	171	7	\mathbf	\mathbf	PROPN
bracis-19052	171	8	{	{	PUNCT
bracis-19052	171	9	y}_\mathcal	y}_\mathcal	PROPN
bracis-19052	171	10	{	{	PUNCT
bracis-19052	171	11	u}=	u}=	PROPN
bracis-19052	171	12	0\	0\	PROPN
bracis-19052	171	13	)	)	PUNCT
bracis-19052	171	14	,	,	PUNCT
bracis-19052	171	15	it	it	PRON
bracis-19052	171	16	can	can	AUX
bracis-19052	171	17	be	be	AUX
bracis-19052	171	18	shown	show	VERB
bracis-19052	171	19	that	that	SCONJ
bracis-19052	171	20	$	$	SYM
bracis-19052	171	21	$	$	SYM
bracis-19052	171	22	\begin{aligned	\begin{aligne	VERB
bracis-19052	171	23	}	}	PUNCT
bracis-19052	171	24	\mathbf	\mathbf	PROPN
bracis-19052	171	25	{	{	PUNCT
bracis-19052	171	26	p}_{\mathcal	p}_{\mathcal	ADJ
bracis-19052	171	27	{	{	PUNCT
bracis-19052	171	28	l}\mathcal	l}\mathcal	ADJ
bracis-19052	171	29	{	{	PUNCT
bracis-19052	171	30	l	l	NOUN
bracis-19052	171	31	}	}	PUNCT
bracis-19052	171	32	}	}	PUNCT
bracis-19052	171	33	=	=	SYM
bracis-19052	171	34	\mathbf	\mathbf	PROPN
bracis-19052	171	35	{	{	PUNCT
bracis-19052	171	36	u}_{\mathcal	u}_{\mathcal	ADJ
bracis-19052	171	37	{	{	PUNCT
bracis-19052	171	38	l	l	NOUN
bracis-19052	171	39	}	}	PUNCT
bracis-19052	171	40	}	}	PUNCT
bracis-19052	171	41	\mathbf	\mathbf	PROPN
bracis-19052	171	42	{	{	PUNCT
bracis-19052	171	43	\widetilde{\lambda	\widetilde{\lambda	ADJ
bracis-19052	171	44	}	}	PUNCT
bracis-19052	171	45	}	}	PUNCT
bracis-19052	171	46	(	(	PUNCT
bracis-19052	171	47	\mathbf	\mathbf	PROPN
bracis-19052	171	48	{	{	PUNCT
bracis-19052	171	49	u}_{\mathcal	u}_{\mathcal	ADJ
bracis-19052	171	50	{	{	PUNCT
bracis-19052	171	51	l}}^\top	l}}^\top	NOUN
bracis-19052	171	52	\mathbf	\mathbf	PROPN
bracis-19052	171	53	{	{	PUNCT
bracis-19052	171	54	y}_\mathcal	y}_\mathcal	X
bracis-19052	171	55	{	{	PUNCT
bracis-19052	171	56	l	l	NOUN
bracis-19052	171	57	}	}	PUNCT
bracis-19052	171	58	)	)	PUNCT
bracis-19052	171	59	\end{aligned}$$	\end{aligned}$$	PROPN
bracis-19052	171	60	(	(	PUNCT
bracis-19052	171	61	42	42	NUM
bracis-19052	171	62	)	)	PUNCT
bracis-19052	171	63	we	we	PRON
bracis-19052	171	64	can	can	AUX
bracis-19052	171	65	precompute	precompute	VERB
bracis-19052	171	66	with	with	ADP
bracis-19052	171	67	\(\mathcal	\(\mathcal	ADJ
bracis-19052	171	68	{	{	PUNCT
bracis-19052	171	69	o}(plc)\	o}(plc)\	NOUN
bracis-19052	171	70	)	)	PUNCT
bracis-19052	171	71	multiplications	multiplication	NOUN
bracis-19052	171	72	.	.	PUNCT
bracis-19052	172	1	for	for	ADP
bracis-19052	172	2	each	each	DET
bracis-19052	172	3	diffusion	diffusion	NOUN
bracis-19052	172	4	rate	rate	NOUN
bracis-19052	172	5	candidate	candidate	NOUN
bracis-19052	172	6	\(\alpha	\(\alpha	NOUN
bracis-19052	172	7	\	\	PROPN
bracis-19052	172	8	)	)	PUNCT
bracis-19052	172	9	,	,	PUNCT
bracis-19052	172	10	we	we	PRON
bracis-19052	172	11	obtain	obtain	VERB
bracis-19052	172	12	by	by	ADP
bracis-19052	172	13	multiplying	multiply	VERB
bracis-19052	172	14	each	each	DET
bracis-19052	172	15	restricted	restrict	VERB
bracis-19052	172	16	eigenfunction	eigenfunction	NOUN
bracis-19052	172	17	with	with	ADP
bracis-19052	172	18	its	its	PRON
bracis-19052	172	19	new	new	ADJ
bracis-19052	172	20	eigenvalue	eigenvalue	NOUN
bracis-19052	172	21	.	.	PUNCT
bracis-19052	173	1	the	the	DET
bracis-19052	173	2	only	only	ADJ
bracis-19052	173	3	thing	thing	NOUN
bracis-19052	173	4	left	leave	VERB
bracis-19052	173	5	is	be	AUX
bracis-19052	173	6	to	to	PART
bracis-19052	173	7	post	post	VERB
bracis-19052	173	8	-	-	VERB
bracis-19052	173	9	multiply	multiply	VERB
bracis-19052	173	10	it	it	PRON
bracis-19052	173	11	by	by	ADP
bracis-19052	173	12	the	the	DET
bracis-19052	173	13	pre	pre	ADJ
bracis-19052	173	14	-	-	ADJ
bracis-19052	173	15	computed	computed	ADJ
bracis-19052	173	16	matrix	matrix	NOUN
bracis-19052	173	17	.	.	PUNCT
bracis-19052	174	1	as	as	ADP
bracis-19052	174	2	a	a	DET
bracis-19052	174	3	result	result	NOUN
bracis-19052	174	4	,	,	PUNCT
bracis-19052	174	5	we	we	PRON
bracis-19052	174	6	can	can	AUX
bracis-19052	174	7	compute	compute	VERB
bracis-19052	174	8	the	the	DET
bracis-19052	174	9	leave	leave	VERB
bracis-19052	174	10	-	-	PUNCT
bracis-19052	174	11	one	one	NUM
bracis-19052	174	12	-	-	PUNCT
bracis-19052	174	13	out	out	NOUN
bracis-19052	174	14	error	error	NOUN
bracis-19052	174	15	for	for	ADP
bracis-19052	174	16	arbitrary	arbitrary	ADJ
bracis-19052	174	17	\(\alpha	\(\alpha	NOUN
bracis-19052	174	18	\	\	NOUN
bracis-19052	174	19	)	)	PUNCT
bracis-19052	174	20	with	with	ADP
bracis-19052	174	21	\(\mathcal	\(\mathcal	ADJ
bracis-19052	174	22	{	{	PUNCT
bracis-19052	174	23	o}(plc)\	o}(plc)\	NOUN
bracis-19052	174	24	)	)	PUNCT
bracis-19052	174	25	operations	operation	NOUN
bracis-19052	174	26	.	.	PUNCT
bracis-19052	175	1	we	we	PRON
bracis-19052	175	2	have	have	AUX
bracis-19052	175	3	shown	show	VERB
bracis-19052	175	4	that	that	SCONJ
bracis-19052	175	5	,	,	PUNCT
bracis-19052	175	6	by	by	ADP
bracis-19052	175	7	using	use	VERB
bracis-19052	175	8	the	the	DET
bracis-19052	175	9	propagation	propagation	NOUN
bracis-19052	175	10	submatrix	submatrix	NOUN
bracis-19052	175	11	,	,	PUNCT
bracis-19052	175	12	we	we	PRON
bracis-19052	175	13	can	can	AUX
bracis-19052	175	14	re	re	VERB
bracis-19052	175	15	-	-	VERB
bracis-19052	175	16	compute	compute	VERB
bracis-19052	175	17	the	the	DET
bracis-19052	175	18	propagation	propagation	NOUN
bracis-19052	175	19	submatrix	submatrix	NOUN
bracis-19052	175	20	\	\	PROPN
bracis-19052	175	21	(	(	PUNCT
bracis-19052	175	22	\mathbf	\mathbf	PROPN
bracis-19052	175	23	{	{	PUNCT
bracis-19052	175	24	p}_{\mathcal	p}_{\mathcal	ADJ
bracis-19052	175	25	{	{	PUNCT
bracis-19052	175	26	l}\mathcal	l}\mathcal	ADJ
bracis-19052	175	27	{	{	PUNCT
bracis-19052	175	28	l}}\	l}}\	NOUN
bracis-19052	175	29	)	)	PUNCT
bracis-19052	175	30	in	in	ADP
bracis-19052	175	31	\(\mathcal	\(\mathcal	ADJ
bracis-19052	175	32	{	{	PUNCT
bracis-19052	175	33	o}(plc)\	o}(plc)\	NOUN
bracis-19052	175	34	)	)	PUNCT
bracis-19052	175	35	time	time	NOUN
bracis-19052	175	36	.	.	PUNCT
bracis-19052	176	1	in	in	ADP
bracis-19052	176	2	comparison	comparison	NOUN
bracis-19052	176	3	,	,	PUNCT
bracis-19052	176	4	the	the	DET
bracis-19052	176	5	previous	previous	ADJ
bracis-19052	176	6	approach	approach	NOUN
bracis-19052	176	7	[	[	X
bracis-19052	176	8	4	4	X
bracis-19052	176	9	]	]	PUNCT
bracis-19052	176	10	requires	require	VERB
bracis-19052	176	11	,	,	PUNCT
bracis-19052	176	12	for	for	ADP
bracis-19052	176	13	each	each	DET
bracis-19052	176	14	diffusion	diffusion	NOUN
bracis-19052	176	15	rate	rate	NOUN
bracis-19052	176	16	,	,	PUNCT
bracis-19052	176	17	a	a	DET
bracis-19052	176	18	total	total	NOUN
bracis-19052	176	19	of	of	ADP
bracis-19052	176	20	o(tknlc	o(tknlc	ADJ
bracis-19052	176	21	)	)	PUNCT
bracis-19052	176	22	operations	operation	NOUN
bracis-19052	176	23	,	,	PUNCT
bracis-19052	176	24	assuming	assume	VERB
bracis-19052	176	25	t	t	NOUN
bracis-19052	176	26	iterations	iteration	NOUN
bracis-19052	176	27	of	of	ADP
bracis-19052	176	28	the	the	DET
bracis-19052	176	29	power	power	NOUN
bracis-19052	176	30	method	method	NOUN
bracis-19052	176	31	and	and	CCONJ
bracis-19052	176	32	a	a	DET
bracis-19052	176	33	sparse	sparse	ADJ
bracis-19052	176	34	affinity	affinity	NOUN
bracis-19052	176	35	matrix	matrix	NOUN
bracis-19052	176	36	with	with	ADP
bracis-19052	176	37	average	average	ADJ
bracis-19052	176	38	node	node	NOUN
bracis-19052	176	39	degree	degree	NOUN
bracis-19052	176	40	equal	equal	ADJ
bracis-19052	176	41	to	to	ADP
bracis-19052	176	42	k.	k.	VERB
bracis-19052	177	1	even	even	ADV
bracis-19052	177	2	if	if	SCONJ
bracis-19052	177	3	we	we	PRON
bracis-19052	177	4	use	use	VERB
bracis-19052	177	5	the	the	DET
bracis-19052	177	6	full	full	ADJ
bracis-19052	177	7	eigendecomposition	eigendecomposition	NOUN
bracis-19052	177	8	(	(	PUNCT
bracis-19052	177	9	\(p	\(p	NOUN
bracis-19052	177	10	=	=	SYM
bracis-19052	177	11	n\	n\	NOUN
bracis-19052	177	12	)	)	PUNCT
bracis-19052	177	13	)	)	PUNCT
bracis-19052	177	14	,	,	PUNCT
bracis-19052	177	15	this	this	DET
bracis-19052	177	16	new	new	ADJ
bracis-19052	177	17	approach	approach	NOUN
bracis-19052	177	18	is	be	AUX
bracis-19052	177	19	significantly	significantly	ADV
bracis-19052	177	20	more	more	ADV
bracis-19052	177	21	viable	viable	ADJ
bracis-19052	177	22	for	for	ADP
bracis-19052	177	23	different	different	ADJ
bracis-19052	177	24	learning	learning	NOUN
bracis-19052	177	25	rates	rate	NOUN
bracis-19052	177	26	.	.	PUNCT
bracis-19052	178	1	moreover	moreover	ADV
bracis-19052	178	2	,	,	PUNCT
bracis-19052	178	3	we	we	PRON
bracis-19052	178	4	can	can	AUX
bracis-19052	178	5	lower	lower	VERB
bracis-19052	178	6	the	the	DET
bracis-19052	178	7	choice	choice	NOUN
bracis-19052	178	8	of	of	ADP
bracis-19052	178	9	p	p	NOUN
bracis-19052	178	10	to	to	PART
bracis-19052	178	11	use	use	VERB
bracis-19052	178	12	a	a	DET
bracis-19052	178	13	faster	fast	ADJ
bracis-19052	178	14	,	,	PUNCT
bracis-19052	178	15	less	less	ADV
bracis-19052	178	16	accurate	accurate	ADJ
bracis-19052	178	17	approximation	approximation	NOUN
bracis-19052	178	18	.	.	PUNCT
bracis-19052	179	1	4	4	NUM
bracis-19052	179	2	methodology	methodology	NOUN
bracis-19052	179	3	basic	basic	ADJ
bracis-19052	179	4	framework	framework	NOUN
bracis-19052	179	5	.	.	PUNCT
bracis-19052	180	1	we	we	PRON
bracis-19052	180	2	have	have	VERB
bracis-19052	180	3	a	a	DET
bracis-19052	180	4	configuration	configuration	NOUN
bracis-19052	180	5	dispatcher	dispatcher	NOUN
bracis-19052	180	6	which	which	PRON
bracis-19052	180	7	enables	enable	VERB
bracis-19052	180	8	us	we	PRON
bracis-19052	180	9	to	to	PART
bracis-19052	180	10	vary	vary	VERB
bracis-19052	180	11	a	a	DET
bracis-19052	180	12	set	set	NOUN
bracis-19052	180	13	of	of	ADP
bracis-19052	180	14	parameters	parameter	NOUN
bracis-19052	180	15	(	(	PUNCT
bracis-19052	180	16	for	for	ADP
bracis-19052	180	17	example	example	NOUN
bracis-19052	180	18	,	,	PUNCT
bracis-19052	180	19	the	the	DET
bracis-19052	180	20	chosen	choose	VERB
bracis-19052	180	21	dataset	dataset	NOUN
bracis-19052	180	22	and	and	CCONJ
bracis-19052	180	23	the	the	DET
bracis-19052	180	24	parameters	parameter	NOUN
bracis-19052	180	25	for	for	ADP
bracis-19052	180	26	affinity	affinity	NOUN
bracis-19052	180	27	matrix	matrix	NOUN
bracis-19052	180	28	generation	generation	NOUN
bracis-19052	180	29	)	)	PUNCT
bracis-19052	180	30	.	.	PUNCT
bracis-19052	181	1	we	we	PRON
bracis-19052	181	2	start	start	VERB
bracis-19052	181	3	out	out	ADP
bracis-19052	181	4	by	by	ADP
bracis-19052	181	5	reading	read	VERB
bracis-19052	181	6	our	our	PRON
bracis-19052	181	7	dataset	dataset	NOUN
bracis-19052	181	8	,	,	PUNCT
bracis-19052	181	9	including	include	VERB
bracis-19052	181	10	features	feature	NOUN
bracis-19052	181	11	and	and	CCONJ
bracis-19052	181	12	labels	label	NOUN
bracis-19052	181	13	.	.	PUNCT
bracis-19052	182	1	we	we	PRON
bracis-19052	182	2	use	use	VERB
bracis-19052	182	3	the	the	DET
bracis-19052	182	4	random	random	ADJ
bracis-19052	182	5	seed	seed	NOUN
bracis-19052	182	6	to	to	PART
bracis-19052	182	7	select	select	VERB
bracis-19052	182	8	the	the	DET
bracis-19052	182	9	sampled	sample	VERB
bracis-19052	182	10	labels	label	NOUN
bracis-19052	182	11	,	,	PUNCT
bracis-19052	182	12	and	and	CCONJ
bracis-19052	182	13	create	create	VERB
bracis-19052	182	14	the	the	DET
bracis-19052	182	15	affinity	affinity	NOUN
bracis-19052	182	16	matrix	matrix	NOUN
bracis-19052	182	17	\	\	PROPN
bracis-19052	182	18	(	(	PUNCT
bracis-19052	182	19	\mathbf	\mathbf	PROPN
bracis-19052	182	20	{	{	PUNCT
bracis-19052	182	21	w}\	w}\	PROPN
bracis-19052	182	22	)	)	PUNCT
bracis-19052	182	23	necessary	necessary	ADJ
bracis-19052	182	24	for	for	ADP
bracis-19052	182	25	lgc	lgc	ADJ
bracis-19052	182	26	.	.	PUNCT
bracis-19052	183	1	for	for	ADP
bracis-19052	183	2	automatic	automatic	ADJ
bracis-19052	183	3	label	label	NOUN
bracis-19052	183	4	correction	correction	NOUN
bracis-19052	183	5	,	,	PUNCT
bracis-19052	183	6	we	we	PRON
bracis-19052	183	7	assume	assume	VERB
bracis-19052	183	8	that	that	SCONJ
bracis-19052	183	9	\(\alpha	\(\alpha	ADV
bracis-19052	183	10	\	\	NOUN
bracis-19052	183	11	)	)	PUNCT
bracis-19052	183	12	is	be	AUX
bracis-19052	183	13	given	give	VERB
bracis-19052	183	14	as	as	ADP
bracis-19052	183	15	a	a	DET
bracis-19052	183	16	parameter	parameter	NOUN
bracis-19052	183	17	.	.	PUNCT
bracis-19052	184	1	for	for	ADP
bracis-19052	184	2	choosing	choose	VERB
bracis-19052	184	3	the	the	DET
bracis-19052	184	4	automatic	automatic	ADJ
bracis-19052	184	5	diffusion	diffusion	NOUN
bracis-19052	184	6	rate	rate	NOUN
bracis-19052	184	7	,	,	PUNCT
bracis-19052	184	8	we	we	PRON
bracis-19052	184	9	need	need	VERB
bracis-19052	184	10	to	to	PART
bracis-19052	184	11	extract	extract	VERB
bracis-19052	184	12	the	the	DET
bracis-19052	184	13	p	p	ADJ
bracis-19052	184	14	smoothest	smooth	ADJ
bracis-19052	184	15	eigenfunctions	eigenfunction	NOUN
bracis-19052	184	16	as	as	ADP
bracis-19052	184	17	a	a	DET
bracis-19052	184	18	pre	pre	ADJ
bracis-19052	184	19	-	-	ADJ
bracis-19052	184	20	processing	processing	ADJ
bracis-19052	184	21	step	step	NOUN
bracis-19052	184	22	.	.	PUNCT
bracis-19052	185	1	next	next	ADV
bracis-19052	185	2	,	,	PUNCT
bracis-19052	185	3	we	we	PRON
bracis-19052	185	4	repeatedly	repeatedly	ADV
bracis-19052	185	5	calculate	calculate	VERB
bracis-19052	185	6	the	the	DET
bracis-19052	185	7	gradient	gradient	NOUN
bracis-19052	185	8	and	and	CCONJ
bracis-19052	185	9	update	update	VERB
bracis-19052	185	10	either	either	CCONJ
bracis-19052	185	11	\(\alpha	\(\alpha	NOUN
bracis-19052	185	12	\	\	NOUN
bracis-19052	185	13	)	)	PUNCT
bracis-19052	185	14	or	or	CCONJ
bracis-19052	185	15	\	\	PROPN
bracis-19052	185	16	(	(	PUNCT
bracis-19052	185	17	\mathbf	\mathbf	PROPN
bracis-19052	185	18	{	{	PUNCT
bracis-19052	185	19	\omega	\omega	PROPN
bracis-19052	185	20	}	}	PUNCT
bracis-19052	185	21	\	\	NOUN
bracis-19052	185	22	)	)	PUNCT
bracis-19052	185	23	to	to	PART
bracis-19052	185	24	minimize	minimize	VERB
bracis-19052	185	25	loo	loo	NOUN
bracis-19052	185	26	error	error	NOUN
bracis-19052	185	27	.	.	PUNCT
bracis-19052	186	1	after	after	ADP
bracis-19052	186	2	a	a	DET
bracis-19052	186	3	set	set	NOUN
bracis-19052	186	4	amount	amount	NOUN
bracis-19052	186	5	of	of	ADP
bracis-19052	186	6	iterations	iteration	NOUN
bracis-19052	186	7	,	,	PUNCT
bracis-19052	186	8	we	we	PRON
bracis-19052	186	9	return	return	VERB
bracis-19052	186	10	the	the	DET
bracis-19052	186	11	final	final	ADJ
bracis-19052	186	12	classification	classification	NOUN
bracis-19052	186	13	and	and	CCONJ
bracis-19052	186	14	perform	perform	VERB
bracis-19052	186	15	an	an	DET
bracis-19052	186	16	evaluation	evaluation	NOUN
bracis-19052	186	17	on	on	ADP
bracis-19052	186	18	unlabeled	unlabeled	ADJ
bracis-19052	186	19	examples	example	NOUN
bracis-19052	186	20	.	.	PUNCT
bracis-19052	187	1	the	the	DET
bracis-19052	187	2	programming	programming	NOUN
bracis-19052	187	3	language	language	NOUN
bracis-19052	187	4	of	of	ADP
bracis-19052	187	5	choice	choice	NOUN
bracis-19052	187	6	is	be	AUX
bracis-19052	187	7	python	python	NOUN
bracis-19052	187	8	3	3	NUM
bracis-19052	187	9	,	,	PUNCT
bracis-19052	187	10	for	for	ADP
bracis-19052	187	11	its	its	PRON
bracis-19052	187	12	versatility	versatility	NOUN
bracis-19052	187	13	and	and	CCONJ
bracis-19052	187	14	support	support	NOUN
bracis-19052	187	15	.	.	PUNCT
bracis-19052	188	1	we	we	PRON
bracis-19052	188	2	also	also	ADV
bracis-19052	188	3	make	make	VERB
bracis-19052	188	4	use	use	NOUN
bracis-19052	188	5	of	of	ADP
bracis-19052	188	6	the	the	DET
bracis-19052	188	7	tensorflow	tensorflow	NOUN
bracis-19052	188	8	-	-	PUNCT
bracis-19052	188	9	gpu	gpu	NOUN
bracis-19052	188	10	[	[	X
bracis-19052	188	11	1	1	NUM
bracis-19052	188	12	]	]	X
bracis-19052	188	13	package	package	NOUN
bracis-19052	188	14	,	,	PUNCT
bracis-19052	188	15	which	which	PRON
bracis-19052	188	16	massively	massively	ADV
bracis-19052	188	17	speeds	speed	VERB
bracis-19052	188	18	up	up	ADP
bracis-19052	188	19	our	our	PRON
bracis-19052	188	20	calculations	calculation	NOUN
bracis-19052	188	21	and	and	CCONJ
bracis-19052	188	22	also	also	ADV
bracis-19052	188	23	enables	enable	VERB
bracis-19052	188	24	automatic	automatic	ADJ
bracis-19052	188	25	differentiation	differentiation	NOUN
bracis-19052	188	26	of	of	ADP
bracis-19052	188	27	loss	loss	NOUN
bracis-19052	188	28	functions	function	NOUN
bracis-19052	188	29	.	.	PUNCT
bracis-19052	189	1	we	we	PRON
bracis-19052	189	2	use	use	VERB
bracis-19052	189	3	a	a	DET
bracis-19052	189	4	geforce	geforce	NOUN
bracis-19052	189	5	gtx	gtx	PROPN
bracis-19052	189	6	1070	1070	NUM
bracis-19052	189	7	gpu	gpu	X
bracis-19052	189	8	to	to	PART
bracis-19052	189	9	speed	speed	VERB
bracis-19052	189	10	up	up	ADP
bracis-19052	189	11	inference	inference	NOUN
bracis-19052	189	12	,	,	PUNCT
bracis-19052	189	13	and	and	CCONJ
bracis-19052	189	14	also	also	ADV
bracis-19052	189	15	for	for	ADP
bracis-19052	189	16	calculating	calculate	VERB
bracis-19052	189	17	the	the	DET
bracis-19052	189	18	k	k	NOUN
bracis-19052	189	19	-	-	PUNCT
bracis-19052	189	20	nearest	near	ADJ
bracis-19052	189	21	neighbors	neighbor	NOUN
bracis-19052	189	22	of	of	ADP
bracis-19052	189	23	each	each	DET
bracis-19052	189	24	instance	instance	NOUN
bracis-19052	189	25	with	with	ADP
bracis-19052	189	26	the	the	DET
bracis-19052	189	27	faiss	faiss	NOUN
bracis-19052	189	28	-	-	PUNCT
bracis-19052	189	29	gpu	gpu	NOUN
bracis-19052	189	30	package	package	NOUN
bracis-19052	189	31	[	[	X
bracis-19052	189	32	7	7	NUM
bracis-19052	189	33	]	]	PUNCT
bracis-19052	189	34	.	.	PUNCT
bracis-19052	190	1	evaluation	evaluation	NOUN
bracis-19052	190	2	and	and	CCONJ
bracis-19052	190	3	baselines	baseline	NOUN
bracis-19052	190	4	.	.	PUNCT
bracis-19052	191	1	in	in	ADP
bracis-19052	191	2	this	this	DET
bracis-19052	191	3	work	work	NOUN
bracis-19052	191	4	,	,	PUNCT
bracis-19052	191	5	our	our	PRON
bracis-19052	191	6	datasets	dataset	NOUN
bracis-19052	191	7	have	have	VERB
bracis-19052	191	8	a	a	DET
bracis-19052	191	9	roughly	roughly	ADV
bracis-19052	191	10	equal	equal	ADJ
bracis-19052	191	11	number	number	NOUN
bracis-19052	191	12	of	of	ADP
bracis-19052	191	13	labels	label	NOUN
bracis-19052	191	14	for	for	ADP
bracis-19052	191	15	each	each	DET
bracis-19052	191	16	class	class	NOUN
bracis-19052	191	17	.	.	PUNCT
bracis-19052	192	1	as	as	ADP
bracis-19052	192	2	such	such	ADJ
bracis-19052	192	3	,	,	PUNCT
bracis-19052	192	4	we	we	PRON
bracis-19052	192	5	will	will	AUX
bracis-19052	192	6	report	report	VERB
bracis-19052	192	7	the	the	DET
bracis-19052	192	8	mean	mean	ADJ
bracis-19052	192	9	accuracy	accuracy	NOUN
bracis-19052	192	10	,	,	PUNCT
bracis-19052	192	11	as	as	ADV
bracis-19052	192	12	well	well	ADV
bracis-19052	192	13	as	as	ADP
bracis-19052	192	14	its	its	PRON
bracis-19052	192	15	standard	standard	ADJ
bracis-19052	192	16	deviation	deviation	NOUN
bracis-19052	192	17	.	.	PUNCT
bracis-19052	193	1	however	however	ADV
bracis-19052	193	2	,	,	PUNCT
bracis-19052	193	3	one	one	NUM
bracis-19052	193	4	distinction	distinction	NOUN
bracis-19052	193	5	is	be	AUX
bracis-19052	193	6	that	that	SCONJ
bracis-19052	193	7	we	we	PRON
bracis-19052	193	8	calculate	calculate	VERB
bracis-19052	193	9	the	the	DET
bracis-19052	193	10	accuracy	accuracy	NOUN
bracis-19052	193	11	independently	independently	ADV
bracis-19052	193	12	on	on	ADP
bracis-19052	193	13	labeled	label	VERB
bracis-19052	193	14	and	and	CCONJ
bracis-19052	193	15	unlabeled	unlabeled	ADJ
bracis-19052	193	16	data	datum	NOUN
bracis-19052	193	17	.	.	PUNCT
bracis-19052	194	1	this	this	PRON
bracis-19052	194	2	is	be	AUX
bracis-19052	194	3	done	do	VERB
bracis-19052	194	4	to	to	PART
bracis-19052	194	5	better	well	ADV
bracis-19052	194	6	assess	assess	VERB
bracis-19052	194	7	whether	whether	SCONJ
bracis-19052	194	8	our	our	PRON
bracis-19052	194	9	algorithms	algorithm	NOUN
bracis-19052	194	10	are	be	AUX
bracis-19052	194	11	improving	improve	VERB
bracis-19052	194	12	classification	classification	NOUN
bracis-19052	194	13	on	on	ADP
bracis-19052	194	14	instances	instance	NOUN
bracis-19052	194	15	outside	outside	ADP
bracis-19052	194	16	the	the	DET
bracis-19052	194	17	labeled	label	VERB
bracis-19052	194	18	set	set	NOUN
bracis-19052	194	19	,	,	PUNCT
bracis-19052	194	20	or	or	CCONJ
bracis-19052	194	21	if	if	SCONJ
bracis-19052	194	22	it	it	PRON
bracis-19052	194	23	outperforms	outperform	VERB
bracis-19052	194	24	its	its	PRON
bracis-19052	194	25	lgc	lgc	ADJ
bracis-19052	194	26	baseline	baseline	NOUN
bracis-19052	194	27	only	only	ADV
bracis-19052	194	28	when	when	SCONJ
bracis-19052	194	29	performing	perform	VERB
bracis-19052	194	30	diagnosis	diagnosis	NOUN
bracis-19052	194	31	of	of	ADP
bracis-19052	194	32	labels	label	NOUN
bracis-19052	194	33	.	.	PUNCT
bracis-19052	195	1	our	our	PRON
bracis-19052	195	2	approach	approach	NOUN
bracis-19052	195	3	,	,	PUNCT
bracis-19052	195	4	\(\texttt	\(\texttt	X
bracis-19052	195	5	{	{	PUNCT
bracis-19052	195	6	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	195	7	{	{	PUNCT
bracis-19052	195	8	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	195	9	{	{	PUNCT
bracis-19052	195	10	auto}\	auto}\	PROPN
bracis-19052	195	11	)	)	PUNCT
bracis-19052	195	12	,	,	PUNCT
bracis-19052	195	13	is	be	AUX
bracis-19052	195	14	compatible	compatible	ADJ
bracis-19052	195	15	with	with	ADP
bracis-19052	195	16	any	any	DET
bracis-19052	195	17	differentiable	differentiable	ADJ
bracis-19052	195	18	loss	loss	NOUN
bracis-19052	195	19	function	function	NOUN
bracis-19052	195	20	,	,	PUNCT
bracis-19052	195	21	such	such	ADJ
bracis-19052	195	22	as	as	ADP
bracis-19052	195	23	mean	mean	NOUN
bracis-19052	195	24	squared	square	VERB
bracis-19052	195	25	error	error	NOUN
bracis-19052	195	26	(	(	PUNCT
bracis-19052	195	27	mse	mse	NOUN
bracis-19052	195	28	)	)	PUNCT
bracis-19052	195	29	or	or	CCONJ
bracis-19052	195	30	cross	cross	NOUN
bracis-19052	195	31	-	-	NOUN
bracis-19052	195	32	entropy	entropy	ADJ
bracis-19052	195	33	(	(	PUNCT
bracis-19052	195	34	xent	xent	PROPN
bracis-19052	195	35	)	)	PUNCT
bracis-19052	195	36	.	.	PUNCT
bracis-19052	196	1	the	the	DET
bracis-19052	196	2	chosen	choose	VERB
bracis-19052	196	3	optimizer	optimizer	NOUN
bracis-19052	196	4	was	be	AUX
bracis-19052	196	5	adam	adam	PROPN
bracis-19052	196	6	,	,	PUNCT
bracis-19052	196	7	with	with	ADP
bracis-19052	196	8	a	a	DET
bracis-19052	196	9	learning	learn	VERB
bracis-19052	196	10	rate	rate	NOUN
bracis-19052	196	11	of	of	ADP
bracis-19052	196	12	0.7	0.7	NUM
bracis-19052	196	13	and	and	CCONJ
bracis-19052	196	14	5000	5000	NUM
bracis-19052	196	15	iterations	iteration	NOUN
bracis-19052	196	16	.	.	PUNCT
bracis-19052	197	1	for	for	ADP
bracis-19052	197	2	the	the	DET
bracis-19052	197	3	approximation	approximation	NOUN
bracis-19052	197	4	of	of	ADP
bracis-19052	197	5	the	the	DET
bracis-19052	197	6	propagation	propagation	NOUN
bracis-19052	197	7	matrix	matrix	NOUN
bracis-19052	197	8	in	in	ADP
bracis-19052	197	9	\(\texttt	\(\texttt	NOUN
bracis-19052	197	10	{	{	PUNCT
bracis-19052	197	11	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	197	12	{	{	PUNCT
bracis-19052	197	13	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	197	14	{	{	PUNCT
bracis-19052	197	15	autol}\	autol}\	PROPN
bracis-19052	197	16	)	)	PUNCT
bracis-19052	197	17	,	,	PUNCT
bracis-19052	197	18	we	we	PRON
bracis-19052	197	19	used	use	VERB
bracis-19052	197	20	\(t=1000\	\(t=1000\	NOUN
bracis-19052	197	21	)	)	PUNCT
bracis-19052	197	22	iterations	iteration	NOUN
bracis-19052	197	23	throughout	throughout	ADP
bracis-19052	197	24	.	.	PUNCT
bracis-19052	198	1	perhaps	perhaps	ADV
bracis-19052	198	2	the	the	DET
bracis-19052	198	3	most	most	ADV
bracis-19052	198	4	interesting	interesting	ADJ
bracis-19052	198	5	classifier	classifier	NOUN
bracis-19052	198	6	to	to	PART
bracis-19052	198	7	compare	compare	VERB
bracis-19052	198	8	our	our	PRON
bracis-19052	198	9	approach	approach	NOUN
bracis-19052	198	10	to	to	ADP
bracis-19052	198	11	is	be	AUX
bracis-19052	198	12	the	the	DET
bracis-19052	198	13	lgc	lgc	ADJ
bracis-19052	198	14	algorithm	algorithm	NOUN
bracis-19052	198	15	,	,	PUNCT
bracis-19052	198	16	as	as	SCONJ
bracis-19052	198	17	that	that	PRON
bracis-19052	198	18	is	be	AUX
bracis-19052	198	19	the	the	DET
bracis-19052	198	20	starting	starting	NOUN
bracis-19052	198	21	point	point	NOUN
bracis-19052	198	22	and	and	CCONJ
bracis-19052	198	23	the	the	DET
bracis-19052	198	24	backbone	backbone	NOUN
bracis-19052	198	25	of	of	ADP
bracis-19052	198	26	our	our	PRON
bracis-19052	198	27	own	own	ADJ
bracis-19052	198	28	approach	approach	NOUN
bracis-19052	198	29	.	.	PUNCT
bracis-19052	199	1	we	we	PRON
bracis-19052	199	2	will	will	AUX
bracis-19052	199	3	also	also	ADV
bracis-19052	199	4	be	be	AUX
bracis-19052	199	5	comparing	compare	VERB
bracis-19052	199	6	our	our	PRON
bracis-19052	199	7	results	result	NOUN
bracis-19052	199	8	with	with	ADP
bracis-19052	199	9	the	the	DET
bracis-19052	199	10	ones	one	NOUN
bracis-19052	199	11	reported	report	VERB
bracis-19052	199	12	by	by	ADP
bracis-19052	199	13	[	[	X
bracis-19052	199	14	6	6	NUM
bracis-19052	199	15	]	]	PUNCT
bracis-19052	199	16	.	.	PUNCT
bracis-19052	200	1	these	these	PRON
bracis-19052	200	2	include	include	VERB
bracis-19052	200	3	:	:	PUNCT
bracis-19052	200	4	gaussian	gaussian	ADJ
bracis-19052	200	5	fields	field	NOUN
bracis-19052	200	6	and	and	CCONJ
bracis-19052	200	7	harmonic	harmonic	ADJ
bracis-19052	200	8	functions	function	NOUN
bracis-19052	200	9	(	(	PUNCT
bracis-19052	200	10	gfhf	gfhf	NOUN
bracis-19052	200	11	)	)	PUNCT
bracis-19052	201	1	[	[	X
bracis-19052	201	2	18	18	NUM
bracis-19052	201	3	]	]	PUNCT
bracis-19052	201	4	,	,	PUNCT
bracis-19052	201	5	graph	graph	NOUN
bracis-19052	201	6	trend	trend	NOUN
bracis-19052	201	7	filtering	filter	VERB
bracis-19052	201	8	[	[	X
bracis-19052	201	9	15	15	NUM
bracis-19052	201	10	]	]	X
bracis-19052	201	11	,	,	PUNCT
bracis-19052	201	12	large	large	ADJ
bracis-19052	201	13	-	-	PUNCT
bracis-19052	201	14	scale	scale	NOUN
bracis-19052	201	15	sparse	sparse	ADJ
bracis-19052	201	16	coding	code	VERB
bracis-19052	201	17	(	(	PUNCT
bracis-19052	201	18	lssc	lssc	NOUN
bracis-19052	201	19	)	)	PUNCT
bracis-19052	202	1	[	[	X
bracis-19052	202	2	10	10	NUM
bracis-19052	202	3	]	]	PUNCT
bracis-19052	202	4	and	and	CCONJ
bracis-19052	202	5	eigenfunction	eigenfunction	VERB
bracis-19052	202	6	[	[	X
bracis-19052	202	7	5	5	NUM
bracis-19052	202	8	]	]	PUNCT
bracis-19052	202	9	.	.	PUNCT
bracis-19052	203	1	5	5	NUM
bracis-19052	203	2	results	result	VERB
bracis-19052	203	3	this	this	DET
bracis-19052	203	4	section	section	NOUN
bracis-19052	203	5	presents	present	VERB
bracis-19052	203	6	the	the	DET
bracis-19052	203	7	results	result	NOUN
bracis-19052	203	8	of	of	ADP
bracis-19052	203	9	employing	employ	VERB
bracis-19052	203	10	our	our	PRON
bracis-19052	203	11	two	two	NUM
bracis-19052	203	12	approaches	approach	NOUN
bracis-19052	203	13	\(\texttt	\(\texttt	NOUN
bracis-19052	203	14	{	{	PUNCT
bracis-19052	203	15	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	203	16	{	{	PUNCT
bracis-19052	203	17	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	203	18	{	{	PUNCT
bracis-19052	203	19	autol}\	autol}\	PROPN
bracis-19052	203	20	)	)	PUNCT
bracis-19052	203	21	and	and	CCONJ
bracis-19052	203	22	\(\texttt	\(\texttt	NOUN
bracis-19052	203	23	{	{	PUNCT
bracis-19052	203	24	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	203	25	{	{	PUNCT
bracis-19052	203	26	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	203	27	{	{	PUNCT
bracis-19052	203	28	autod}\	autod}\	PROPN
bracis-19052	203	29	)	)	PUNCT
bracis-19052	203	30	on	on	ADP
bracis-19052	203	31	isolet	isolet	NOUN
bracis-19052	203	32	and	and	CCONJ
bracis-19052	203	33	mnist	mnist	NOUN
bracis-19052	203	34	datasets	dataset	NOUN
bracis-19052	203	35	,	,	PUNCT
bracis-19052	203	36	compared	compare	VERB
bracis-19052	203	37	to	to	ADP
bracis-19052	203	38	other	other	ADJ
bracis-19052	203	39	graph	graph	NOUN
bracis-19052	203	40	-	-	PUNCT
bracis-19052	203	41	based	base	VERB
bracis-19052	203	42	ssl	ssl	ADJ
bracis-19052	203	43	algorithms	algorithm	NOUN
bracis-19052	203	44	from	from	ADP
bracis-19052	203	45	the	the	DET
bracis-19052	203	46	literature	literature	NOUN
bracis-19052	203	47	.	.	PUNCT
bracis-19052	204	1	5.1	5.1	NUM
bracis-19052	204	2	experiment	experiment	NOUN
bracis-19052	204	3	1	1	NUM
bracis-19052	204	4	:	:	SYM
bracis-19052	204	5	\(\texttt	\(\texttt	NOUN
bracis-19052	204	6	{	{	PUNCT
bracis-19052	204	7	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	204	8	{	{	PUNCT
bracis-19052	204	9	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	204	10	{	{	PUNCT
bracis-19052	204	11	autol}\	autol}\	PROPN
bracis-19052	204	12	)	)	PUNCT
bracis-19052	204	13	on	on	ADP
bracis-19052	204	14	 	 	SPACE
bracis-19052	204	15	isolet	isolet	NOUN
bracis-19052	204	16	experiment	experiment	NOUN
bracis-19052	204	17	setting	setting	NOUN
bracis-19052	204	18	.	.	PUNCT
bracis-19052	205	1	in	in	ADP
bracis-19052	205	2	this	this	DET
bracis-19052	205	3	experiment	experiment	NOUN
bracis-19052	205	4	,	,	PUNCT
bracis-19052	205	5	we	we	PRON
bracis-19052	205	6	compared	compare	VERB
bracis-19052	205	7	\(\texttt	\(\texttt	NOUN
bracis-19052	205	8	{	{	PUNCT
bracis-19052	205	9	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	205	10	{	{	PUNCT
bracis-19052	205	11	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	205	12	{	{	PUNCT
bracis-19052	205	13	autol}\	autol}\	PROPN
bracis-19052	205	14	)	)	PUNCT
bracis-19052	205	15	to	to	ADP
bracis-19052	205	16	the	the	DET
bracis-19052	205	17	baselines	baseline	NOUN
bracis-19052	205	18	reported	report	VERB
bracis-19052	205	19	in	in	ADP
bracis-19052	205	20	[	[	X
bracis-19052	205	21	6	6	NUM
bracis-19052	205	22	]	]	PUNCT
bracis-19052	205	23	,	,	PUNCT
bracis-19052	205	24	specifically	specifically	ADV
bracis-19052	205	25	for	for	ADP
bracis-19052	205	26	the	the	DET
bracis-19052	205	27	isolet	isolet	NOUN
bracis-19052	205	28	dataset	dataset	NOUN
bracis-19052	205	29	.	.	PUNCT
bracis-19052	206	1	unlike	unlike	ADP
bracis-19052	206	2	the	the	DET
bracis-19052	206	3	authors	author	NOUN
bracis-19052	206	4	,	,	PUNCT
bracis-19052	206	5	our	our	PRON
bracis-19052	206	6	20	20	NUM
bracis-19052	206	7	different	different	ADJ
bracis-19052	206	8	seeds	seed	NOUN
bracis-19052	206	9	also	also	ADV
bracis-19052	206	10	control	control	VERB
bracis-19052	206	11	both	both	CCONJ
bracis-19052	206	12	the	the	DET
bracis-19052	206	13	label	label	NOUN
bracis-19052	206	14	selection	selection	NOUN
bracis-19052	206	15	and	and	CCONJ
bracis-19052	206	16	noise	noise	NOUN
bracis-19052	206	17	processes	process	NOUN
bracis-19052	206	18	.	.	PUNCT
bracis-19052	207	1	the	the	DET
bracis-19052	207	2	graph	graph	NOUN
bracis-19052	207	3	construction	construction	NOUN
bracis-19052	207	4	was	be	AUX
bracis-19052	207	5	performed	perform	VERB
bracis-19052	207	6	exactly	exactly	ADV
bracis-19052	207	7	as	as	ADP
bracis-19052	207	8	in	in	ADP
bracis-19052	207	9	[	[	PUNCT
bracis-19052	207	10	6	6	NUM
bracis-19052	207	11	]	]	PUNCT
bracis-19052	207	12	,	,	PUNCT
bracis-19052	207	13	a	a	DET
bracis-19052	207	14	symmetric	symmetric	ADJ
bracis-19052	207	15	10	10	NUM
bracis-19052	207	16	-	-	PUNCT
bracis-19052	207	17	nearest	near	ADJ
bracis-19052	207	18	neighbors	neighbor	NOUN
bracis-19052	207	19	graph	graph	VERB
bracis-19052	207	20	with	with	ADP
bracis-19052	207	21	the	the	DET
bracis-19052	207	22	width	width	ADJ
bracis-19052	207	23	\(\sigma	\(\sigma	NOUN
bracis-19052	207	24	\	\	NOUN
bracis-19052	207	25	)	)	PUNCT
bracis-19052	207	26	of	of	ADP
bracis-19052	207	27	the	the	DET
bracis-19052	207	28	rbf	rbf	PROPN
bracis-19052	207	29	kernel	kernel	PROPN
bracis-19052	207	30	set	set	VERB
bracis-19052	207	31	to	to	ADP
bracis-19052	207	32	100	100	NUM
bracis-19052	207	33	.	.	PUNCT
bracis-19052	208	1	we	we	PRON
bracis-19052	208	2	emphasize	emphasize	VERB
bracis-19052	208	3	that	that	SCONJ
bracis-19052	208	4	the	the	DET
bracis-19052	208	5	reported	report	VERB
bracis-19052	208	6	results	result	NOUN
bracis-19052	208	7	by	by	ADP
bracis-19052	208	8	the	the	DET
bracis-19052	208	9	authors	author	NOUN
bracis-19052	208	10	correspond	correspond	VERB
bracis-19052	208	11	to	to	ADP
bracis-19052	208	12	the	the	DET
bracis-19052	208	13	best	well	ADV
bracis-19052	208	14	-	-	PUNCT
bracis-19052	208	15	performing	perform	VERB
bracis-19052	208	16	parameters	parameter	NOUN
bracis-19052	208	17	,	,	PUNCT
bracis-19052	208	18	divided	divide	VERB
bracis-19052	208	19	for	for	ADP
bracis-19052	208	20	each	each	DET
bracis-19052	208	21	individual	individual	ADJ
bracis-19052	208	22	noise	noise	NOUN
bracis-19052	208	23	level	level	NOUN
bracis-19052	208	24	.	.	PUNCT
bracis-19052	209	1	in	in	ADP
bracis-19052	209	2	[	[	X
bracis-19052	209	3	6	6	NUM
bracis-19052	209	4	]	]	PUNCT
bracis-19052	209	5	,	,	PUNCT
bracis-19052	209	6	\(\lambda	\(\lambda	PUNCT
bracis-19052	209	7	_	_	NOUN
bracis-19052	209	8	1\	1\	NUM
bracis-19052	209	9	)	)	PUNCT
bracis-19052	209	10	is	be	AUX
bracis-19052	209	11	set	set	VERB
bracis-19052	209	12	to	to	ADP
bracis-19052	209	13	\(10	\(10	ADJ
bracis-19052	209	14	^	^	NOUN
bracis-19052	209	15	5\	5\	PROPN
bracis-19052	209	16	)	)	PUNCT
bracis-19052	209	17	,	,	PUNCT
bracis-19052	209	18	\(10	\(10	NUM
bracis-19052	209	19	^	^	SYM
bracis-19052	209	20	2\	2\	NUM
bracis-19052	209	21	)	)	PUNCT
bracis-19052	209	22	,	,	PUNCT
bracis-19052	209	23	\(10	\(10	ADJ
bracis-19052	209	24	^	^	SYM
bracis-19052	209	25	2\	2\	NUM
bracis-19052	209	26	)	)	PUNCT
bracis-19052	209	27	and	and	CCONJ
bracis-19052	209	28	\(10	\(10	ADJ
bracis-19052	209	29	^	^	SYM
bracis-19052	209	30	2\	2\	NUM
bracis-19052	209	31	)	)	PUNCT
bracis-19052	209	32	for	for	ADP
bracis-19052	209	33	the	the	DET
bracis-19052	209	34	respective	respective	ADJ
bracis-19052	209	35	noise	noise	NOUN
bracis-19052	209	36	rates	rate	NOUN
bracis-19052	209	37	of	of	ADP
bracis-19052	209	38	0	0	NUM
bracis-19052	209	39	%	%	NOUN
bracis-19052	209	40	,	,	PUNCT
bracis-19052	209	41	20	20	NUM
bracis-19052	209	42	%	%	NOUN
bracis-19052	209	43	,	,	PUNCT
bracis-19052	209	44	40	40	NUM
bracis-19052	209	45	%	%	NOUN
bracis-19052	209	46	and	and	CCONJ
bracis-19052	209	47	60	60	NUM
bracis-19052	209	48	%	%	NOUN
bracis-19052	209	49	;	;	PUNCT
bracis-19052	209	50	\(\lambda	\(\lambda	PUNCT
bracis-19052	210	1	_	_	PUNCT
bracis-19052	210	2	2\	2\	X
bracis-19052	210	3	)	)	PUNCT
bracis-19052	210	4	is	be	AUX
bracis-19052	210	5	kept	keep	VERB
bracis-19052	210	6	to	to	ADP
bracis-19052	210	7	10	10	NUM
bracis-19052	210	8	,	,	PUNCT
bracis-19052	210	9	and	and	CCONJ
bracis-19052	210	10	the	the	DET
bracis-19052	210	11	number	number	NOUN
bracis-19052	210	12	of	of	ADP
bracis-19052	210	13	eigenfunctions	eigenfunction	NOUN
bracis-19052	210	14	is	be	AUX
bracis-19052	210	15	\(m=30\	\(m=30\	VERB
bracis-19052	210	16	)	)	PUNCT
bracis-19052	210	17	.	.	PUNCT
bracis-19052	211	1	we	we	PRON
bracis-19052	211	2	could	could	AUX
bracis-19052	211	3	not	not	PART
bracis-19052	211	4	find	find	VERB
bracis-19052	211	5	any	any	DET
bracis-19052	211	6	implementation	implementation	NOUN
bracis-19052	211	7	code	code	NOUN
bracis-19052	211	8	for	for	ADP
bracis-19052	211	9	siis	siis	NOUN
bracis-19052	211	10	,	,	PUNCT
bracis-19052	211	11	so	so	SCONJ
bracis-19052	211	12	we	we	PRON
bracis-19052	211	13	had	have	VERB
bracis-19052	211	14	to	to	PART
bracis-19052	211	15	manually	manually	ADV
bracis-19052	211	16	reproduce	reproduce	VERB
bracis-19052	211	17	it	it	PRON
bracis-19052	211	18	ourselves	ourselves	PRON
bracis-19052	211	19	.	.	PUNCT
bracis-19052	212	1	as	as	ADP
bracis-19052	212	2	for	for	ADP
bracis-19052	212	3	parameter	parameter	NOUN
bracis-19052	212	4	selection	selection	NOUN
bracis-19052	212	5	for	for	ADP
bracis-19052	212	6	\(\texttt	\(\texttt	NOUN
bracis-19052	212	7	{	{	PUNCT
bracis-19052	212	8	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	212	9	{	{	PUNCT
bracis-19052	212	10	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	212	11	{	{	PUNCT
bracis-19052	212	12	autol}\	autol}\	PROPN
bracis-19052	212	13	)	)	PUNCT
bracis-19052	212	14	,	,	PUNCT
bracis-19052	212	15	we	we	PRON
bracis-19052	212	16	simply	simply	ADV
bracis-19052	212	17	set	set	VERB
bracis-19052	212	18	\(\alpha	\(\alpha	NOUN
bracis-19052	212	19	=	=	SYM
bracis-19052	212	20	0.9\	0.9\	NOUN
bracis-19052	212	21	)	)	PUNCT
bracis-19052	212	22	(	(	PUNCT
bracis-19052	212	23	equivalently	equivalently	ADV
bracis-19052	212	24	,	,	PUNCT
bracis-19052	212	25	\(\mu	\(\mu	PROPN
bracis-19052	212	26	=	=	NOUN
bracis-19052	212	27	0.1111\	0.1111\	NOUN
bracis-19052	212	28	)	)	PUNCT
bracis-19052	212	29	)	)	PUNCT
bracis-19052	212	30	.	.	PUNCT
bracis-19052	213	1	we	we	PRON
bracis-19052	213	2	reiterate	reiterate	VERB
bracis-19052	213	3	that	that	SCONJ
bracis-19052	213	4	having	have	VERB
bracis-19052	213	5	a	a	DET
bracis-19052	213	6	single	single	ADJ
bracis-19052	213	7	parameter	parameter	NOUN
bracis-19052	213	8	is	be	AUX
bracis-19052	213	9	a	a	DET
bracis-19052	213	10	strength	strength	NOUN
bracis-19052	213	11	of	of	ADP
bracis-19052	213	12	our	our	PRON
bracis-19052	213	13	approach	approach	NOUN
bracis-19052	213	14	.	.	PUNCT
bracis-19052	214	1	in	in	ADP
bracis-19052	214	2	future	future	ADJ
bracis-19052	214	3	work	work	NOUN
bracis-19052	214	4	,	,	PUNCT
bracis-19052	214	5	we	we	PRON
bracis-19052	214	6	will	will	AUX
bracis-19052	214	7	try	try	VERB
bracis-19052	214	8	to	to	PART
bracis-19052	214	9	combine	combine	VERB
bracis-19052	214	10	\(\texttt	\(\texttt	NOUN
bracis-19052	214	11	{	{	PUNCT
bracis-19052	214	12	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	214	13	{	{	PUNCT
bracis-19052	214	14	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	214	15	{	{	PUNCT
bracis-19052	214	16	autol}\	autol}\	PROPN
bracis-19052	214	17	)	)	PUNCT
bracis-19052	214	18	with	with	ADP
bracis-19052	214	19	\(\texttt	\(\texttt	NOUN
bracis-19052	214	20	{	{	PUNCT
bracis-19052	214	21	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	214	22	{	{	PUNCT
bracis-19052	214	23	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	214	24	{	{	PUNCT
bracis-19052	214	25	autod}\	autod}\	PROPN
bracis-19052	214	26	)	)	PUNCT
bracis-19052	214	27	to	to	PART
bracis-19052	214	28	fully	fully	ADV
bracis-19052	214	29	eliminate	eliminate	VERB
bracis-19052	214	30	the	the	DET
bracis-19052	214	31	need	need	NOUN
bracis-19052	214	32	for	for	ADP
bracis-19052	214	33	parameter	parameter	NOUN
bracis-19052	214	34	selection	selection	NOUN
bracis-19052	214	35	.	.	PUNCT
bracis-19052	215	1	experiment	experiment	NOUN
bracis-19052	215	2	results	result	NOUN
bracis-19052	215	3	.	.	PUNCT
bracis-19052	216	1	the	the	DET
bracis-19052	216	2	results	result	NOUN
bracis-19052	216	3	are	be	AUX
bracis-19052	216	4	contained	contain	VERB
bracis-19052	216	5	in	in	ADP
bracis-19052	216	6	tables	table	NOUN
bracis-19052	216	7	1a	1a	NOUN
bracis-19052	216	8	and	and	CCONJ
bracis-19052	216	9	b.	b.	NOUN
bracis-19052	216	10	with	with	ADP
bracis-19052	216	11	respect	respect	NOUN
bracis-19052	216	12	to	to	ADP
bracis-19052	216	13	the	the	DET
bracis-19052	216	14	accuracy	accuracy	NOUN
bracis-19052	216	15	on	on	ADP
bracis-19052	216	16	unlabeled	unlabeled	ADJ
bracis-19052	216	17	examples	example	NOUN
bracis-19052	216	18	,	,	PUNCT
bracis-19052	216	19	we	we	PRON
bracis-19052	216	20	observed	observe	VERB
bracis-19052	216	21	that	that	SCONJ
bracis-19052	216	22	:	:	PUNCT
bracis-19052	216	23	siis	siis	PROPN
bracis-19052	216	24	appeared	appear	VERB
bracis-19052	216	25	to	to	PART
bracis-19052	216	26	have	have	VERB
bracis-19052	216	27	a	a	DET
bracis-19052	216	28	slight	slight	ADJ
bracis-19052	216	29	edge	edge	NOUN
bracis-19052	216	30	in	in	ADP
bracis-19052	216	31	the	the	DET
bracis-19052	216	32	noiseless	noiseless	ADJ
bracis-19052	216	33	scenario	scenario	NOUN
bracis-19052	216	34	.	.	PUNCT
bracis-19052	217	1	lgc	lgc	PROPN
bracis-19052	217	2	’s	’s	PART
bracis-19052	217	3	own	own	ADJ
bracis-19052	217	4	inherent	inherent	ADJ
bracis-19052	217	5	robustness	robustness	NOUN
bracis-19052	217	6	was	be	AUX
bracis-19052	217	7	evident	evident	ADJ
bracis-19052	217	8	.	.	PUNCT
bracis-19052	218	1	when	when	SCONJ
bracis-19052	218	2	60	60	NUM
bracis-19052	218	3	%	%	NOUN
bracis-19052	218	4	noise	noise	NOUN
bracis-19052	218	5	was	be	AUX
bracis-19052	218	6	injected	inject	VERB
bracis-19052	218	7	,	,	PUNCT
bracis-19052	218	8	it	it	PRON
bracis-19052	218	9	went	go	VERB
bracis-19052	218	10	from	from	ADP
bracis-19052	218	11	84.72	84.72	NUM
bracis-19052	218	12	to	to	ADP
bracis-19052	218	13	70.69	70.69	NUM
bracis-19052	218	14	,	,	PUNCT
bracis-19052	218	15	a	a	DET
bracis-19052	218	16	decrease	decrease	NOUN
bracis-19052	218	17	of	of	ADP
bracis-19052	218	18	\(16.55\%\	\(16.55\%\	PROPN
bracis-19052	218	19	)	)	PUNCT
bracis-19052	218	20	.	.	PUNCT
bracis-19052	219	1	in	in	ADP
bracis-19052	219	2	comparison	comparison	NOUN
bracis-19052	219	3	,	,	PUNCT
bracis-19052	219	4	siis	siis	PROPN
bracis-19052	219	5	had	have	VERB
bracis-19052	219	6	a	a	DET
bracis-19052	219	7	decrease	decrease	NOUN
bracis-19052	219	8	of	of	ADP
bracis-19052	219	9	\(14.39\%\	\(14.39\%\	PROPN
bracis-19052	219	10	)	)	PUNCT
bracis-19052	219	11	;	;	PUNCT
bracis-19052	219	12	gfhf	gfhf	VERB
bracis-19052	219	13	a	a	DET
bracis-19052	219	14	decrease	decrease	NOUN
bracis-19052	219	15	of	of	ADP
bracis-19052	219	16	\(22.08\%\	\(22.08\%\	PROPN
bracis-19052	219	17	)	)	PUNCT
bracis-19052	219	18	;	;	PUNCT
bracis-19052	219	19	gtf	gtf	PROPN
bracis-19052	219	20	a	a	DET
bracis-19052	219	21	decrease	decrease	NOUN
bracis-19052	219	22	of	of	ADP
bracis-19052	219	23	\(21.82\%\	\(21.82\%\	PROPN
bracis-19052	219	24	)	)	PUNCT
bracis-19052	219	25	.	.	PUNCT
bracis-19052	220	1	with	with	ADP
bracis-19052	220	2	\(60\%	\(60\%	PRON
bracis-19052	220	3	\	\	NOUN
bracis-19052	220	4	)	)	PUNCT
bracis-19052	220	5	noise	noise	NOUN
bracis-19052	220	6	,	,	PUNCT
bracis-19052	220	7	\(\texttt	\(\texttt	X
bracis-19052	220	8	{	{	PUNCT
bracis-19052	220	9	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	220	10	{	{	PUNCT
bracis-19052	220	11	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	220	12	{	{	PUNCT
bracis-19052	220	13	autol}\)(xent	autol}\)(xent	NOUN
bracis-19052	220	14	)	)	PUNCT
bracis-19052	220	15	decreased	decrease	VERB
bracis-19052	220	16	its	its	PRON
bracis-19052	220	17	accuracy	accuracy	NOUN
bracis-19052	220	18	by	by	ADP
bracis-19052	220	19	\(11.52\%\	\(11.52\%\	NOUN
bracis-19052	220	20	)	)	PUNCT
bracis-19052	220	21	,	,	PUNCT
bracis-19052	220	22	so	so	ADV
bracis-19052	220	23	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	220	24	{	{	PUNCT
bracis-19052	220	25	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	PROPN
bracis-19052	220	26	{	{	PUNCT
bracis-19052	220	27	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	NOUN
bracis-19052	220	28	{	{	PUNCT
bracis-19052	220	29	\mathtt{{autol}}}}}\)(xent	\mathtt{{autol}}}}}\)(xent	NOUN
bracis-19052	220	30	)	)	PUNCT
bracis-19052	220	31	had	have	VERB
bracis-19052	220	32	the	the	DET
bracis-19052	220	33	lowest	low	ADJ
bracis-19052	220	34	percentual	percentual	ADJ
bracis-19052	220	35	decrease	decrease	NOUN
bracis-19052	220	36	.	.	PUNCT
bracis-19052	221	1	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	221	2	{	{	PUNCT
bracis-19052	221	3	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	PROPN
bracis-19052	221	4	{	{	PUNCT
bracis-19052	221	5	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	NOUN
bracis-19052	221	6	{	{	PUNCT
bracis-19052	221	7	\mathtt{{autol}}}}}\)(mse	\mathtt{{autol}}}}}\)(mse	NOUN
bracis-19052	221	8	)	)	PUNCT
bracis-19052	221	9	disappointed	disappoint	VERB
bracis-19052	221	10	for	for	ADP
bracis-19052	221	11	both	both	DET
bracis-19052	221	12	labeled	label	VERB
bracis-19052	221	13	and	and	CCONJ
bracis-19052	221	14	unlabeled	unlabeled	ADJ
bracis-19052	221	15	instances	instance	NOUN
bracis-19052	221	16	.	.	PUNCT
bracis-19052	222	1	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	222	2	{	{	PUNCT
bracis-19052	222	3	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	PROPN
bracis-19052	222	4	{	{	PUNCT
bracis-19052	222	5	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	VERB
bracis-19052	222	6	{	{	PUNCT
bracis-19052	222	7	\mathtt{{autol}}}}}\	\mathtt{{autol}}}}}\	NOUN
bracis-19052	222	8	)	)	PUNCT
bracis-19052	222	9	was	be	AUX
bracis-19052	222	10	not	not	PART
bracis-19052	222	11	noticeably	noticeably	ADV
bracis-19052	222	12	superior	superior	ADJ
bracis-19052	222	13	to	to	AUX
bracis-19052	222	14	lgc	lgc	ADJ
bracis-19052	222	15	when	when	SCONJ
bracis-19052	222	16	there	there	PRON
bracis-19052	222	17	was	be	VERB
bracis-19052	222	18	less	less	ADJ
bracis-19052	222	19	than	than	ADP
bracis-19052	222	20	60	60	NUM
bracis-19052	222	21	%	%	NOUN
bracis-19052	222	22	noise	noise	NOUN
bracis-19052	222	23	.	.	PUNCT
bracis-19052	223	1	with	with	ADP
bracis-19052	223	2	respect	respect	NOUN
bracis-19052	223	3	to	to	ADP
bracis-19052	223	4	the	the	DET
bracis-19052	223	5	accuracy	accuracy	NOUN
bracis-19052	223	6	on	on	ADP
bracis-19052	223	7	unlabeled	unlabeled	ADJ
bracis-19052	223	8	examples	example	NOUN
bracis-19052	223	9	,	,	PUNCT
bracis-19052	223	10	we	we	PRON
bracis-19052	223	11	observed	observe	VERB
bracis-19052	223	12	that	that	SCONJ
bracis-19052	223	13	:	:	PUNCT
bracis-19052	223	14	lgc	lgc	ADJ
bracis-19052	223	15	was	be	AUX
bracis-19052	223	16	unable	unable	ADJ
bracis-19052	223	17	to	to	PART
bracis-19052	223	18	correct	correct	VERB
bracis-19052	223	19	noisy	noisy	ADJ
bracis-19052	223	20	labels	label	NOUN
bracis-19052	223	21	.	.	PUNCT
bracis-19052	224	1	\(\texttt	\(\texttt	NOUN
bracis-19052	224	2	{	{	PUNCT
bracis-19052	224	3	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	224	4	{	{	PUNCT
bracis-19052	224	5	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	224	6	{	{	PUNCT
bracis-19052	224	7	autol}(xent)\	autol}(xent)\	NOUN
bracis-19052	224	8	)	)	PUNCT
bracis-19052	224	9	discarded	discard	VERB
bracis-19052	224	10	only	only	ADV
bracis-19052	224	11	5	5	NUM
bracis-19052	224	12	%	%	NOUN
bracis-19052	224	13	of	of	ADP
bracis-19052	224	14	the	the	DET
bracis-19052	224	15	labels	label	NOUN
bracis-19052	224	16	for	for	ADP
bracis-19052	224	17	the	the	DET
bracis-19052	224	18	noiseless	noiseless	ADJ
bracis-19052	224	19	scenario	scenario	NOUN
bracis-19052	224	20	,	,	PUNCT
bracis-19052	224	21	which	which	PRON
bracis-19052	224	22	is	be	AUX
bracis-19052	224	23	better	well	ADJ
bracis-19052	224	24	than	than	ADP
bracis-19052	224	25	siis	siis	NOUN
bracis-19052	224	26	and	and	CCONJ
bracis-19052	224	27	lssc	lssc	NOUN
bracis-19052	224	28	.	.	PUNCT
bracis-19052	225	1	moreover	moreover	ADV
bracis-19052	225	2	,	,	PUNCT
bracis-19052	225	3	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	225	4	{	{	PUNCT
bracis-19052	225	5	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	NOUN
bracis-19052	225	6	{	{	PUNCT
bracis-19052	225	7	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	PROPN
bracis-19052	225	8	{	{	PUNCT
bracis-19052	225	9	\mathtt{{autol}}}}}(xent)\	\mathtt{{autol}}}}}(xent)\	NUM
bracis-19052	225	10	)	)	PUNCT
bracis-19052	225	11	had	have	VERB
bracis-19052	225	12	the	the	DET
bracis-19052	225	13	highest	high	ADJ
bracis-19052	225	14	average	average	ADJ
bracis-19052	225	15	accuracy	accuracy	NOUN
bracis-19052	225	16	on	on	ADP
bracis-19052	225	17	labeled	label	VERB
bracis-19052	225	18	instances	instance	NOUN
bracis-19052	225	19	for	for	ADP
bracis-19052	225	20	\(20\%,40\%,60\%\	\(20\%,40\%,60\%\	NOUN
bracis-19052	225	21	)	)	PUNCT
bracis-19052	225	22	label	label	NOUN
bracis-19052	225	23	noise	noise	NOUN
bracis-19052	225	24	.	.	PUNCT
bracis-19052	226	1	table	table	NOUN
bracis-19052	226	2	1	1	NUM
bracis-19052	226	3	.	.	PUNCT
bracis-19052	226	4	accuracy	accuracy	NOUN
bracis-19052	226	5	on	on	ADP
bracis-19052	226	6	isolet	isolet	NOUN
bracis-19052	226	7	datasetfull	datasetfull	ADJ
bracis-19052	226	8	size	size	NOUN
bracis-19052	226	9	table	table	NOUN
bracis-19052	226	10	5.2	5.2	NUM
bracis-19052	226	11	experiment	experiment	NOUN
bracis-19052	226	12	2	2	NUM
bracis-19052	226	13	:	:	SYM
bracis-19052	226	14	\(\texttt	\(\texttt	NOUN
bracis-19052	226	15	{	{	PUNCT
bracis-19052	226	16	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	226	17	{	{	PUNCT
bracis-19052	226	18	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	226	19	{	{	PUNCT
bracis-19052	226	20	autol}\	autol}\	PROPN
bracis-19052	226	21	)	)	PUNCT
bracis-19052	226	22	on	on	ADP
bracis-19052	226	23	 	 	SPACE
bracis-19052	226	24	mnist	mnist	NOUN
bracis-19052	226	25	experiment	experiment	NOUN
bracis-19052	226	26	setting	setting	NOUN
bracis-19052	226	27	.	.	PUNCT
bracis-19052	227	1	this	this	DET
bracis-19052	227	2	experiment	experiment	NOUN
bracis-19052	227	3	was	be	AUX
bracis-19052	227	4	based	base	VERB
bracis-19052	227	5	on	on	ADP
bracis-19052	227	6	[	[	X
bracis-19052	227	7	10	10	NUM
bracis-19052	227	8	]	]	PUNCT
bracis-19052	227	9	,	,	PUNCT
bracis-19052	227	10	where	where	SCONJ
bracis-19052	227	11	a	a	DET
bracis-19052	227	12	few	few	ADJ
bracis-19052	227	13	classifiers	classifier	NOUN
bracis-19052	227	14	were	be	AUX
bracis-19052	227	15	tested	test	VERB
bracis-19052	227	16	on	on	ADP
bracis-19052	227	17	the	the	DET
bracis-19052	227	18	mnist	mnist	NOUN
bracis-19052	227	19	dataset	dataset	PROPN
bracis-19052	227	20	subject	subject	ADJ
bracis-19052	227	21	to	to	ADP
bracis-19052	227	22	label	label	NOUN
bracis-19052	227	23	noise	noise	NOUN
bracis-19052	227	24	.	.	PUNCT
bracis-19052	228	1	in	in	ADP
bracis-19052	228	2	that	that	DET
bracis-19052	228	3	paper	paper	NOUN
bracis-19052	228	4	,	,	PUNCT
bracis-19052	228	5	the	the	DET
bracis-19052	228	6	parameters	parameter	NOUN
bracis-19052	228	7	for	for	ADP
bracis-19052	228	8	the	the	DET
bracis-19052	228	9	graph	graph	NOUN
bracis-19052	228	10	were	be	AUX
bracis-19052	228	11	tuned	tune	VERB
bracis-19052	228	12	to	to	PART
bracis-19052	228	13	minimize	minimize	VERB
bracis-19052	228	14	cross	cross	ADJ
bracis-19052	228	15	-	-	ADJ
bracis-19052	228	16	validation	validation	ADJ
bracis-19052	228	17	errors	error	NOUN
bracis-19052	228	18	.	.	PUNCT
bracis-19052	229	1	moreover	moreover	ADV
bracis-19052	229	2	,	,	PUNCT
bracis-19052	229	3	an	an	DET
bracis-19052	229	4	anchor	anchor	NOUN
bracis-19052	229	5	graph	graph	NOUN
bracis-19052	229	6	was	be	AUX
bracis-19052	229	7	used	use	VERB
bracis-19052	229	8	,	,	PUNCT
bracis-19052	229	9	which	which	PRON
bracis-19052	229	10	is	be	AUX
bracis-19052	229	11	a	a	DET
bracis-19052	229	12	large	large	ADJ
bracis-19052	229	13	-	-	PUNCT
bracis-19052	229	14	scale	scale	NOUN
bracis-19052	229	15	solution	solution	NOUN
bracis-19052	229	16	.	.	PUNCT
bracis-19052	230	1	we	we	PRON
bracis-19052	230	2	did	do	AUX
bracis-19052	230	3	not	not	PART
bracis-19052	230	4	use	use	VERB
bracis-19052	230	5	such	such	DET
bracis-19052	230	6	a	a	DET
bracis-19052	230	7	graph	graph	NOUN
bracis-19052	230	8	,	,	PUNCT
bracis-19052	230	9	as	as	SCONJ
bracis-19052	230	10	our	our	PRON
bracis-19052	230	11	tensorflow	tensorflow	NOUN
bracis-19052	230	12	iterative	iterative	NOUN
bracis-19052	230	13	implementation	implementation	NOUN
bracis-19052	230	14	of	of	ADP
bracis-19052	230	15	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	230	16	{	{	PUNCT
bracis-19052	230	17	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	PROPN
bracis-19052	230	18	{	{	PUNCT
bracis-19052	230	19	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	VERB
bracis-19052	230	20	{	{	PUNCT
bracis-19052	230	21	\mathtt{{autol}}}}}\	\mathtt{{autol}}}}}\	PROPN
bracis-19052	230	22	)	)	PUNCT
bracis-19052	230	23	was	be	AUX
bracis-19052	230	24	efficient	efficient	ADJ
bracis-19052	230	25	enough	enough	ADV
bracis-19052	230	26	to	to	PART
bracis-19052	230	27	perform	perform	VERB
bracis-19052	230	28	classification	classification	NOUN
bracis-19052	230	29	on	on	ADP
bracis-19052	230	30	mnist	mnist	NOUN
bracis-19052	230	31	in	in	ADP
bracis-19052	230	32	just	just	ADV
bracis-19052	230	33	a	a	DET
bracis-19052	230	34	few	few	ADJ
bracis-19052	230	35	seconds	second	NOUN
bracis-19052	230	36	.	.	PUNCT
bracis-19052	231	1	as	as	SCONJ
bracis-19052	231	2	we	we	PRON
bracis-19052	231	3	also	also	ADV
bracis-19052	231	4	included	include	VERB
bracis-19052	231	5	the	the	DET
bracis-19052	231	6	results	result	NOUN
bracis-19052	231	7	for	for	ADP
bracis-19052	231	8	lgc	lgc	ADJ
bracis-19052	231	9	(	(	PUNCT
bracis-19052	231	10	without	without	ADP
bracis-19052	231	11	anchor	anchor	NOUN
bracis-19052	231	12	graph	graph	NOUN
bracis-19052	231	13	)	)	PUNCT
bracis-19052	231	14	,	,	PUNCT
bracis-19052	231	15	it	it	PRON
bracis-19052	231	16	is	be	AUX
bracis-19052	231	17	interesting	interesting	ADJ
bracis-19052	231	18	to	to	PART
bracis-19052	231	19	observe	observe	VERB
bracis-19052	231	20	that	that	SCONJ
bracis-19052	231	21	its	its	PRON
bracis-19052	231	22	accuracy	accuracy	NOUN
bracis-19052	231	23	decreases	decrease	VERB
bracis-19052	231	24	similarly	similarly	ADV
bracis-19052	231	25	to	to	ADP
bracis-19052	231	26	the	the	DET
bracis-19052	231	27	previously	previously	ADV
bracis-19052	231	28	reported	report	VERB
bracis-19052	231	29	results	result	NOUN
bracis-19052	231	30	:	:	PUNCT
bracis-19052	231	31	the	the	DET
bracis-19052	231	32	main	main	ADJ
bracis-19052	231	33	difference	difference	NOUN
bracis-19052	231	34	is	be	AUX
bracis-19052	231	35	better	well	ADJ
bracis-19052	231	36	performance	performance	NOUN
bracis-19052	231	37	for	for	ADP
bracis-19052	231	38	the	the	DET
bracis-19052	231	39	noiseless	noiseless	ADJ
bracis-19052	231	40	scenario	scenario	NOUN
bracis-19052	231	41	,	,	PUNCT
bracis-19052	231	42	which	which	PRON
bracis-19052	231	43	is	be	AUX
bracis-19052	231	44	to	to	PART
bracis-19052	231	45	be	be	AUX
bracis-19052	231	46	expected	expect	VERB
bracis-19052	231	47	(	(	PUNCT
bracis-19052	231	48	the	the	DET
bracis-19052	231	49	anchor	anchor	NOUN
bracis-19052	231	50	graph	graph	NOUN
bracis-19052	231	51	is	be	AUX
bracis-19052	231	52	an	an	DET
bracis-19052	231	53	approximation	approximation	NOUN
bracis-19052	231	54	)	)	PUNCT
bracis-19052	231	55	.	.	PUNCT
bracis-19052	232	1	once	once	ADV
bracis-19052	232	2	again	again	ADV
bracis-19052	232	3	,	,	PUNCT
bracis-19052	232	4	we	we	PRON
bracis-19052	232	5	simply	simply	ADV
bracis-19052	232	6	set	set	VERB
bracis-19052	232	7	\(\alpha	\(\alpha	NOUN
bracis-19052	232	8	=	=	NOUN
bracis-19052	232	9	0.9\	0.9\	NOUN
bracis-19052	232	10	)	)	PUNCT
bracis-19052	232	11	for	for	ADP
bracis-19052	232	12	\(\texttt	\(\texttt	NOUN
bracis-19052	232	13	{	{	PUNCT
bracis-19052	232	14	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	232	15	{	{	PUNCT
bracis-19052	232	16	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	232	17	{	{	PUNCT
bracis-19052	232	18	autol}\	autol}\	PROPN
bracis-19052	232	19	)	)	PUNCT
bracis-19052	232	20	.	.	PUNCT
bracis-19052	233	1	we	we	PRON
bracis-19052	233	2	used	use	VERB
bracis-19052	233	3	a	a	DET
bracis-19052	233	4	symknn	symknn	NOUN
bracis-19052	233	5	matrix	matrix	NOUN
bracis-19052	233	6	with	with	ADP
bracis-19052	233	7	\(k=15\	\(k=15\	NOUN
bracis-19052	233	8	)	)	PUNCT
bracis-19052	233	9	neighbors	neighbor	NOUN
bracis-19052	233	10	,	,	PUNCT
bracis-19052	233	11	and	and	CCONJ
bracis-19052	233	12	a	a	DET
bracis-19052	233	13	heuristic	heuristic	ADJ
bracis-19052	233	14	sigma	sigma	NOUN
bracis-19052	233	15	\(\sigma	\(\sigma	NOUN
bracis-19052	233	16	=	=	SYM
bracis-19052	233	17	423.57\	423.57\	NOUN
bracis-19052	233	18	)	)	PUNCT
bracis-19052	233	19	obtained	obtain	VERB
bracis-19052	233	20	by	by	ADP
bracis-19052	233	21	taking	take	VERB
bracis-19052	233	22	one	one	NUM
bracis-19052	233	23	-	-	PUNCT
bracis-19052	233	24	third	third	NOUN
bracis-19052	233	25	of	of	ADP
bracis-19052	233	26	the	the	DET
bracis-19052	233	27	mean	mean	ADJ
bracis-19052	233	28	distance	distance	NOUN
bracis-19052	233	29	to	to	ADP
bracis-19052	233	30	the	the	DET
bracis-19052	233	31	10th	10th	ADJ
bracis-19052	233	32	neighbor	neighbor	NOUN
bracis-19052	233	33	(	(	PUNCT
bracis-19052	233	34	as	as	ADP
bracis-19052	233	35	in	in	ADP
bracis-19052	233	36	[	[	X
bracis-19052	233	37	3	3	NUM
bracis-19052	233	38	]	]	NUM
bracis-19052	233	39	)	)	PUNCT
bracis-19052	233	40	.	.	PUNCT
bracis-19052	234	1	table	table	NOUN
bracis-19052	234	2	2	2	NUM
bracis-19052	234	3	.	.	PUNCT
bracis-19052	234	4	accuracy	accuracy	NOUN
bracis-19052	234	5	on	on	ADP
bracis-19052	234	6	mnist	mnist	NOUN
bracis-19052	234	7	datasetfull	datasetfull	ADJ
bracis-19052	234	8	size	size	NOUN
bracis-19052	234	9	table	table	NOUN
bracis-19052	234	10	experiment	experiment	NOUN
bracis-19052	234	11	results	result	NOUN
bracis-19052	234	12	.	.	PUNCT
bracis-19052	235	1	the	the	DET
bracis-19052	235	2	results	result	NOUN
bracis-19052	235	3	are	be	AUX
bracis-19052	235	4	found	find	VERB
bracis-19052	235	5	in	in	ADP
bracis-19052	235	6	tables	table	NOUN
bracis-19052	235	7	 	 	SPACE
bracis-19052	235	8	2a	2a	NUM
bracis-19052	235	9	and	and	CCONJ
bracis-19052	235	10	b.	b.	NOUN
bracis-19052	235	11	with	with	ADP
bracis-19052	235	12	respect	respect	NOUN
bracis-19052	235	13	to	to	ADP
bracis-19052	235	14	the	the	DET
bracis-19052	235	15	accuracy	accuracy	NOUN
bracis-19052	235	16	on	on	ADP
bracis-19052	235	17	unlabeled	unlabeled	ADJ
bracis-19052	235	18	examples	example	NOUN
bracis-19052	235	19	,	,	PUNCT
bracis-19052	235	20	we	we	PRON
bracis-19052	235	21	observed	observe	VERB
bracis-19052	235	22	that	that	SCONJ
bracis-19052	235	23	:	:	PUNCT
bracis-19052	235	24	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	235	25	{	{	PUNCT
bracis-19052	235	26	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	PROPN
bracis-19052	235	27	{	{	PUNCT
bracis-19052	235	28	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	VERB
bracis-19052	235	29	{	{	PUNCT
bracis-19052	235	30	\mathtt{{autol}}}}}\	\mathtt{{autol}}}}}\	NOUN
bracis-19052	235	31	)	)	PUNCT
bracis-19052	235	32	with	with	ADP
bracis-19052	235	33	cross	cross	NOUN
bracis-19052	235	34	-	-	ADJ
bracis-19052	235	35	entropy	entropy	NOUN
bracis-19052	235	36	improved	improve	VERB
bracis-19052	235	37	the	the	DET
bracis-19052	235	38	lgc	lgc	ADJ
bracis-19052	235	39	baseline	baseline	NOUN
bracis-19052	235	40	significantly	significantly	ADV
bracis-19052	235	41	on	on	ADP
bracis-19052	235	42	unlabeled	unlabeled	ADJ
bracis-19052	235	43	instances	instance	NOUN
bracis-19052	235	44	.	.	PUNCT
bracis-19052	236	1	for	for	ADP
bracis-19052	236	2	30	30	NUM
bracis-19052	236	3	%	%	NOUN
bracis-19052	236	4	label	label	NOUN
bracis-19052	236	5	noise	noise	NOUN
bracis-19052	236	6	,	,	PUNCT
bracis-19052	236	7	mean	mean	ADJ
bracis-19052	236	8	accuracy	accuracy	NOUN
bracis-19052	236	9	increases	increase	VERB
bracis-19052	236	10	from	from	ADP
bracis-19052	236	11	74.58	74.58	NUM
bracis-19052	236	12	%	%	NOUN
bracis-19052	236	13	to	to	ADP
bracis-19052	236	14	84.46	84.46	NUM
bracis-19052	236	15	%	%	NOUN
bracis-19052	236	16	.	.	PUNCT
bracis-19052	237	1	the	the	DET
bracis-19052	237	2	mean	mean	ADJ
bracis-19052	237	3	squared	square	VERB
bracis-19052	237	4	error	error	NOUN
bracis-19052	237	5	loss	loss	NOUN
bracis-19052	237	6	is	be	AUX
bracis-19052	237	7	once	once	ADV
bracis-19052	237	8	again	again	ADV
bracis-19052	237	9	consistently	consistently	ADV
bracis-19052	237	10	inferior	inferior	ADJ
bracis-19052	237	11	to	to	ADP
bracis-19052	237	12	cross	cross	VERB
bracis-19052	237	13	-	-	NOUN
bracis-19052	237	14	entropy	entropy	ADJ
bracis-19052	237	15	when	when	SCONJ
bracis-19052	237	16	there	there	PRON
bracis-19052	237	17	is	be	VERB
bracis-19052	237	18	noise	noise	NOUN
bracis-19052	237	19	.	.	PUNCT
bracis-19052	238	1	\(\texttt	\(\texttt	NOUN
bracis-19052	238	2	{	{	PUNCT
bracis-19052	238	3	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	238	4	{	{	PUNCT
bracis-19052	238	5	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	238	6	{	{	PUNCT
bracis-19052	238	7	autol}\	autol}\	PROPN
bracis-19052	238	8	)	)	PUNCT
bracis-19052	238	9	was	be	AUX
bracis-19052	238	10	not	not	PART
bracis-19052	238	11	able	able	ADJ
bracis-19052	238	12	to	to	PART
bracis-19052	238	13	obtain	obtain	VERB
bracis-19052	238	14	better	well	ADJ
bracis-19052	238	15	results	result	NOUN
bracis-19052	238	16	than	than	ADP
bracis-19052	238	17	lssc	lssc	NOUN
bracis-19052	238	18	.	.	PUNCT
bracis-19052	239	1	with	with	ADP
bracis-19052	239	2	respect	respect	NOUN
bracis-19052	239	3	to	to	ADP
bracis-19052	239	4	the	the	DET
bracis-19052	239	5	accuracy	accuracy	NOUN
bracis-19052	239	6	on	on	ADP
bracis-19052	239	7	labeled	label	VERB
bracis-19052	239	8	examples	example	NOUN
bracis-19052	239	9	,	,	PUNCT
bracis-19052	239	10	we	we	PRON
bracis-19052	239	11	observed	observe	VERB
bracis-19052	239	12	that	that	SCONJ
bracis-19052	239	13	:	:	PUNCT
bracis-19052	239	14	lgc	lgc	ADJ
bracis-19052	239	15	was	be	AUX
bracis-19052	239	16	not	not	PART
bracis-19052	239	17	able	able	ADJ
bracis-19052	239	18	to	to	PART
bracis-19052	239	19	correct	correct	VERB
bracis-19052	239	20	the	the	DET
bracis-19052	239	21	labeled	label	VERB
bracis-19052	239	22	instances	instance	NOUN
bracis-19052	239	23	.	.	PUNCT
bracis-19052	240	1	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	240	2	{	{	PUNCT
bracis-19052	240	3	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	PROPN
bracis-19052	240	4	{	{	PUNCT
bracis-19052	240	5	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	VERB
bracis-19052	240	6	{	{	PUNCT
bracis-19052	240	7	\mathtt{{autol}}}}}\	\mathtt{{autol}}}}}\	NOUN
bracis-19052	240	8	)	)	PUNCT
bracis-19052	240	9	with	with	ADP
bracis-19052	240	10	cross	cross	NOUN
bracis-19052	240	11	-	-	ADJ
bracis-19052	240	12	entropy	entropy	NOUN
bracis-19052	240	13	improved	improve	VERB
bracis-19052	240	14	the	the	DET
bracis-19052	240	15	lgc	lgc	ADJ
bracis-19052	240	16	baseline	baseline	NOUN
bracis-19052	240	17	significantly	significantly	ADV
bracis-19052	240	18	on	on	ADP
bracis-19052	240	19	labeled	label	VERB
bracis-19052	240	20	instances	instance	NOUN
bracis-19052	240	21	.	.	PUNCT
bracis-19052	241	1	with	with	ADP
bracis-19052	241	2	30	30	NUM
bracis-19052	241	3	%	%	NOUN
bracis-19052	241	4	noise	noise	NOUN
bracis-19052	241	5	,	,	PUNCT
bracis-19052	241	6	accuracy	accuracy	NOUN
bracis-19052	241	7	goes	go	VERB
bracis-19052	241	8	from	from	ADP
bracis-19052	241	9	70.00	70.00	NUM
bracis-19052	241	10	%	%	NOUN
bracis-19052	241	11	to	to	ADP
bracis-19052	241	12	89.75	89.75	NUM
bracis-19052	241	13	%	%	NOUN
bracis-19052	241	14	.	.	PUNCT
bracis-19052	242	1	5.3	5.3	NUM
bracis-19052	242	2	experiment	experiment	NOUN
bracis-19052	242	3	3	3	NUM
bracis-19052	242	4	:	:	SYM
bracis-19052	242	5	\(\texttt	\(\texttt	NOUN
bracis-19052	242	6	{	{	PUNCT
bracis-19052	242	7	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	242	8	{	{	PUNCT
bracis-19052	242	9	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	242	10	{	{	PUNCT
bracis-19052	242	11	autod}\	autod}\	PROPN
bracis-19052	242	12	)	)	PUNCT
bracis-19052	242	13	on	on	ADP
bracis-19052	242	14	 	 	SPACE
bracis-19052	242	15	mnist	mnist	NOUN
bracis-19052	242	16	experiment	experiment	NOUN
bracis-19052	242	17	settings	setting	NOUN
bracis-19052	242	18	were	be	AUX
bracis-19052	242	19	kept	keep	VERB
bracis-19052	242	20	the	the	DET
bracis-19052	242	21	same	same	ADJ
bracis-19052	242	22	as	as	ADP
bracis-19052	242	23	experiment	experiment	NOUN
bracis-19052	242	24	2	2	NUM
bracis-19052	242	25	(	(	PUNCT
bracis-19052	242	26	without	without	ADP
bracis-19052	242	27	noise	noise	NOUN
bracis-19052	242	28	)	)	PUNCT
bracis-19052	242	29	,	,	PUNCT
bracis-19052	242	30	and	and	CCONJ
bracis-19052	242	31	\(p	\(p	X
bracis-19052	242	32	=	=	SYM
bracis-19052	242	33	300\	300\	NUM
bracis-19052	242	34	)	)	PUNCT
bracis-19052	242	35	eigenfunctions	eigenfunction	NOUN
bracis-19052	242	36	were	be	AUX
bracis-19052	242	37	extracted	extract	VERB
bracis-19052	242	38	.	.	PUNCT
bracis-19052	243	1	in	in	ADP
bracis-19052	243	2	fig	fig	NOUN
bracis-19052	243	3	.	.	PUNCT
bracis-19052	243	4	 	 	SPACE
bracis-19052	243	5	2	2	NUM
bracis-19052	243	6	,	,	PUNCT
bracis-19052	243	7	we	we	PRON
bracis-19052	243	8	show	show	VERB
bracis-19052	243	9	accuracy	accuracy	NOUN
bracis-19052	243	10	on	on	ADP
bracis-19052	243	11	the	the	DET
bracis-19052	243	12	labeled	label	VERB
bracis-19052	243	13	set	set	NOUN
bracis-19052	243	14	as	as	ADP
bracis-19052	243	15	red	red	ADJ
bracis-19052	243	16	,	,	PUNCT
bracis-19052	243	17	and	and	CCONJ
bracis-19052	243	18	on	on	ADP
bracis-19052	243	19	the	the	DET
bracis-19052	243	20	unlabeled	unlabele	VERB
bracis-19052	243	21	set	set	VERB
bracis-19052	243	22	as	as	ADP
bracis-19052	243	23	purple	purple	ADJ
bracis-19052	243	24	.	.	PUNCT
bracis-19052	244	1	the	the	DET
bracis-19052	244	2	x	x	ADJ
bracis-19052	244	3	values	value	NOUN
bracis-19052	244	4	on	on	ADP
bracis-19052	244	5	the	the	DET
bracis-19052	244	6	horizontal	horizontal	ADJ
bracis-19052	244	7	axis	axis	NOUN
bracis-19052	244	8	relate	relate	VERB
bracis-19052	244	9	to	to	ADP
bracis-19052	244	10	\(\alpha	\(\alpha	PROPN
bracis-19052	244	11	\	\	NOUN
bracis-19052	244	12	)	)	PUNCT
bracis-19052	244	13	as	as	ADP
bracis-19052	244	14	following	follow	VERB
bracis-19052	244	15	:	:	PUNCT
bracis-19052	244	16	\(\alpha	\(\alpha	NOUN
bracis-19052	244	17	=	=	SYM
bracis-19052	244	18	2^{-1	2^{-1	NUM
bracis-19052	244	19	/	/	SYM
bracis-19052	244	20	x}\	x}\	PROPN
bracis-19052	244	21	)	)	PUNCT
bracis-19052	244	22	.	.	PUNCT
bracis-19052	245	1	looking	look	VERB
bracis-19052	245	2	at	at	ADP
bracis-19052	245	3	fig	fig	NOUN
bracis-19052	245	4	.	.	PUNCT
bracis-19052	245	5	 	 	SPACE
bracis-19052	246	1	2b	2b	NOUN
bracis-19052	246	2	,	,	PUNCT
bracis-19052	246	3	we	we	PRON
bracis-19052	246	4	can	can	AUX
bracis-19052	246	5	see	see	VERB
bracis-19052	246	6	that	that	SCONJ
bracis-19052	246	7	,	,	PUNCT
bracis-19052	246	8	if	if	SCONJ
bracis-19052	246	9	we	we	PRON
bracis-19052	246	10	do	do	AUX
bracis-19052	246	11	not	not	PART
bracis-19052	246	12	remove	remove	VERB
bracis-19052	246	13	the	the	DET
bracis-19052	246	14	diagonal	diagonal	ADJ
bracis-19052	246	15	,	,	PUNCT
bracis-19052	246	16	there	there	PRON
bracis-19052	246	17	is	be	VERB
bracis-19052	246	18	much	much	ADV
bracis-19052	246	19	overfitting	overfitting	NOUN
bracis-19052	246	20	and	and	CCONJ
bracis-19052	246	21	the	the	DET
bracis-19052	246	22	losses	loss	NOUN
bracis-19052	246	23	reach	reach	VERB
bracis-19052	246	24	their	their	PRON
bracis-19052	246	25	minimum	minimum	ADJ
bracis-19052	246	26	value	value	NOUN
bracis-19052	246	27	much	much	ADV
bracis-19052	246	28	earlier	early	ADV
bracis-19052	246	29	than	than	SCONJ
bracis-19052	246	30	does	do	VERB
bracis-19052	246	31	the	the	DET
bracis-19052	246	32	accuracy	accuracy	NOUN
bracis-19052	246	33	on	on	ADP
bracis-19052	246	34	unlabeled	unlabeled	ADJ
bracis-19052	246	35	examples	example	NOUN
bracis-19052	246	36	.	.	PUNCT
bracis-19052	247	1	when	when	SCONJ
bracis-19052	247	2	the	the	DET
bracis-19052	247	3	diagonal	diagonal	ADJ
bracis-19052	247	4	is	be	AUX
bracis-19052	247	5	removed	remove	VERB
bracis-19052	247	6	,	,	PUNCT
bracis-19052	247	7	the	the	DET
bracis-19052	247	8	loss	loss	NOUN
bracis-19052	247	9	-	-	PUNCT
bracis-19052	247	10	minimizing	minimize	VERB
bracis-19052	247	11	estimates	estimate	NOUN
bracis-19052	247	12	for	for	ADP
bracis-19052	247	13	\(\alpha	\(\alpha	NOUN
bracis-19052	247	14	\	\	NOUN
bracis-19052	247	15	)	)	PUNCT
bracis-19052	247	16	get	get	VERB
bracis-19052	247	17	much	much	ADV
bracis-19052	247	18	closer	close	ADJ
bracis-19052	247	19	to	to	ADP
bracis-19052	247	20	the	the	DET
bracis-19052	247	21	optimal	optimal	ADJ
bracis-19052	247	22	one	one	NOUN
bracis-19052	247	23	(	(	PUNCT
bracis-19052	247	24	fig	fig	NOUN
bracis-19052	247	25	.	.	PUNCT
bracis-19052	247	26	 	 	SPACE
bracis-19052	247	27	2a	2a	NUM
bracis-19052	247	28	)	)	PUNCT
bracis-19052	247	29	.	.	PUNCT
bracis-19052	248	1	moreover	moreover	ADV
bracis-19052	248	2	,	,	PUNCT
bracis-19052	248	3	by	by	ADP
bracis-19052	248	4	removing	remove	VERB
bracis-19052	248	5	the	the	DET
bracis-19052	248	6	diagonal	diagonal	ADJ
bracis-19052	248	7	we	we	PRON
bracis-19052	248	8	obtain	obtain	VERB
bracis-19052	248	9	a	a	DET
bracis-19052	248	10	much	much	ADV
bracis-19052	248	11	better	well	ADJ
bracis-19052	248	12	estimation	estimation	NOUN
bracis-19052	248	13	of	of	ADP
bracis-19052	248	14	the	the	DET
bracis-19052	248	15	accuracy	accuracy	NOUN
bracis-19052	248	16	on	on	ADP
bracis-19052	248	17	unlabeled	unlabeled	ADJ
bracis-19052	248	18	data	datum	NOUN
bracis-19052	248	19	.	.	PUNCT
bracis-19052	249	1	therefore	therefore	ADV
bracis-19052	249	2	,	,	PUNCT
bracis-19052	249	3	we	we	PRON
bracis-19052	249	4	can	can	AUX
bracis-19052	249	5	simply	simply	ADV
bracis-19052	249	6	select	select	VERB
bracis-19052	249	7	the	the	DET
bracis-19052	249	8	\(\alpha	\(\alpha	NOUN
bracis-19052	249	9	\	\	NOUN
bracis-19052	249	10	)	)	PUNCT
bracis-19052	249	11	corresponding	correspond	VERB
bracis-19052	249	12	to	to	ADP
bracis-19052	249	13	the	the	DET
bracis-19052	249	14	best	good	ADJ
bracis-19052	249	15	accuracy	accuracy	NOUN
bracis-19052	249	16	on	on	ADP
bracis-19052	249	17	known	know	VERB
bracis-19052	249	18	labels	label	NOUN
bracis-19052	249	19	.	.	PUNCT
bracis-19052	250	1	fig	fig	NOUN
bracis-19052	250	2	.	.	PUNCT
bracis-19052	251	1	2	2	NUM
bracis-19052	251	2	.	.	NUM
bracis-19052	251	3	\(\texttt	\(\texttt	NOUN
bracis-19052	251	4	{	{	PUNCT
bracis-19052	251	5	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	251	6	{	{	PUNCT
bracis-19052	251	7	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	251	8	{	{	PUNCT
bracis-19052	251	9	autod}\	autod}\	PROPN
bracis-19052	251	10	)	)	PUNCT
bracis-19052	251	11	on	on	ADP
bracis-19052	251	12	mnist	mnist	NOUN
bracis-19052	251	13	.	.	PUNCT
bracis-19052	252	1	the	the	DET
bracis-19052	252	2	x	x	ADJ
bracis-19052	252	3	coordinate	coordinate	NOUN
bracis-19052	252	4	on	on	ADP
bracis-19052	252	5	the	the	DET
bracis-19052	252	6	horizontal	horizontal	ADJ
bracis-19052	252	7	axis	axis	NOUN
bracis-19052	252	8	determines	determine	VERB
bracis-19052	252	9	diffusion	diffusion	NOUN
bracis-19052	252	10	rate	rate	NOUN
bracis-19052	252	11	\(\alpha	\(\alpha	NOUN
bracis-19052	252	12	=	=	SYM
bracis-19052	252	13	2^{-1	2^{-1	NUM
bracis-19052	252	14	/	/	SYM
bracis-19052	252	15	x}\	x}\	PROPN
bracis-19052	252	16	)	)	PUNCT
bracis-19052	252	17	for	for	ADP
bracis-19052	252	18	\(x\ge	\(x\ge	PROPN
bracis-19052	252	19	1\	1\	NUM
bracis-19052	252	20	)	)	PUNCT
bracis-19052	252	21	.	.	PUNCT
bracis-19052	253	1	the	the	DET
bracis-19052	253	2	orange	orange	ADJ
bracis-19052	253	3	,	,	PUNCT
bracis-19052	253	4	blue	blue	ADJ
bracis-19052	253	5	and	and	CCONJ
bracis-19052	253	6	green	green	ADJ
bracis-19052	253	7	curves	curve	NOUN
bracis-19052	253	8	represent	represent	VERB
bracis-19052	253	9	the	the	DET
bracis-19052	253	10	surrogate	surrogate	ADJ
bracis-19052	253	11	losses	loss	NOUN
bracis-19052	253	12	:	:	PUNCT
bracis-19052	253	13	mean	mean	VERB
bracis-19052	253	14	absolute	absolute	ADJ
bracis-19052	253	15	error	error	NOUN
bracis-19052	253	16	,	,	PUNCT
bracis-19052	253	17	mean	mean	NOUN
bracis-19052	253	18	squared	square	VERB
bracis-19052	253	19	error	error	NOUN
bracis-19052	253	20	,	,	PUNCT
bracis-19052	253	21	cross	cross	NOUN
bracis-19052	253	22	-	-	NOUN
bracis-19052	253	23	entropy	entropy	NOUN
bracis-19052	253	24	.	.	PUNCT
bracis-19052	254	1	moreover	moreover	ADV
bracis-19052	254	2	,	,	PUNCT
bracis-19052	254	3	the	the	DET
bracis-19052	254	4	accuracy	accuracy	NOUN
bracis-19052	254	5	on	on	ADP
bracis-19052	254	6	the	the	DET
bracis-19052	254	7	known	know	VERB
bracis-19052	254	8	labeled	label	VERB
bracis-19052	254	9	data	datum	NOUN
bracis-19052	254	10	is	be	AUX
bracis-19052	254	11	shown	show	VERB
bracis-19052	254	12	in	in	ADP
bracis-19052	254	13	red	red	ADJ
bracis-19052	254	14	,	,	PUNCT
bracis-19052	254	15	and	and	CCONJ
bracis-19052	254	16	the	the	DET
bracis-19052	254	17	accuracy	accuracy	NOUN
bracis-19052	254	18	on	on	ADP
bracis-19052	254	19	unlabeled	unlabeled	ADJ
bracis-19052	254	20	data	datum	NOUN
bracis-19052	254	21	in	in	ADP
bracis-19052	254	22	purple	purple	NOUN
bracis-19052	254	23	.	.	PUNCT
bracis-19052	255	1	(	(	PUNCT
bracis-19052	255	2	color	color	NOUN
bracis-19052	255	3	figure	figure	NOUN
bracis-19052	255	4	online	online	ADV
bracis-19052	255	5	)	)	PUNCT
bracis-19052	255	6	full	full	ADJ
bracis-19052	255	7	size	size	NOUN
bracis-19052	255	8	image	image	NOUN
bracis-19052	255	9	6	6	NUM
bracis-19052	255	10	concluding	conclude	VERB
bracis-19052	255	11	remarks	remark	NOUN
bracis-19052	255	12	we	we	PRON
bracis-19052	255	13	have	have	AUX
bracis-19052	255	14	proposed	propose	VERB
bracis-19052	255	15	the	the	DET
bracis-19052	255	16	\(\texttt	\(\texttt	NOUN
bracis-19052	255	17	{	{	PUNCT
bracis-19052	255	18	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	255	19	{	{	PUNCT
bracis-19052	255	20	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	255	21	{	{	PUNCT
bracis-19052	255	22	auto}\	auto}\	PROPN
bracis-19052	255	23	)	)	PUNCT
bracis-19052	255	24	framework	framework	NOUN
bracis-19052	255	25	,	,	PUNCT
bracis-19052	255	26	based	base	VERB
bracis-19052	255	27	on	on	ADP
bracis-19052	255	28	leave	leave	VERB
bracis-19052	255	29	-	-	PUNCT
bracis-19052	255	30	one	one	NUM
bracis-19052	255	31	-	-	PUNCT
bracis-19052	255	32	out	out	ADP
bracis-19052	255	33	validation	validation	NOUN
bracis-19052	255	34	of	of	ADP
bracis-19052	255	35	the	the	DET
bracis-19052	255	36	lgc	lgc	ADJ
bracis-19052	255	37	algorithm	algorithm	NOUN
bracis-19052	255	38	.	.	PUNCT
bracis-19052	256	1	this	this	PRON
bracis-19052	256	2	encompasses	encompass	VERB
bracis-19052	256	3	two	two	NUM
bracis-19052	256	4	methods	method	NOUN
bracis-19052	256	5	,	,	PUNCT
bracis-19052	256	6	\(\texttt	\(\texttt	X
bracis-19052	256	7	{	{	PUNCT
bracis-19052	256	8	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	256	9	{	{	PUNCT
bracis-19052	256	10	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	256	11	{	{	PUNCT
bracis-19052	256	12	autol}\	autol}\	PROPN
bracis-19052	256	13	)	)	PUNCT
bracis-19052	256	14	and	and	CCONJ
bracis-19052	256	15	\(\texttt	\(\texttt	NOUN
bracis-19052	256	16	{	{	PUNCT
bracis-19052	256	17	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	256	18	{	{	PUNCT
bracis-19052	256	19	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	256	20	{	{	PUNCT
bracis-19052	256	21	autod}\	autod}\	PROPN
bracis-19052	256	22	)	)	PUNCT
bracis-19052	256	23	,	,	PUNCT
bracis-19052	256	24	for	for	ADP
bracis-19052	256	25	estimating	estimate	VERB
bracis-19052	256	26	label	label	NOUN
bracis-19052	256	27	reliability	reliability	NOUN
bracis-19052	256	28	and	and	CCONJ
bracis-19052	256	29	diffusion	diffusion	NOUN
bracis-19052	256	30	rates	rate	NOUN
bracis-19052	256	31	.	.	PUNCT
bracis-19052	257	1	we	we	PRON
bracis-19052	257	2	use	use	VERB
bracis-19052	257	3	automatic	automatic	ADJ
bracis-19052	257	4	differentiation	differentiation	NOUN
bracis-19052	257	5	for	for	ADP
bracis-19052	257	6	parameter	parameter	NOUN
bracis-19052	257	7	estimation	estimation	NOUN
bracis-19052	257	8	,	,	PUNCT
bracis-19052	257	9	and	and	CCONJ
bracis-19052	257	10	the	the	DET
bracis-19052	257	11	eigenfunction	eigenfunction	NOUN
bracis-19052	257	12	approximation	approximation	NOUN
bracis-19052	257	13	is	be	AUX
bracis-19052	257	14	used	use	VERB
bracis-19052	257	15	to	to	PART
bracis-19052	257	16	derive	derive	VERB
bracis-19052	257	17	a	a	DET
bracis-19052	257	18	faster	fast	ADJ
bracis-19052	257	19	solution	solution	NOUN
bracis-19052	257	20	for	for	ADP
bracis-19052	257	21	\(\texttt	\(\texttt	NOUN
bracis-19052	257	22	{	{	PUNCT
bracis-19052	257	23	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	257	24	{	{	PUNCT
bracis-19052	257	25	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	257	26	{	{	PUNCT
bracis-19052	257	27	autod}\	autod}\	PROPN
bracis-19052	257	28	)	)	PUNCT
bracis-19052	257	29	,	,	PUNCT
bracis-19052	257	30	in	in	ADP
bracis-19052	257	31	particular	particular	ADJ
bracis-19052	257	32	when	when	SCONJ
bracis-19052	257	33	having	have	VERB
bracis-19052	257	34	to	to	PART
bracis-19052	257	35	recalculate	recalculate	VERB
bracis-19052	257	36	the	the	DET
bracis-19052	257	37	propagation	propagation	NOUN
bracis-19052	257	38	matrix	matrix	NOUN
bracis-19052	257	39	for	for	ADP
bracis-19052	257	40	different	different	ADJ
bracis-19052	257	41	diffusion	diffusion	NOUN
bracis-19052	257	42	rates	rate	NOUN
bracis-19052	257	43	.	.	PUNCT
bracis-19052	258	1	overall	overall	ADJ
bracis-19052	258	2	,	,	PUNCT
bracis-19052	258	3	\(\texttt	\(\texttt	X
bracis-19052	258	4	{	{	PUNCT
bracis-19052	258	5	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	258	6	{	{	PUNCT
bracis-19052	258	7	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	258	8	{	{	PUNCT
bracis-19052	258	9	autol}\	autol}\	PROPN
bracis-19052	258	10	)	)	PUNCT
bracis-19052	258	11	produced	produce	VERB
bracis-19052	258	12	interesting	interesting	ADJ
bracis-19052	258	13	results	result	NOUN
bracis-19052	258	14	.	.	PUNCT
bracis-19052	259	1	for	for	ADP
bracis-19052	259	2	the	the	DET
bracis-19052	259	3	isolet	isolet	NOUN
bracis-19052	259	4	dataset	dataset	NOUN
bracis-19052	259	5	,	,	PUNCT
bracis-19052	259	6	it	it	PRON
bracis-19052	259	7	was	be	AUX
bracis-19052	259	8	very	very	ADV
bracis-19052	259	9	successful	successful	ADJ
bracis-19052	259	10	at	at	ADP
bracis-19052	259	11	the	the	DET
bracis-19052	259	12	task	task	NOUN
bracis-19052	259	13	of	of	ADP
bracis-19052	259	14	label	label	NOUN
bracis-19052	259	15	diagnosis	diagnosis	NOUN
bracis-19052	259	16	,	,	PUNCT
bracis-19052	259	17	being	be	AUX
bracis-19052	259	18	able	able	ADJ
bracis-19052	259	19	to	to	PART
bracis-19052	259	20	detect	detect	VERB
bracis-19052	259	21	and	and	CCONJ
bracis-19052	259	22	remove	remove	VERB
bracis-19052	259	23	labels	label	NOUN
bracis-19052	259	24	with	with	ADP
bracis-19052	259	25	overall	overall	ADJ
bracis-19052	259	26	better	well	ADJ
bracis-19052	259	27	performance	performance	NOUN
bracis-19052	259	28	than	than	ADP
bracis-19052	259	29	every	every	DET
bracis-19052	259	30	\(\ell	\(\ell	NOUN
bracis-19052	260	1	_	_	PUNCT
bracis-19052	260	2	1\)-norm	1\)-norm	NOUN
bracis-19052	260	3	method	method	NOUN
bracis-19052	260	4	.	.	PUNCT
bracis-19052	261	1	on	on	ADP
bracis-19052	261	2	the	the	DET
bracis-19052	261	3	other	other	ADJ
bracis-19052	261	4	hand	hand	NOUN
bracis-19052	261	5	,	,	PUNCT
bracis-19052	261	6	did	do	AUX
bracis-19052	261	7	not	not	PART
bracis-19052	261	8	translate	translate	VERB
bracis-19052	261	9	too	too	ADV
bracis-19052	261	10	well	well	ADV
bracis-19052	261	11	for	for	ADP
bracis-19052	261	12	unlabeled	unlabeled	ADJ
bracis-19052	261	13	instance	instance	NOUN
bracis-19052	261	14	classification	classification	NOUN
bracis-19052	261	15	.	.	PUNCT
bracis-19052	262	1	for	for	ADP
bracis-19052	262	2	the	the	DET
bracis-19052	262	3	mnist	mnist	PROPN
bracis-19052	262	4	dataset	dataset	NOUN
bracis-19052	262	5	,	,	PUNCT
bracis-19052	262	6	performance	performance	NOUN
bracis-19052	262	7	is	be	AUX
bracis-19052	262	8	massively	massively	ADV
bracis-19052	262	9	boosted	boost	VERB
bracis-19052	262	10	for	for	ADP
bracis-19052	262	11	unlabeled	unlabeled	ADJ
bracis-19052	262	12	instances	instance	NOUN
bracis-19052	262	13	as	as	ADV
bracis-19052	262	14	well	well	ADV
bracis-19052	262	15	.	.	PUNCT
bracis-19052	263	1	in	in	ADP
bracis-19052	263	2	spite	spite	NOUN
bracis-19052	263	3	of	of	ADP
bracis-19052	263	4	outperforming	outperform	VERB
bracis-19052	263	5	its	its	PRON
bracis-19052	263	6	lgc	lgc	ADJ
bracis-19052	263	7	baseline	baseline	NOUN
bracis-19052	263	8	by	by	ADP
bracis-19052	263	9	a	a	DET
bracis-19052	263	10	wide	wide	ADJ
bracis-19052	263	11	margin	margin	NOUN
bracis-19052	263	12	,	,	PUNCT
bracis-19052	263	13	it	it	PRON
bracis-19052	263	14	could	could	AUX
bracis-19052	263	15	not	not	PART
bracis-19052	263	16	match	match	VERB
bracis-19052	263	17	the	the	DET
bracis-19052	263	18	reported	report	VERB
bracis-19052	263	19	results	result	NOUN
bracis-19052	263	20	of	of	ADP
bracis-19052	263	21	lssc	lssc	NOUN
bracis-19052	263	22	on	on	ADP
bracis-19052	263	23	mnist	mnist	PROPN
bracis-19052	263	24	.	.	PUNCT
bracis-19052	264	1	preliminary	preliminary	ADJ
bracis-19052	264	2	results	result	NOUN
bracis-19052	264	3	showed	show	VERB
bracis-19052	264	4	that	that	SCONJ
bracis-19052	264	5	\({{\mathbf	\({{\mathbf	PROPN
bracis-19052	264	6	{	{	PUNCT
bracis-19052	264	7	\mathtt{{lgc}}}}}\_{{\mathbf	\mathtt{{lgc}}}}}\_{{\mathbf	NOUN
bracis-19052	264	8	{	{	PUNCT
bracis-19052	264	9	\mathtt{{lvo}}}}}\_{{\mathbf	\mathtt{{lvo}}}}}\_{{\mathbf	NOUN
bracis-19052	264	10	{	{	PUNCT
bracis-19052	264	11	\mathtt{{autod}}}}}\	\mathtt{{autod}}}}}\	NOUN
bracis-19052	264	12	)	)	PUNCT
bracis-19052	264	13	is	be	AUX
bracis-19052	264	14	a	a	DET
bracis-19052	264	15	viable	viable	ADJ
bracis-19052	264	16	way	way	NOUN
bracis-19052	264	17	to	to	PART
bracis-19052	264	18	get	get	VERB
bracis-19052	264	19	a	a	DET
bracis-19052	264	20	good	good	ADJ
bracis-19052	264	21	estimate	estimate	NOUN
bracis-19052	264	22	of	of	ADP
bracis-19052	264	23	the	the	DET
bracis-19052	264	24	optimal	optimal	ADJ
bracis-19052	264	25	diffusion	diffusion	NOUN
bracis-19052	264	26	rate	rate	NOUN
bracis-19052	264	27	,	,	PUNCT
bracis-19052	264	28	and	and	CCONJ
bracis-19052	264	29	removing	remove	VERB
bracis-19052	264	30	the	the	DET
bracis-19052	264	31	diagonal	diagonal	ADJ
bracis-19052	264	32	entries	entry	NOUN
bracis-19052	264	33	proved	prove	VERB
bracis-19052	264	34	to	to	PART
bracis-19052	264	35	be	be	AUX
bracis-19052	264	36	the	the	DET
bracis-19052	264	37	crucial	crucial	ADJ
bracis-19052	264	38	step	step	NOUN
bracis-19052	264	39	for	for	ADP
bracis-19052	264	40	avoiding	avoid	VERB
bracis-19052	264	41	overfitting	overfitte	VERB
bracis-19052	264	42	.	.	PUNCT
bracis-19052	265	1	for	for	ADP
bracis-19052	265	2	future	future	ADJ
bracis-19052	265	3	work	work	NOUN
bracis-19052	265	4	,	,	PUNCT
bracis-19052	265	5	we	we	PRON
bracis-19052	265	6	will	will	AUX
bracis-19052	265	7	be	be	AUX
bracis-19052	265	8	further	far	ADV
bracis-19052	265	9	evaluating	evaluate	VERB
bracis-19052	265	10	\(\texttt	\(\texttt	NOUN
bracis-19052	265	11	{	{	PUNCT
bracis-19052	265	12	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	265	13	{	{	PUNCT
bracis-19052	265	14	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	265	15	{	{	PUNCT
bracis-19052	265	16	autod}\	autod}\	PROPN
bracis-19052	265	17	)	)	PUNCT
bracis-19052	265	18	.	.	PUNCT
bracis-19052	266	1	we	we	PRON
bracis-19052	266	2	will	will	AUX
bracis-19052	266	3	also	also	ADV
bracis-19052	266	4	try	try	VERB
bracis-19052	266	5	to	to	PART
bracis-19052	266	6	integrate	integrate	VERB
bracis-19052	266	7	\(\texttt	\(\texttt	NOUN
bracis-19052	266	8	{	{	PUNCT
bracis-19052	266	9	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	266	10	{	{	PUNCT
bracis-19052	266	11	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	266	12	{	{	PUNCT
bracis-19052	266	13	autod}\	autod}\	PROPN
bracis-19052	266	14	)	)	PUNCT
bracis-19052	266	15	and	and	CCONJ
bracis-19052	266	16	\(\texttt	\(\texttt	NOUN
bracis-19052	266	17	{	{	PUNCT
bracis-19052	266	18	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	266	19	{	{	PUNCT
bracis-19052	266	20	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	266	21	{	{	PUNCT
bracis-19052	266	22	autol}\	autol}\	PROPN
bracis-19052	266	23	)	)	PUNCT
bracis-19052	266	24	together	together	ADV
bracis-19052	266	25	into	into	ADP
bracis-19052	266	26	one	one	NUM
bracis-19052	266	27	single	single	ADJ
bracis-19052	266	28	algorithm	algorithm	NOUN
bracis-19052	266	29	.	.	PUNCT
bracis-19052	267	1	lastly	lastly	ADV
bracis-19052	267	2	,	,	PUNCT
bracis-19052	267	3	we	we	PRON
bracis-19052	267	4	will	will	AUX
bracis-19052	267	5	aim	aim	VERB
bracis-19052	267	6	to	to	PART
bracis-19052	267	7	extend	extend	VERB
bracis-19052	267	8	\(\texttt	\(\texttt	NOUN
bracis-19052	267	9	{	{	PUNCT
bracis-19052	267	10	lgc}\_\texttt	lgc}\_\texttt	NOUN
bracis-19052	267	11	{	{	PUNCT
bracis-19052	267	12	lvo}\_\texttt	lvo}\_\texttt	PROPN
bracis-19052	267	13	{	{	PUNCT
bracis-19052	267	14	autod}\	autod}\	PROPN
bracis-19052	267	15	)	)	PUNCT
bracis-19052	267	16	to	to	ADP
bracis-19052	267	17	a	a	DET
bracis-19052	267	18	broader	broad	ADJ
bracis-19052	267	19	class	class	NOUN
bracis-19052	267	20	of	of	ADP
bracis-19052	267	21	graph	graph	NOUN
bracis-19052	267	22	-	-	PUNCT
bracis-19052	267	23	based	base	VERB
bracis-19052	267	24	kernels	kernel	NOUN
bracis-19052	267	25	,	,	PUNCT
bracis-19052	267	26	in	in	ADP
bracis-19052	267	27	addition	addition	NOUN
bracis-19052	267	28	to	to	ADP
bracis-19052	267	29	the	the	DET
bracis-19052	267	30	one	one	NUM
bracis-19052	267	31	resulting	result	VERB
bracis-19052	267	32	from	from	ADP
bracis-19052	267	33	the	the	DET
bracis-19052	267	34	lgc	lgc	ADJ
bracis-19052	267	35	baseline	baseline	NOUN
bracis-19052	267	36	.	.	PUNCT
bracis-19052	268	1	references	reference	NOUN
bracis-19052	268	2	abadi	abadi	PROPN
bracis-19052	268	3	,	,	PUNCT
bracis-19052	268	4	m.	m.	NOUN
bracis-19052	268	5	,	,	PUNCT
bracis-19052	268	6	et	et	PROPN
bracis-19052	268	7	al	al	PROPN
bracis-19052	268	8	.	.	PUNCT
bracis-19052	268	9	:	:	PUNCT
bracis-19052	269	1	tensorflow	tensorflow	NOUN
bracis-19052	269	2	:	:	PUNCT
bracis-19052	269	3	large	large	ADJ
bracis-19052	269	4	-	-	PUNCT
bracis-19052	269	5	scale	scale	NOUN
bracis-19052	269	6	machine	machine	NOUN
bracis-19052	269	7	learning	learn	VERB
bracis-19052	269	8	on	on	ADP
bracis-19052	269	9	heterogeneous	heterogeneous	ADJ
bracis-19052	269	10	systems	system	NOUN
bracis-19052	269	11	(	(	PUNCT
bracis-19052	269	12	2015	2015	NUM
bracis-19052	269	13	)	)	PUNCT
bracis-19052	269	14	.	.	PUNCT
bracis-19052	270	1	http://tensorflow.org/	http://tensorflow.org/	NOUN
bracis-19052	270	2	,	,	PUNCT
bracis-19052	270	3	software	software	NOUN
bracis-19052	270	4	available	available	ADJ
bracis-19052	270	5	from	from	ADP
bracis-19052	270	6	tensorflow.org	tensorflow.org	X
bracis-19052	270	7	de	de	PROPN
bracis-19052	270	8	aquino	aquino	PROPN
bracis-19052	270	9	afonso	afonso	PROPN
bracis-19052	270	10	,	,	PUNCT
bracis-19052	270	11	b.k	b.k	PROPN
bracis-19052	270	12	.	.	PUNCT
bracis-19052	270	13	:	:	PUNCT
bracis-19052	270	14	analysis	analysis	NOUN
bracis-19052	270	15	of	of	ADP
bracis-19052	270	16	label	label	NOUN
bracis-19052	270	17	noise	noise	NOUN
bracis-19052	270	18	in	in	ADP
bracis-19052	270	19	graph	graph	NOUN
bracis-19052	270	20	-	-	PUNCT
bracis-19052	270	21	based	base	VERB
bracis-19052	270	22	semi	semi	ADJ
bracis-19052	270	23	-	-	ADJ
bracis-19052	270	24	supervised	supervised	ADJ
bracis-19052	270	25	learning	learning	NOUN
bracis-19052	270	26	.	.	PUNCT
bracis-19052	271	1	master	master	NOUN
bracis-19052	271	2	’s	’s	PART
bracis-19052	271	3	thesis	thesis	NOUN
bracis-19052	271	4	(	(	PUNCT
bracis-19052	271	5	2020	2020	NUM
bracis-19052	271	6	)	)	PUNCT
bracis-19052	271	7	google	google	PROPN
bracis-19052	271	8	scholar	scholar	NOUN
bracis-19052	271	9	  	  	SPACE
bracis-19052	271	10	chapelle	chapelle	NOUN
bracis-19052	271	11	,	,	PUNCT
bracis-19052	271	12	o.	o.	PROPN
bracis-19052	271	13	,	,	PUNCT
bracis-19052	271	14	schölkopf	schölkopf	NOUN
bracis-19052	271	15	,	,	PUNCT
bracis-19052	271	16	b.	b.	PROPN
bracis-19052	271	17	,	,	PUNCT
bracis-19052	271	18	zien	zien	PROPN
bracis-19052	271	19	,	,	PUNCT
bracis-19052	271	20	a.	a.	PROPN
bracis-19052	271	21	(	(	PUNCT
bracis-19052	271	22	eds	eds	PROPN
bracis-19052	271	23	.	.	PROPN
bracis-19052	271	24	):	):	PUNCT
bracis-19052	271	25	semi	semi	ADJ
bracis-19052	271	26	-	-	ADJ
bracis-19052	271	27	supervised	supervised	ADJ
bracis-19052	271	28	learning	learning	NOUN
bracis-19052	271	29	.	.	PUNCT
bracis-19052	272	1	mit	mit	PROPN
bracis-19052	272	2	press	press	PROPN
bracis-19052	272	3	,	,	PUNCT
bracis-19052	272	4	cambridge	cambridge	PROPN
bracis-19052	272	5	(	(	PUNCT
bracis-19052	272	6	2006	2006	NUM
bracis-19052	272	7	)	)	PUNCT
bracis-19052	272	8	.	.	PUNCT
bracis-19052	273	1	http://www.kyb.tuebingen.mpg.de/ssl-book	http://www.kyb.tuebingen.mpg.de/ssl-book	VERB
bracis-19052	273	2	de	de	PROPN
bracis-19052	273	3	aquino	aquino	PROPN
bracis-19052	273	4	afonso	afonso	PROPN
bracis-19052	273	5	,	,	PUNCT
bracis-19052	273	6	b.k	b.k	PROPN
bracis-19052	273	7	.	.	PROPN
bracis-19052	273	8	,	,	PUNCT
bracis-19052	273	9	berton	berton	PROPN
bracis-19052	273	10	,	,	PUNCT
bracis-19052	273	11	l.	l.	PROPN
bracis-19052	273	12	:	:	PUNCT
bracis-19052	273	13	identifying	identify	VERB
bracis-19052	273	14	noisy	noisy	ADJ
bracis-19052	273	15	labels	label	NOUN
bracis-19052	273	16	with	with	ADP
bracis-19052	273	17	a	a	DET
bracis-19052	273	18	transductive	transductive	ADJ
bracis-19052	273	19	semi	semi	ADJ
bracis-19052	273	20	-	-	ADJ
bracis-19052	273	21	supervised	supervised	ADJ
bracis-19052	273	22	leave	leave	VERB
bracis-19052	273	23	-	-	PUNCT
bracis-19052	273	24	one	one	NUM
bracis-19052	273	25	-	-	PUNCT
bracis-19052	273	26	out	out	ADP
bracis-19052	273	27	filter	filter	NOUN
bracis-19052	273	28	.	.	PUNCT
bracis-19052	274	1	pattern	pattern	NOUN
bracis-19052	274	2	recognit	recognit	VERB
bracis-19052	274	3	.	.	PUNCT
bracis-19052	275	1	lett	lett	PROPN
bracis-19052	275	2	.	.	PROPN
bracis-19052	276	1	140	140	NUM
bracis-19052	276	2	,	,	PUNCT
bracis-19052	276	3	127–134	127–134	NUM
bracis-19052	276	4	(	(	PUNCT
bracis-19052	276	5	2020	2020	NUM
bracis-19052	276	6	)	)	PUNCT
bracis-19052	276	7	.	.	PUNCT
bracis-19052	277	1	https://doi.org/10.1016/j.patrec.2020.09.024	https://doi.org/10.1016/j.patrec.2020.09.024	PROPN
bracis-19052	277	2	.	.	PUNCT
bracis-19052	278	1	http://www.sciencedirect.com/science/article/pii/s0167865520303603	http://www.sciencedirect.com/science/article/pii/s0167865520303603	PROPN
bracis-19052	278	2	article	article	NOUN
bracis-19052	278	3	  	  	SPACE
bracis-19052	278	4	google	google	PROPN
bracis-19052	278	5	scholar	scholar	NOUN
bracis-19052	278	6	  	  	SPACE
bracis-19052	278	7	fergus	fergus	PROPN
bracis-19052	278	8	,	,	PUNCT
bracis-19052	278	9	r.	r.	PROPN
bracis-19052	278	10	,	,	PUNCT
bracis-19052	278	11	weiss	weiss	PROPN
bracis-19052	278	12	,	,	PUNCT
bracis-19052	278	13	y.	y.	PROPN
bracis-19052	278	14	,	,	PUNCT
bracis-19052	278	15	torralba	torralba	PROPN
bracis-19052	278	16	,	,	PUNCT
bracis-19052	278	17	a.	a.	NOUN
bracis-19052	278	18	:	:	PUNCT
bracis-19052	278	19	semi	semi	ADJ
bracis-19052	278	20	-	-	ADJ
bracis-19052	278	21	supervised	supervised	ADJ
bracis-19052	278	22	learning	learning	NOUN
bracis-19052	278	23	in	in	ADP
bracis-19052	278	24	gigantic	gigantic	ADJ
bracis-19052	278	25	image	image	NOUN
bracis-19052	278	26	collections	collection	NOUN
bracis-19052	278	27	.	.	PUNCT
bracis-19052	279	1	in	in	ADP
bracis-19052	279	2	:	:	PUNCT
bracis-19052	279	3	advances	advance	NOUN
bracis-19052	279	4	in	in	ADP
bracis-19052	279	5	neural	neural	ADJ
bracis-19052	279	6	information	information	NOUN
bracis-19052	279	7	processing	processing	NOUN
bracis-19052	279	8	systems	system	NOUN
bracis-19052	279	9	,	,	PUNCT
bracis-19052	279	10	pp	pp	ADV
bracis-19052	279	11	.	.	PUNCT
bracis-19052	280	1	522–530	522–530	NUM
bracis-19052	280	2	(	(	PUNCT
bracis-19052	280	3	2009	2009	NUM
bracis-19052	280	4	)	)	PUNCT
bracis-19052	280	5	google	google	PROPN
bracis-19052	280	6	scholar	scholar	NOUN
bracis-19052	280	7	  	  	SPACE
bracis-19052	280	8	gong	gong	NOUN
bracis-19052	280	9	,	,	PUNCT
bracis-19052	280	10	c.	c.	PROPN
bracis-19052	280	11	,	,	PUNCT
bracis-19052	280	12	zhang	zhang	PROPN
bracis-19052	280	13	,	,	PUNCT
bracis-19052	280	14	h.	h.	PROPN
bracis-19052	280	15	,	,	PUNCT
bracis-19052	280	16	yang	yang	PROPN
bracis-19052	280	17	,	,	PUNCT
bracis-19052	280	18	j.	j.	PROPN
bracis-19052	280	19	,	,	PUNCT
bracis-19052	280	20	tao	tao	PROPN
bracis-19052	280	21	,	,	PUNCT
bracis-19052	280	22	d.	d.	PROPN
bracis-19052	280	23	:	:	PUNCT
bracis-19052	280	24	learning	learn	VERB
bracis-19052	280	25	with	with	ADP
bracis-19052	280	26	inadequate	inadequate	ADJ
bracis-19052	280	27	and	and	CCONJ
bracis-19052	280	28	incorrect	incorrect	ADJ
bracis-19052	280	29	supervision	supervision	NOUN
bracis-19052	280	30	.	.	PUNCT
bracis-19052	281	1	in	in	ADP
bracis-19052	281	2	:	:	PUNCT
bracis-19052	281	3	2017	2017	NUM
bracis-19052	281	4	ieee	ieee	NOUN
bracis-19052	281	5	international	international	ADJ
bracis-19052	281	6	conference	conference	NOUN
bracis-19052	281	7	on	on	ADP
bracis-19052	281	8	data	datum	NOUN
bracis-19052	281	9	mining	mining	NOUN
bracis-19052	281	10	(	(	PUNCT
bracis-19052	281	11	icdm	icdm	NOUN
bracis-19052	281	12	)	)	PUNCT
bracis-19052	281	13	,	,	PUNCT
bracis-19052	281	14	pp	pp	ADP
bracis-19052	281	15	.	.	PUNCT
bracis-19052	282	1	889–894	889–894	NUM
bracis-19052	282	2	.	.	PUNCT
bracis-19052	282	3	ieee	ieee	NOUN
bracis-19052	282	4	(	(	PUNCT
bracis-19052	282	5	2017	2017	NUM
bracis-19052	282	6	)	)	PUNCT
bracis-19052	282	7	google	google	PROPN
bracis-19052	282	8	scholar	scholar	NOUN
bracis-19052	282	9	  	  	SPACE
bracis-19052	282	10	johnson	johnson	PROPN
bracis-19052	282	11	,	,	PUNCT
bracis-19052	282	12	j.	j.	PROPN
bracis-19052	282	13	,	,	PUNCT
bracis-19052	282	14	douze	douze	PROPN
bracis-19052	282	15	,	,	PUNCT
bracis-19052	282	16	m.	m.	NOUN
bracis-19052	282	17	,	,	PUNCT
bracis-19052	282	18	jégou	jégou	PROPN
bracis-19052	282	19	,	,	PUNCT
bracis-19052	282	20	h.	h.	NOUN
bracis-19052	282	21	:	:	PUNCT
bracis-19052	282	22	billion	billion	NUM
bracis-19052	282	23	-	-	PUNCT
bracis-19052	282	24	scale	scale	NOUN
bracis-19052	282	25	similarity	similarity	NOUN
bracis-19052	282	26	search	search	NOUN
bracis-19052	282	27	with	with	ADP
bracis-19052	282	28	gpus	gpus	PROPN
bracis-19052	282	29	.	.	PUNCT
bracis-19052	283	1	ieee	ieee	PROPN
bracis-19052	283	2	trans	trans	PROPN
bracis-19052	283	3	.	.	PUNCT
bracis-19052	284	1	big	big	ADJ
bracis-19052	284	2	data	datum	NOUN
bracis-19052	284	3	(	(	PUNCT
bracis-19052	284	4	2019	2019	NUM
bracis-19052	284	5	)	)	PUNCT
bracis-19052	284	6	google	google	NOUN
bracis-19052	284	7	scholar	scholar	NOUN
bracis-19052	284	8	  	  	SPACE
bracis-19052	284	9	kearnes	kearne	NOUN
bracis-19052	284	10	,	,	PUNCT
bracis-19052	284	11	s.	s.	PROPN
bracis-19052	284	12	,	,	PUNCT
bracis-19052	284	13	mccloskey	mccloskey	PROPN
bracis-19052	284	14	,	,	PUNCT
bracis-19052	284	15	k.	k.	PROPN
bracis-19052	284	16	,	,	PUNCT
bracis-19052	284	17	berndl	berndl	PROPN
bracis-19052	284	18	,	,	PUNCT
bracis-19052	284	19	m.	m.	NOUN
bracis-19052	284	20	,	,	PUNCT
bracis-19052	284	21	pande	pande	NOUN
bracis-19052	284	22	,	,	PUNCT
bracis-19052	284	23	v.	v.	PROPN
bracis-19052	284	24	,	,	PUNCT
bracis-19052	284	25	riley	riley	PROPN
bracis-19052	284	26	,	,	PUNCT
bracis-19052	284	27	p.	p.	NOUN
bracis-19052	284	28	:	:	PUNCT
bracis-19052	284	29	molecular	molecular	ADJ
bracis-19052	284	30	graph	graph	NOUN
bracis-19052	284	31	convolutions	convolution	NOUN
bracis-19052	284	32	:	:	PUNCT
bracis-19052	284	33	moving	move	VERB
bracis-19052	284	34	beyond	beyond	ADP
bracis-19052	284	35	fingerprints	fingerprint	NOUN
bracis-19052	284	36	.	.	PUNCT
bracis-19052	285	1	j.	j.	PROPN
bracis-19052	285	2	comput.-aided	comput.-aided	PROPN
bracis-19052	285	3	mol	mol	PROPN
bracis-19052	285	4	.	.	PUNCT
bracis-19052	286	1	des	des	PROPN
bracis-19052	286	2	.	.	PROPN
bracis-19052	286	3	30(8	30(8	NUM
bracis-19052	286	4	)	)	PUNCT
bracis-19052	286	5	,	,	PUNCT
bracis-19052	286	6	595–608	595–608	NUM
bracis-19052	286	7	(	(	PUNCT
bracis-19052	286	8	2016	2016	NUM
bracis-19052	286	9	)	)	PUNCT
bracis-19052	286	10	.	.	PUNCT
bracis-19052	287	1	https://doi.org/10.1007/s10822-016-9938-8	https://doi.org/10.1007/s10822-016-9938-8	PROPN
bracis-19052	287	2	article	article	PROPN
bracis-19052	287	3	  	  	SPACE
bracis-19052	287	4	google	google	PROPN
bracis-19052	287	5	scholar	scholar	NOUN
bracis-19052	287	6	  	  	SPACE
bracis-19052	287	7	krijthe	krijthe	NOUN
bracis-19052	287	8	,	,	PUNCT
bracis-19052	287	9	j.h	j.h	PROPN
bracis-19052	287	10	.	.	PROPN
bracis-19052	287	11	:	:	PUNCT
bracis-19052	287	12	robust	robust	ADJ
bracis-19052	287	13	semi	semi	ADJ
bracis-19052	287	14	-	-	ADJ
bracis-19052	287	15	supervised	supervised	ADJ
bracis-19052	287	16	learning	learning	NOUN
bracis-19052	287	17	:	:	PUNCT
bracis-19052	288	1	projections	projection	NOUN
bracis-19052	288	2	,	,	PUNCT
bracis-19052	288	3	limits	limit	NOUN
bracis-19052	288	4	and	and	CCONJ
bracis-19052	288	5	constraints	constraint	NOUN
bracis-19052	288	6	.	.	PUNCT
bracis-19052	289	1	ph.d	ph.d	PROPN
bracis-19052	289	2	.	.	PUNCT
bracis-19052	290	1	thesis	thesis	PROPN
bracis-19052	290	2	,	,	PUNCT
bracis-19052	290	3	leiden	leiden	PROPN
bracis-19052	290	4	university	university	PROPN
bracis-19052	290	5	(	(	PUNCT
bracis-19052	290	6	2018	2018	NUM
bracis-19052	290	7	)	)	PUNCT
bracis-19052	290	8	google	google	PROPN
bracis-19052	290	9	scholar	scholar	NOUN
bracis-19052	290	10	  	  	SPACE
bracis-19052	290	11	lu	lu	PROPN
bracis-19052	290	12	,	,	PUNCT
bracis-19052	290	13	z.	z.	PROPN
bracis-19052	290	14	,	,	PUNCT
bracis-19052	290	15	gao	gao	PROPN
bracis-19052	290	16	,	,	PUNCT
bracis-19052	290	17	x.	x.	PROPN
bracis-19052	290	18	,	,	PUNCT
bracis-19052	290	19	wang	wang	PROPN
bracis-19052	290	20	,	,	PUNCT
bracis-19052	290	21	l.	l.	PROPN
bracis-19052	290	22	,	,	PUNCT
bracis-19052	290	23	wen	wen	PROPN
bracis-19052	290	24	,	,	PUNCT
bracis-19052	290	25	j.r	j.r	PROPN
bracis-19052	290	26	.	.	PROPN
bracis-19052	290	27	,	,	PUNCT
bracis-19052	290	28	huang	huang	PROPN
bracis-19052	290	29	,	,	PUNCT
bracis-19052	290	30	s.	s.	PROPN
bracis-19052	290	31	:	:	PUNCT
bracis-19052	290	32	noise	noise	NOUN
bracis-19052	290	33	-	-	PUNCT
bracis-19052	290	34	robust	robust	ADJ
bracis-19052	290	35	semi	semi	ADJ
bracis-19052	290	36	-	-	ADJ
bracis-19052	290	37	supervised	supervised	ADJ
bracis-19052	290	38	learning	learning	NOUN
bracis-19052	290	39	by	by	ADP
bracis-19052	290	40	large	large	ADJ
bracis-19052	290	41	-	-	PUNCT
bracis-19052	290	42	scale	scale	NOUN
bracis-19052	290	43	sparse	sparse	ADJ
bracis-19052	290	44	coding	coding	NOUN
bracis-19052	290	45	.	.	PUNCT
bracis-19052	291	1	in	in	ADP
bracis-19052	291	2	:	:	PUNCT
bracis-19052	291	3	aaai	aaai	PROPN
bracis-19052	291	4	,	,	PUNCT
bracis-19052	291	5	pp	pp	ADJ
bracis-19052	291	6	.	.	PUNCT
bracis-19052	292	1	2828–2834	2828–2834	NUM
bracis-19052	292	2	(	(	PUNCT
bracis-19052	292	3	2015	2015	NUM
bracis-19052	292	4	)	)	PUNCT
bracis-19052	292	5	google	google	PROPN
bracis-19052	292	6	scholar	scholar	NOUN
bracis-19052	292	7	  	  	SPACE
bracis-19052	292	8	mitchell	mitchell	NOUN
bracis-19052	292	9	,	,	PUNCT
bracis-19052	292	10	t.	t.	PROPN
bracis-19052	292	11	:	:	PUNCT
bracis-19052	292	12	machine	machine	NOUN
bracis-19052	292	13	learning	learning	NOUN
bracis-19052	292	14	.	.	PUNCT
bracis-19052	293	1	mcgraw	mcgraw	PROPN
bracis-19052	293	2	-	-	PUNCT
bracis-19052	293	3	hill	hill	PROPN
bracis-19052	293	4	,	,	PUNCT
bracis-19052	293	5	new	new	PROPN
bracis-19052	293	6	york	york	PROPN
bracis-19052	293	7	(	(	PUNCT
bracis-19052	293	8	1997	1997	NUM
bracis-19052	293	9	)	)	PUNCT
bracis-19052	293	10	math	math	NOUN
bracis-19052	293	11	  	  	SPACE
bracis-19052	293	12	google	google	PROPN
bracis-19052	293	13	scholar	scholar	NOUN
bracis-19052	293	14	  	  	SPACE
bracis-19052	293	15	miyato	miyato	NOUN
bracis-19052	293	16	,	,	PUNCT
bracis-19052	293	17	t.	t.	PROPN
bracis-19052	293	18	,	,	PUNCT
bracis-19052	293	19	maeda	maeda	PROPN
bracis-19052	293	20	,	,	PUNCT
bracis-19052	293	21	s.i	s.i	PROPN
bracis-19052	293	22	.	.	PROPN
bracis-19052	293	23	,	,	PUNCT
bracis-19052	293	24	ishii	ishii	PROPN
bracis-19052	293	25	,	,	PUNCT
bracis-19052	293	26	s.	s.	PROPN
bracis-19052	293	27	,	,	PUNCT
bracis-19052	293	28	koyama	koyama	PROPN
bracis-19052	293	29	,	,	PUNCT
bracis-19052	293	30	m.	m.	NOUN
bracis-19052	293	31	:	:	PUNCT
bracis-19052	293	32	virtual	virtual	ADJ
bracis-19052	293	33	adversarial	adversarial	ADJ
bracis-19052	293	34	training	training	NOUN
bracis-19052	293	35	:	:	PUNCT
bracis-19052	293	36	a	a	DET
bracis-19052	293	37	regularization	regularization	NOUN
bracis-19052	293	38	method	method	NOUN
bracis-19052	293	39	for	for	ADP
bracis-19052	293	40	supervised	supervised	ADJ
bracis-19052	293	41	and	and	CCONJ
bracis-19052	293	42	semi	semi	ADJ
bracis-19052	293	43	-	-	ADJ
bracis-19052	293	44	supervised	supervised	ADJ
bracis-19052	293	45	learning	learning	NOUN
bracis-19052	293	46	.	.	PUNCT
bracis-19052	294	1	ieee	ieee	PROPN
bracis-19052	294	2	trans	trans	PROPN
bracis-19052	294	3	.	.	PUNCT
bracis-19052	294	4	pattern	pattern	PROPN
bracis-19052	294	5	anal	anal	PROPN
bracis-19052	294	6	.	.	PUNCT
bracis-19052	295	1	mach	mach	PROPN
bracis-19052	295	2	.	.	PUNCT
bracis-19052	296	1	intell	intell	PROPN
bracis-19052	296	2	.	.	PUNCT
bracis-19052	297	1	41	41	NUM
bracis-19052	297	2	,	,	PUNCT
bracis-19052	297	3	1979–1993	1979–1993	NUM
bracis-19052	297	4	(	(	PUNCT
bracis-19052	297	5	2018	2018	NUM
bracis-19052	297	6	)	)	PUNCT
bracis-19052	297	7	article	article	NOUN
bracis-19052	297	8	  	  	SPACE
bracis-19052	297	9	google	google	PROPN
bracis-19052	297	10	scholar	scholar	NOUN
bracis-19052	297	11	  	  	SPACE
bracis-19052	297	12	shao	shao	PROPN
bracis-19052	297	13	,	,	PUNCT
bracis-19052	297	14	y.	y.	PROPN
bracis-19052	297	15	,	,	PUNCT
bracis-19052	297	16	sang	sing	VERB
bracis-19052	297	17	,	,	PUNCT
bracis-19052	297	18	n.	n.	NOUN
bracis-19052	297	19	,	,	PUNCT
bracis-19052	297	20	gao	gao	PROPN
bracis-19052	297	21	,	,	PUNCT
bracis-19052	297	22	c.	c.	PROPN
bracis-19052	297	23	,	,	PUNCT
bracis-19052	297	24	ma	ma	PROPN
bracis-19052	297	25	,	,	PUNCT
bracis-19052	297	26	l.	l.	PROPN
bracis-19052	297	27	:	:	PUNCT
bracis-19052	297	28	probabilistic	probabilistic	ADJ
bracis-19052	297	29	class	class	NOUN
bracis-19052	297	30	structure	structure	NOUN
bracis-19052	297	31	regularized	regularize	VERB
bracis-19052	297	32	sparse	sparse	ADJ
bracis-19052	297	33	representation	representation	NOUN
bracis-19052	297	34	graph	graph	NOUN
bracis-19052	297	35	for	for	ADP
bracis-19052	297	36	semi	semi	ADJ
bracis-19052	297	37	-	-	ADJ
bracis-19052	297	38	supervised	supervised	ADJ
bracis-19052	297	39	hyperspectral	hyperspectral	ADJ
bracis-19052	297	40	image	image	NOUN
bracis-19052	297	41	classification	classification	NOUN
bracis-19052	297	42	.	.	PUNCT
bracis-19052	298	1	pattern	pattern	NOUN
bracis-19052	298	2	recognit	recognit	VERB
bracis-19052	298	3	.	.	PUNCT
bracis-19052	299	1	63	63	NUM
bracis-19052	299	2	,	,	PUNCT
bracis-19052	299	3	102–114	102–114	NUM
bracis-19052	299	4	(	(	PUNCT
bracis-19052	299	5	2017	2017	NUM
bracis-19052	299	6	)	)	PUNCT
bracis-19052	299	7	article	article	NOUN
bracis-19052	299	8	  	  	SPACE
bracis-19052	299	9	google	google	PROPN
bracis-19052	299	10	scholar	scholar	NOUN
bracis-19052	299	11	  	  	SPACE
bracis-19052	299	12	van	van	PROPN
bracis-19052	299	13	engelen	engelen	NOUN
bracis-19052	299	14	,	,	PUNCT
bracis-19052	299	15	j.e	j.e	PROPN
bracis-19052	299	16	.	.	PROPN
bracis-19052	299	17	,	,	PUNCT
bracis-19052	299	18	hoos	hoos	PROPN
bracis-19052	299	19	,	,	PUNCT
bracis-19052	299	20	h.h	h.h	PROPN
bracis-19052	299	21	.	.	PROPN
bracis-19052	299	22	:	:	PUNCT
bracis-19052	299	23	a	a	DET
bracis-19052	299	24	survey	survey	NOUN
bracis-19052	299	25	on	on	ADP
bracis-19052	299	26	semi	semi	ADJ
bracis-19052	299	27	-	-	ADJ
bracis-19052	299	28	supervised	supervised	ADJ
bracis-19052	299	29	learning	learning	NOUN
bracis-19052	299	30	.	.	PUNCT
bracis-19052	300	1	mach	mach	PROPN
bracis-19052	300	2	.	.	PUNCT
bracis-19052	301	1	learn	learn	VERB
bracis-19052	301	2	.	.	PUNCT
bracis-19052	302	1	109(2	109(2	NUM
bracis-19052	302	2	)	)	PUNCT
bracis-19052	302	3	,	,	PUNCT
bracis-19052	302	4	373–440	373–440	NUM
bracis-19052	302	5	(	(	PUNCT
bracis-19052	302	6	2020	2020	NUM
bracis-19052	302	7	)	)	PUNCT
bracis-19052	302	8	.	.	PUNCT
bracis-19052	303	1	https://doi.org/10.1007/s10994-019-05855-6	https://doi.org/10.1007/s10994-019-05855-6	NUM
bracis-19052	303	2	article	article	NOUN
bracis-19052	303	3	  	  	SPACE
bracis-19052	303	4	mathscinet	mathscinet	NOUN
bracis-19052	303	5	  	  	SPACE
bracis-19052	303	6	math	math	NOUN
bracis-19052	303	7	  	  	SPACE
bracis-19052	303	8	google	google	PROPN
bracis-19052	303	9	scholar	scholar	NOUN
bracis-19052	303	10	  	  	SPACE
bracis-19052	303	11	wang	wang	PROPN
bracis-19052	303	12	,	,	PUNCT
bracis-19052	303	13	y.x	y.x	PROPN
bracis-19052	303	14	.	.	PROPN
bracis-19052	303	15	,	,	PUNCT
bracis-19052	303	16	sharpnack	sharpnack	VERB
bracis-19052	303	17	,	,	PUNCT
bracis-19052	303	18	j.	j.	PROPN
bracis-19052	303	19	,	,	PUNCT
bracis-19052	303	20	smola	smola	PROPN
bracis-19052	303	21	,	,	PUNCT
bracis-19052	303	22	a.j	a.j	PROPN
bracis-19052	303	23	.	.	PROPN
bracis-19052	303	24	,	,	PUNCT
bracis-19052	303	25	tibshirani	tibshirani	PROPN
bracis-19052	303	26	,	,	PUNCT
bracis-19052	303	27	r.j	r.j	PROPN
bracis-19052	303	28	.	.	PROPN
bracis-19052	303	29	:	:	PUNCT
bracis-19052	304	1	trend	trend	NOUN
bracis-19052	304	2	filtering	filter	VERB
bracis-19052	304	3	on	on	ADP
bracis-19052	304	4	graphs	graph	NOUN
bracis-19052	304	5	.	.	PUNCT
bracis-19052	305	1	j.	j.	PROPN
bracis-19052	305	2	mach	mach	PROPN
bracis-19052	305	3	.	.	PUNCT
bracis-19052	306	1	learn	learn	VERB
bracis-19052	306	2	.	.	PUNCT
bracis-19052	307	1	res	re	NOUN
bracis-19052	307	2	.	.	PUNCT
bracis-19052	308	1	17(1	17(1	NUM
bracis-19052	308	2	)	)	PUNCT
bracis-19052	308	3	,	,	PUNCT
bracis-19052	308	4	3651–3691	3651–3691	NUM
bracis-19052	308	5	(	(	PUNCT
bracis-19052	308	6	2016	2016	NUM
bracis-19052	308	7	)	)	PUNCT
bracis-19052	308	8	mathscinet	mathscinet	NOUN
bracis-19052	308	9	  	  	SPACE
bracis-19052	308	10	math	math	NOUN
bracis-19052	308	11	  	  	SPACE
bracis-19052	308	12	google	google	PROPN
bracis-19052	308	13	scholar	scholar	NOUN
bracis-19052	308	14	  	  	SPACE
bracis-19052	308	15	ying	ying	PROPN
bracis-19052	308	16	,	,	PUNCT
bracis-19052	308	17	r.	r.	PROPN
bracis-19052	308	18	,	,	PUNCT
bracis-19052	308	19	he	he	PRON
bracis-19052	308	20	,	,	PUNCT
bracis-19052	308	21	r.	r.	PROPN
bracis-19052	308	22	,	,	PUNCT
bracis-19052	308	23	chen	chen	PROPN
bracis-19052	308	24	,	,	PUNCT
bracis-19052	308	25	k.	k.	PROPN
bracis-19052	308	26	,	,	PUNCT
bracis-19052	308	27	eksombatchai	eksombatchai	ADJ
bracis-19052	308	28	,	,	PUNCT
bracis-19052	308	29	p.	p.	PROPN
bracis-19052	308	30	,	,	PUNCT
bracis-19052	308	31	hamilton	hamilton	PROPN
bracis-19052	308	32	,	,	PUNCT
bracis-19052	308	33	w.l	w.l	PROPN
bracis-19052	308	34	.	.	PROPN
bracis-19052	308	35	,	,	PUNCT
bracis-19052	308	36	leskovec	leskovec	PROPN
bracis-19052	308	37	,	,	PUNCT
bracis-19052	308	38	j.	j.	PROPN
bracis-19052	308	39	:	:	PUNCT
bracis-19052	308	40	graph	graph	VERB
bracis-19052	308	41	convolutional	convolutional	ADJ
bracis-19052	308	42	neural	neural	ADJ
bracis-19052	308	43	networks	network	NOUN
bracis-19052	308	44	for	for	ADP
bracis-19052	308	45	web	web	NOUN
bracis-19052	308	46	-	-	ADJ
bracis-19052	308	47	scale	scale	ADJ
bracis-19052	308	48	recommender	recommender	NOUN
bracis-19052	308	49	systems	system	NOUN
bracis-19052	308	50	.	.	PUNCT
bracis-19052	309	1	in	in	ADP
bracis-19052	309	2	:	:	PUNCT
bracis-19052	309	3	proceedings	proceeding	NOUN
bracis-19052	309	4	of	of	ADP
bracis-19052	309	5	the	the	DET
bracis-19052	309	6	24th	24th	PROPN
bracis-19052	309	7	acm	acm	PROPN
bracis-19052	309	8	sigkdd	sigkdd	NOUN
bracis-19052	309	9	international	international	ADJ
bracis-19052	309	10	conference	conference	NOUN
bracis-19052	309	11	on	on	ADP
bracis-19052	309	12	knowledge	knowledge	NOUN
bracis-19052	309	13	discovery	discovery	PROPN
bracis-19052	309	14	and	and	CCONJ
bracis-19052	309	15	data	datum	NOUN
bracis-19052	309	16	mining	mining	NOUN
bracis-19052	309	17	,	,	PUNCT
bracis-19052	309	18	pp	pp	ADJ
bracis-19052	309	19	.	.	PUNCT
bracis-19052	310	1	974–983	974–983	NUM
bracis-19052	310	2	(	(	PUNCT
bracis-19052	310	3	2018	2018	NUM
bracis-19052	310	4	)	)	PUNCT
bracis-19052	310	5	google	google	PROPN
bracis-19052	310	6	scholar	scholar	NOUN
bracis-19052	310	7	  	  	SPACE
bracis-19052	310	8	zhou	zhou	PROPN
bracis-19052	310	9	,	,	PUNCT
bracis-19052	310	10	d.	d.	PROPN
bracis-19052	310	11	,	,	PUNCT
bracis-19052	310	12	bousquet	bousquet	PROPN
bracis-19052	310	13	,	,	PUNCT
bracis-19052	310	14	o.	o.	PROPN
bracis-19052	310	15	,	,	PUNCT
bracis-19052	310	16	lal	lal	PROPN
bracis-19052	310	17	,	,	PUNCT
bracis-19052	310	18	t.n	t.n	PROPN
bracis-19052	310	19	.	.	PROPN
bracis-19052	310	20	,	,	PUNCT
bracis-19052	310	21	weston	weston	PROPN
bracis-19052	310	22	,	,	PUNCT
bracis-19052	310	23	j.	j.	PROPN
bracis-19052	310	24	,	,	PUNCT
bracis-19052	310	25	schölkopf	schölkopf	NOUN
bracis-19052	310	26	,	,	PUNCT
bracis-19052	310	27	b.	b.	PROPN
bracis-19052	310	28	:	:	PUNCT
bracis-19052	311	1	learning	learn	VERB
bracis-19052	311	2	with	with	ADP
bracis-19052	311	3	local	local	ADJ
bracis-19052	311	4	and	and	CCONJ
bracis-19052	311	5	global	global	ADJ
bracis-19052	311	6	consistency	consistency	NOUN
bracis-19052	311	7	.	.	PUNCT
bracis-19052	312	1	in	in	ADP
bracis-19052	312	2	:	:	PUNCT
bracis-19052	312	3	advances	advance	NOUN
bracis-19052	312	4	in	in	ADP
bracis-19052	312	5	neural	neural	ADJ
bracis-19052	312	6	information	information	NOUN
bracis-19052	312	7	processing	processing	NOUN
bracis-19052	312	8	systems	system	NOUN
bracis-19052	312	9	,	,	PUNCT
bracis-19052	312	10	pp	pp	ADP
bracis-19052	312	11	.	.	PUNCT
bracis-19052	313	1	321–328	321–328	NUM
bracis-19052	313	2	(	(	PUNCT
bracis-19052	313	3	2004	2004	NUM
bracis-19052	313	4	)	)	PUNCT
bracis-19052	313	5	google	google	PROPN
bracis-19052	313	6	scholar	scholar	NOUN
bracis-19052	313	7	  	  	SPACE
bracis-19052	313	8	zhu	zhu	PROPN
bracis-19052	313	9	,	,	PUNCT
bracis-19052	313	10	x.	x.	PROPN
bracis-19052	313	11	,	,	PUNCT
bracis-19052	313	12	ghahramani	ghahramani	PROPN
bracis-19052	313	13	,	,	PUNCT
bracis-19052	313	14	z.	z.	PROPN
bracis-19052	313	15	,	,	PUNCT
bracis-19052	313	16	lafferty	lafferty	PROPN
bracis-19052	313	17	,	,	PUNCT
bracis-19052	313	18	j.	j.	PROPN
bracis-19052	313	19	:	:	PUNCT
bracis-19052	313	20	semi	semi	ADJ
bracis-19052	313	21	-	-	ADJ
bracis-19052	313	22	supervised	supervised	ADJ
bracis-19052	313	23	learning	learning	NOUN
bracis-19052	313	24	using	use	VERB
bracis-19052	313	25	gaussian	gaussian	ADJ
bracis-19052	313	26	fields	field	NOUN
bracis-19052	313	27	and	and	CCONJ
bracis-19052	313	28	harmonic	harmonic	ADJ
bracis-19052	313	29	functions	function	NOUN
bracis-19052	313	30	.	.	PUNCT
bracis-19052	314	1	in	in	ADP
bracis-19052	314	2	:	:	PUNCT
bracis-19052	314	3	proceedings	proceeding	NOUN
bracis-19052	314	4	of	of	ADP
bracis-19052	314	5	the	the	DET
bracis-19052	314	6	twentieth	twentieth	ADJ
bracis-19052	314	7	international	international	ADJ
bracis-19052	314	8	conference	conference	NOUN
bracis-19052	314	9	on	on	ADP
bracis-19052	314	10	international	international	ADJ
bracis-19052	314	11	conference	conference	NOUN
bracis-19052	314	12	on	on	ADP
bracis-19052	314	13	machine	machine	NOUN
bracis-19052	314	14	learning	learning	NOUN
bracis-19052	314	15	,	,	PUNCT
bracis-19052	314	16	pp	pp	ADP
bracis-19052	314	17	.	.	PUNCT
bracis-19052	315	1	912–919	912–919	NUM
bracis-19052	315	2	.	.	PUNCT
bracis-19052	316	1	aaai	aaai	PROPN
bracis-19052	316	2	press	press	PROPN
bracis-19052	316	3	(	(	PUNCT
bracis-19052	316	4	2003	2003	NUM
bracis-19052	316	5	)	)	PUNCT
bracis-19052	316	6	google	google	PROPN
bracis-19052	316	7	scholar	scholar	NOUN
bracis-19052	316	8	  	  	SPACE
bracis-19052	316	9	catunda	catunda	NOUN
bracis-19052	316	10	,	,	PUNCT
bracis-19052	316	11	j.p.k	j.p.k	PROPN
bracis-19052	316	12	.	.	PROPN
bracis-19052	316	13	,	,	PUNCT
bracis-19052	316	14	da	da	PROPN
bracis-19052	316	15	silva	silva	PROPN
bracis-19052	316	16	,	,	PUNCT
bracis-19052	316	17	a.t	a.t	PROPN
bracis-19052	316	18	.	.	PROPN
bracis-19052	316	19	,	,	PUNCT
bracis-19052	316	20	berton	berton	PROPN
bracis-19052	316	21	,	,	PUNCT
bracis-19052	316	22	l.	l.	PROPN
bracis-19052	316	23	:	:	PUNCT
bracis-19052	316	24	car	car	NOUN
bracis-19052	316	25	plate	plate	NOUN
bracis-19052	316	26	character	character	NOUN
bracis-19052	316	27	recognition	recognition	NOUN
bracis-19052	316	28	via	via	ADP
bracis-19052	316	29	semi	semi	ADJ
bracis-19052	316	30	-	-	ADJ
bracis-19052	316	31	supervised	supervised	ADJ
bracis-19052	316	32	learning	learning	NOUN
bracis-19052	316	33	.	.	PUNCT
bracis-19052	317	1	in	in	ADP
bracis-19052	317	2	:	:	PUNCT
bracis-19052	317	3	2019	2019	NUM
bracis-19052	317	4	8th	8th	ADJ
bracis-19052	317	5	brazilian	brazilian	ADJ
bracis-19052	317	6	conference	conference	NOUN
bracis-19052	317	7	on	on	ADP
bracis-19052	317	8	intelligent	intelligent	ADJ
bracis-19052	317	9	systems	system	NOUN
bracis-19052	317	10	(	(	PUNCT
bracis-19052	317	11	bracis	bracis	NOUN
bracis-19052	317	12	)	)	PUNCT
bracis-19052	317	13	,	,	PUNCT
bracis-19052	317	14	pp	pp	ADP
bracis-19052	317	15	.	.	PUNCT
bracis-19052	318	1	735–740	735–740	NUM
bracis-19052	318	2	.	.	PUNCT
bracis-19052	319	1	ieee	ieee	NOUN
bracis-19052	319	2	(	(	PUNCT
bracis-19052	319	3	2019	2019	NUM
bracis-19052	319	4	)	)	PUNCT
bracis-19052	319	5	google	google	NOUN
bracis-19052	319	6	scholar	scholar	NOUN
bracis-19052	319	7	  	  	SPACE
bracis-19052	319	8	download	download	NOUN
bracis-19052	319	9	references	reference	NOUN
bracis-19052	319	10	author	author	NOUN
bracis-19052	319	11	information	information	NOUN
bracis-19052	319	12	authors	author	NOUN
bracis-19052	319	13	and	and	CCONJ
bracis-19052	319	14	affiliations	affiliation	NOUN
bracis-19052	319	15	institute	institute	PROPN
bracis-19052	319	16	of	of	ADP
bracis-19052	319	17	science	science	NOUN
bracis-19052	319	18	and	and	CCONJ
bracis-19052	319	19	technology	technology	NOUN
bracis-19052	319	20	,	,	PUNCT
bracis-19052	319	21	university	university	PROPN
bracis-19052	319	22	of	of	ADP
bracis-19052	319	23	são	são	PROPN
bracis-19052	319	24	paulo	paulo	PROPN
bracis-19052	319	25	,	,	PUNCT
bracis-19052	319	26	são	são	PROPN
bracis-19052	319	27	paulo	paulo	PROPN
bracis-19052	319	28	,	,	PUNCT
bracis-19052	319	29	brazil	brazil	PROPN
bracis-19052	319	30	bruno	bruno	PROPN
bracis-19052	319	31	klaus	klaus	PROPN
bracis-19052	319	32	de	de	PROPN
bracis-19052	319	33	aquino	aquino	PROPN
bracis-19052	319	34	afonso	afonso	PROPN
bracis-19052	319	35	 	 	SPACE
bracis-19052	319	36	&	&	CCONJ
bracis-19052	319	37	 	 	SPACE
bracis-19052	319	38	lilian	lilian	PROPN
bracis-19052	319	39	berton	berton	PROPN
bracis-19052	319	40	authors	author	NOUN
bracis-19052	319	41	bruno	bruno	PROPN
bracis-19052	319	42	klaus	klaus	PROPN
bracis-19052	319	43	de	de	PROPN
bracis-19052	319	44	aquino	aquino	PROPN
bracis-19052	319	45	afonsoview	afonsoview	NOUN
bracis-19052	319	46	author	author	NOUN
bracis-19052	319	47	publications	publication	NOUN
bracis-19052	319	48	search	search	NOUN
bracis-19052	319	49	author	author	NOUN
bracis-19052	319	50	on	on	ADP
bracis-19052	319	51	:	:	PUNCT
bracis-19052	319	52	pubmed	pubmed	PROPN
bracis-19052	319	53	 	 	SPACE
bracis-19052	319	54	google	google	PROPN
bracis-19052	319	55	scholar	scholar	NOUN
bracis-19052	319	56	lilian	lilian	ADJ
bracis-19052	319	57	bertonview	bertonview	NOUN
bracis-19052	319	58	author	author	NOUN
bracis-19052	319	59	publications	publication	VERB
bracis-19052	319	60	search	search	NOUN
bracis-19052	319	61	author	author	NOUN
bracis-19052	319	62	on	on	ADP
bracis-19052	319	63	:	:	PUNCT
bracis-19052	319	64	pubmed	pubmed	PROPN
bracis-19052	319	65	 	 	SPACE
bracis-19052	319	66	google	google	PROPN
bracis-19052	319	67	scholar	scholar	NOUN
bracis-19052	319	68	corresponding	correspond	VERB
bracis-19052	319	69	authors	author	NOUN
bracis-19052	319	70	correspondence	correspondence	NOUN
bracis-19052	319	71	to	to	ADP
bracis-19052	319	72	bruno	bruno	PROPN
bracis-19052	319	73	klaus	klaus	PROPN
bracis-19052	319	74	de	de	PROPN
bracis-19052	319	75	aquino	aquino	PROPN
bracis-19052	319	76	afonso	afonso	PROPN
bracis-19052	319	77	or	or	CCONJ
bracis-19052	319	78	lilian	lilian	PROPN
bracis-19052	319	79	berton	berton	PROPN
bracis-19052	319	80	.	.	PUNCT
bracis-19052	320	1	editor	editor	NOUN
bracis-19052	320	2	information	information	NOUN
bracis-19052	320	3	editors	editor	NOUN
bracis-19052	320	4	and	and	CCONJ
bracis-19052	320	5	affiliations	affiliation	NOUN
bracis-19052	320	6	universidade	universidade	PROPN
bracis-19052	320	7	federal	federal	PROPN
bracis-19052	320	8	de	de	X
bracis-19052	320	9	sergipe	sergipe	PROPN
bracis-19052	320	10	,	,	PUNCT
bracis-19052	320	11	são	são	NOUN
bracis-19052	320	12	cristóvão	cristóvão	PROPN
bracis-19052	320	13	,	,	PUNCT
bracis-19052	320	14	brazil	brazil	PROPN
bracis-19052	320	15	andré	andré	PROPN
bracis-19052	320	16	britto	britto	PROPN
bracis-19052	320	17	universidade	universidade	PROPN
bracis-19052	320	18	de	de	PROPN
bracis-19052	320	19	são	são	PROPN
bracis-19052	320	20	paulo	paulo	PROPN
bracis-19052	320	21	,	,	PUNCT
bracis-19052	320	22	são	são	PROPN
bracis-19052	320	23	paulo	paulo	PROPN
bracis-19052	320	24	,	,	PUNCT
bracis-19052	320	25	brazil	brazil	PROPN
bracis-19052	320	26	karina	karina	PROPN
bracis-19052	320	27	valdivia	valdivia	PROPN
bracis-19052	320	28	delgado	delgado	VERB
bracis-19052	320	29	rights	right	NOUN
bracis-19052	320	30	and	and	CCONJ
bracis-19052	320	31	permissions	permission	NOUN
bracis-19052	320	32	reprints	reprint	NOUN
bracis-19052	320	33	and	and	CCONJ
bracis-19052	320	34	permissions	permission	VERB
bracis-19052	320	35	copyright	copyright	NOUN
bracis-19052	320	36	information	information	NOUN
bracis-19052	320	37	©	©	PROPN
bracis-19052	320	38	2021	2021	NUM
bracis-19052	320	39	springer	springer	NOUN
bracis-19052	320	40	nature	nature	NOUN
bracis-19052	320	41	switzerland	switzerland	PROPN
bracis-19052	320	42	ag	ag	PROPN
bracis-19052	320	43	about	about	ADP
bracis-19052	320	44	this	this	DET
bracis-19052	320	45	paper	paper	NOUN
bracis-19052	320	46	cite	cite	VERB
bracis-19052	320	47	this	this	DET
bracis-19052	320	48	paper	paper	NOUN
bracis-19052	320	49	de	de	X
bracis-19052	320	50	aquino	aquino	PROPN
bracis-19052	320	51	afonso	afonso	PROPN
bracis-19052	320	52	,	,	PUNCT
bracis-19052	320	53	b.k	b.k	PROPN
bracis-19052	320	54	.	.	PROPN
bracis-19052	320	55	,	,	PUNCT
bracis-19052	320	56	berton	berton	PROPN
bracis-19052	320	57	,	,	PUNCT
bracis-19052	320	58	l.	l.	PROPN
bracis-19052	320	59	(	(	PUNCT
bracis-19052	320	60	2021	2021	NUM
bracis-19052	320	61	)	)	PUNCT
bracis-19052	320	62	.	.	PUNCT
bracis-19052	321	1	optimizing	optimize	VERB
bracis-19052	321	2	diffusion	diffusion	NOUN
bracis-19052	321	3	rate	rate	NOUN
bracis-19052	321	4	and	and	CCONJ
bracis-19052	321	5	label	label	NOUN
bracis-19052	321	6	reliability	reliability	NOUN
bracis-19052	321	7	in	in	ADP
bracis-19052	321	8	a	a	DET
bracis-19052	321	9	graph	graph	NOUN
bracis-19052	321	10	-	-	PUNCT
bracis-19052	321	11	based	base	VERB
bracis-19052	321	12	semi	semi	ADJ
bracis-19052	321	13	-	-	ADJ
bracis-19052	321	14	supervised	supervised	ADJ
bracis-19052	321	15	classifier	classifier	NOUN
bracis-19052	321	16	.	.	PUNCT
bracis-19052	322	1	in	in	ADP
bracis-19052	322	2	:	:	PUNCT
bracis-19052	322	3	britto	britto	PROPN
bracis-19052	322	4	,	,	PUNCT
bracis-19052	322	5	a.	a.	PROPN
bracis-19052	322	6	,	,	PUNCT
bracis-19052	322	7	valdivia	valdivia	PROPN
bracis-19052	322	8	delgado	delgado	PROPN
bracis-19052	322	9	,	,	PUNCT
bracis-19052	322	10	k.	k.	PROPN
bracis-19052	322	11	(	(	PUNCT
bracis-19052	322	12	eds	eds	PROPN
bracis-19052	322	13	)	)	PUNCT
bracis-19052	322	14	intelligent	intelligent	ADJ
bracis-19052	322	15	systems	system	NOUN
bracis-19052	322	16	.	.	PUNCT
bracis-19052	323	1	bracis	bracis	PROPN
bracis-19052	323	2	2021	2021	NUM
bracis-19052	323	3	.	.	PUNCT
bracis-19052	324	1	lecture	lecture	NOUN
bracis-19052	324	2	notes	note	NOUN
bracis-19052	324	3	in	in	ADP
bracis-19052	324	4	computer	computer	NOUN
bracis-19052	324	5	science	science	NOUN
bracis-19052	324	6	(	(	PUNCT
bracis-19052	324	7	)	)	PUNCT
bracis-19052	324	8	,	,	PUNCT
bracis-19052	324	9	vol	vol	NOUN
bracis-19052	324	10	13073	13073	NUM
bracis-19052	324	11	.	.	PUNCT
bracis-19052	325	1	springer	springer	NOUN
bracis-19052	325	2	,	,	PUNCT
bracis-19052	325	3	cham	cham	PROPN
bracis-19052	325	4	.	.	PUNCT
bracis-19052	326	1	https://doi.org/10.1007/978-3-030-91702-9_34	https://doi.org/10.1007/978-3-030-91702-9_34	PROPN
bracis-19052	326	2	download	download	NOUN
bracis-19052	326	3	citation	citation	NOUN
bracis-19052	326	4	.ris	.ris	PUNCT
bracis-19052	326	5	.enw	.enw	PROPN
bracis-19052	326	6	.bib	.bib	PUNCT
bracis-19052	327	1	doi	doi	PROPN
bracis-19052	327	2	:	:	PUNCT
bracis-19052	327	3	https://doi.org/10.1007/978-3-030-91702-9_34	https://doi.org/10.1007/978-3-030-91702-9_34	NOUN
bracis-19052	327	4	published	publish	VERB
bracis-19052	327	5	:	:	PUNCT
bracis-19052	327	6	28	28	NUM
bracis-19052	327	7	november	november	PROPN
bracis-19052	327	8	2021	2021	NUM
bracis-19052	327	9	publisher	publisher	NOUN
bracis-19052	327	10	name	name	NOUN
bracis-19052	327	11	:	:	PUNCT
bracis-19052	327	12	springer	springer	NOUN
bracis-19052	327	13	,	,	PUNCT
bracis-19052	327	14	cham	cham	PROPN
bracis-19052	327	15	print	print	PROPN
bracis-19052	327	16	isbn	isbn	PROPN
bracis-19052	327	17	:	:	PUNCT
bracis-19052	327	18	978	978	NUM
bracis-19052	327	19	-	-	SYM
bracis-19052	327	20	3	3	NUM
bracis-19052	327	21	-	-	PUNCT
bracis-19052	327	22	030	030	NUM
bracis-19052	327	23	-	-	PUNCT
bracis-19052	327	24	91701	91701	NUM
bracis-19052	327	25	-	-	SYM
bracis-19052	327	26	2	2	NUM
bracis-19052	327	27	online	online	ADJ
bracis-19052	327	28	isbn	isbn	NOUN
bracis-19052	327	29	:	:	PUNCT
bracis-19052	327	30	978	978	NUM
bracis-19052	327	31	-	-	SYM
bracis-19052	327	32	3	3	NUM
bracis-19052	327	33	-	-	PUNCT
bracis-19052	327	34	030	030	NUM
bracis-19052	327	35	-	-	PUNCT
bracis-19052	327	36	91702	91702	NUM
bracis-19052	327	37	-	-	SYM
bracis-19052	327	38	9	9	NUM
bracis-19052	327	39	ebook	ebook	NOUN
bracis-19052	327	40	packages	package	NOUN
bracis-19052	327	41	:	:	PUNCT
bracis-19052	327	42	computer	computer	NOUN
bracis-19052	327	43	sciencecomputer	sciencecomputer	NOUN
bracis-19052	327	44	science	science	NOUN
bracis-19052	327	45	(	(	PUNCT
bracis-19052	327	46	r0	r0	NOUN
bracis-19052	327	47	)	)	PUNCT
bracis-19052	327	48	share	share	VERB
bracis-19052	327	49	this	this	DET
bracis-19052	327	50	paper	paper	NOUN
bracis-19052	327	51	anyone	anyone	PRON
bracis-19052	327	52	you	you	PRON
bracis-19052	327	53	share	share	VERB
bracis-19052	327	54	the	the	DET
bracis-19052	327	55	following	follow	VERB
bracis-19052	327	56	link	link	NOUN
bracis-19052	327	57	with	with	ADP
bracis-19052	327	58	will	will	AUX
bracis-19052	327	59	be	be	AUX
bracis-19052	327	60	able	able	ADJ
bracis-19052	327	61	to	to	PART
bracis-19052	327	62	read	read	VERB
bracis-19052	327	63	this	this	DET
bracis-19052	327	64	content	content	NOUN
bracis-19052	327	65	:	:	PUNCT
bracis-19052	327	66	get	get	VERB
bracis-19052	327	67	shareable	shareable	ADJ
bracis-19052	327	68	linksorry	linksorry	NOUN
bracis-19052	327	69	,	,	PUNCT
bracis-19052	327	70	a	a	DET
bracis-19052	327	71	shareable	shareable	ADJ
bracis-19052	327	72	link	link	NOUN
bracis-19052	327	73	is	be	AUX
bracis-19052	327	74	not	not	PART
bracis-19052	327	75	currently	currently	ADV
bracis-19052	327	76	available	available	ADJ
bracis-19052	327	77	for	for	ADP
bracis-19052	327	78	this	this	DET
bracis-19052	327	79	article	article	NOUN
bracis-19052	327	80	.	.	PUNCT
bracis-19052	328	1	copy	copy	VERB
bracis-19052	328	2	shareable	shareable	ADJ
bracis-19052	328	3	link	link	NOUN
bracis-19052	328	4	to	to	PART
bracis-19052	328	5	clipboard	clipboard	NOUN
bracis-19052	328	6	provided	provide	VERB
bracis-19052	328	7	by	by	ADP
bracis-19052	328	8	the	the	DET
bracis-19052	328	9	springer	springer	NOUN
bracis-19052	328	10	nature	nature	PROPN
bracis-19052	328	11	sharedit	sharedit	PROPN
bracis-19052	328	12	content	content	NOUN
bracis-19052	328	13	-	-	PUNCT
bracis-19052	328	14	sharing	share	VERB
bracis-19052	328	15	initiative	initiative	NOUN
bracis-19052	328	16	keywords	keyword	NOUN
bracis-19052	328	17	machine	machine	NOUN
bracis-19052	328	18	learning	learn	VERB
bracis-19052	328	19	leave	leave	VERB
bracis-19052	328	20	-	-	PUNCT
bracis-19052	328	21	one	one	NUM
bracis-19052	328	22	-	-	PUNCT
bracis-19052	328	23	out	out	NOUN
bracis-19052	328	24	semi	semi	ADJ
bracis-19052	328	25	-	-	ADJ
bracis-19052	328	26	supervised	supervised	ADJ
bracis-19052	328	27	learning	learning	NOUN
bracis-19052	328	28	graph	graph	NOUN
bracis-19052	328	29	-	-	PUNCT
bracis-19052	328	30	based	base	VERB
bracis-19052	328	31	approaches	approach	NOUN
bracis-19052	328	32	label	label	NOUN
bracis-19052	328	33	propagation	propagation	NOUN
bracis-19052	328	34	eigendecomposition	eigendecomposition	NOUN
bracis-19052	328	35	publish	publish	VERB
bracis-19052	328	36	with	with	ADP
bracis-19052	328	37	us	us	PROPN
bracis-19052	328	38	policies	policy	NOUN
bracis-19052	328	39	and	and	CCONJ
bracis-19052	328	40	ethics	ethic	NOUN
bracis-19052	328	41	search	search	NOUN
bracis-19052	328	42	search	search	NOUN
bracis-19052	328	43	by	by	ADP
bracis-19052	328	44	keyword	keyword	NOUN
bracis-19052	328	45	or	or	CCONJ
bracis-19052	328	46	author	author	NOUN
bracis-19052	328	47	search	search	NOUN
bracis-19052	328	48	navigation	navigation	NOUN
bracis-19052	328	49	find	find	VERB
bracis-19052	328	50	a	a	DET
bracis-19052	328	51	journal	journal	NOUN
bracis-19052	328	52	publish	publish	VERB
bracis-19052	328	53	with	with	ADP
bracis-19052	328	54	us	we	PRON
bracis-19052	328	55	track	track	VERB
bracis-19052	328	56	your	your	PRON
bracis-19052	328	57	research	research	NOUN
bracis-19052	328	58	discover	discover	VERB
bracis-19052	328	59	content	content	NOUN
bracis-19052	328	60	journals	journal	NOUN
bracis-19052	328	61	a	a	DET
bracis-19052	328	62	-	-	PUNCT
bracis-19052	328	63	z	z	NOUN
bracis-19052	328	64	books	book	NOUN
bracis-19052	328	65	a	a	DET
bracis-19052	328	66	-	-	PUNCT
bracis-19052	328	67	z	z	NOUN
bracis-19052	328	68	publish	publish	NOUN
bracis-19052	328	69	with	with	ADP
bracis-19052	328	70	us	us	PROPN
bracis-19052	328	71	journal	journal	PROPN
bracis-19052	328	72	finder	finder	PROPN
bracis-19052	328	73	publish	publish	VERB
bracis-19052	328	74	your	your	PRON
bracis-19052	328	75	research	research	NOUN
bracis-19052	328	76	language	language	NOUN
bracis-19052	328	77	editing	edit	VERB
bracis-19052	328	78	open	open	ADJ
bracis-19052	328	79	access	access	NOUN
bracis-19052	328	80	publishing	publishing	NOUN
bracis-19052	328	81	products	product	NOUN
bracis-19052	328	82	and	and	CCONJ
bracis-19052	328	83	services	service	NOUN
bracis-19052	328	84	our	our	PRON
bracis-19052	328	85	products	product	NOUN
bracis-19052	328	86	librarians	librarian	VERB
bracis-19052	328	87	societies	society	NOUN
bracis-19052	328	88	partners	partner	NOUN
bracis-19052	328	89	and	and	CCONJ
bracis-19052	328	90	advertisers	advertiser	NOUN
bracis-19052	328	91	our	our	PRON
bracis-19052	328	92	brands	brand	NOUN
bracis-19052	328	93	springer	springer	NOUN
bracis-19052	328	94	nature	nature	PROPN
bracis-19052	328	95	portfolio	portfolio	PROPN
bracis-19052	328	96	bmc	bmc	PROPN
bracis-19052	328	97	palgrave	palgrave	PROPN
bracis-19052	328	98	macmillan	macmillan	PROPN
bracis-19052	328	99	apress	apress	PROPN
bracis-19052	328	100	discover	discover	VERB
bracis-19052	328	101	your	your	PRON
bracis-19052	328	102	privacy	privacy	NOUN
bracis-19052	328	103	choices	choice	NOUN
bracis-19052	328	104	/	/	SYM
bracis-19052	328	105	manage	manage	NOUN
bracis-19052	328	106	cookies	cookie	NOUN
bracis-19052	328	107	your	your	PRON
bracis-19052	328	108	us	us	PROPN
bracis-19052	329	1	state	state	NOUN
bracis-19052	329	2	privacy	privacy	NOUN
bracis-19052	329	3	rights	right	NOUN
bracis-19052	329	4	accessibility	accessibility	NOUN
bracis-19052	329	5	statement	statement	NOUN
bracis-19052	329	6	terms	term	NOUN
bracis-19052	329	7	and	and	CCONJ
bracis-19052	329	8	conditions	condition	NOUN
bracis-19052	329	9	privacy	privacy	NOUN
bracis-19052	329	10	policy	policy	NOUN
bracis-19052	329	11	help	help	NOUN
bracis-19052	329	12	and	and	CCONJ
bracis-19052	329	13	support	support	VERB
bracis-19052	329	14	legal	legal	ADJ
bracis-19052	329	15	notice	notice	NOUN
bracis-19052	329	16	cancel	cancel	VERB
bracis-19052	329	17	contracts	contract	NOUN
bracis-19052	329	18	here	here	ADV
bracis-19052	329	19	129.74.145.123	129.74.145.123	NUM
bracis-19052	329	20	hesburgh	hesburgh	PROPN
bracis-19052	329	21	library	library	PROPN
bracis-19052	329	22	er	er	INTJ
bracis-19052	329	23	unit	unit	NOUN
bracis-19052	329	24	(	(	PUNCT
bracis-19052	329	25	3005732405	3005732405	NUM
bracis-19052	329	26	)	)	PUNCT
bracis-19052	329	27	northeast	northeast	ADJ
bracis-19052	329	28	research	research	NOUN
bracis-19052	329	29	libraries	library	NOUN
bracis-19052	329	30	(	(	PUNCT
bracis-19052	329	31	nerl	nerl	PROPN
bracis-19052	329	32	)	)	PUNCT
bracis-19052	329	33	(	(	PUNCT
bracis-19052	329	34	8200828607	8200828607	NUM
bracis-19052	329	35	)	)	PUNCT
bracis-19052	329	36	nerl	nerl	VERB
bracis-19052	329	37	ta	ta	X
bracis-19052	329	38	account	account	NOUN
bracis-19052	329	39	(	(	PUNCT
bracis-19052	329	40	3006206169	3006206169	NUM
bracis-19052	329	41	)	)	PUNCT
bracis-19052	329	42	university	university	NOUN
bracis-19052	329	43	of	of	ADP
bracis-19052	329	44	notre	notre	PROPN
bracis-19052	329	45	dame	dame	PROPN
bracis-19052	329	46	hesburgh	hesburgh	PROPN
bracis-19052	329	47	library	library	NOUN
bracis-19052	329	48	(	(	PUNCT
bracis-19052	329	49	3000184373	3000184373	NUM
bracis-19052	329	50	)	)	PUNCT
bracis-19052	330	1	©	©	ADP
bracis-19052	330	2	2025	2025	NUM
bracis-19052	330	3	springer	springer	NOUN
bracis-19052	330	4	nature	nature	NOUN