id	sid	tid	token	lemma	pos
ijassa-386	1	1	advances	advance	NOUN
ijassa-386	1	2	in	in	ADP
ijassa-386	1	3	systems	system	NOUN
ijassa-386	1	4	science	science	NOUN
ijassa-386	1	5	and	and	CCONJ
ijassa-386	1	6	application(2015	application(2015	ADJ
ijassa-386	1	7	)	)	PUNCT
ijassa-386	1	8	vol.15	vol.15	NOUN
ijassa-386	1	9	no.1	no.1	VERB
ijassa-386	1	10	37	37	NUM
ijassa-386	1	11	-	-	SYM
ijassa-386	1	12	44	44	NUM
ijassa-386	1	13	a	a	DET
ijassa-386	1	14	subspace	subspace	NOUN
ijassa-386	1	15	multi	multi	ADJ
ijassa-386	1	16	-	-	ADJ
ijassa-386	1	17	relation	relation	ADJ
ijassa-386	1	18	model	model	NOUN
ijassa-386	1	19	for	for	ADP
ijassa-386	1	20	the	the	DET
ijassa-386	1	21	expression	expression	NOUN
ijassa-386	1	22	of	of	ADP
ijassa-386	1	23	system	system	NOUN
ijassa-386	1	24	complexity	complexity	NOUN
ijassa-386	1	25	dongyun	dongyun	NOUN
ijassa-386	1	26	yi1,2	yi1,2	PROPN
ijassa-386	1	27	,	,	PUNCT
ijassa-386	1	28	yangyang	yangyang	PROPN
ijassa-386	1	29	liu2	liu2	PROPN
ijassa-386	1	30	,	,	PUNCT
ijassa-386	1	31	xiaojie	xiaojie	PROPN
ijassa-386	1	32	wang2	wang2	PROPN
ijassa-386	1	33	,	,	PUNCT
ijassa-386	1	34	zheng	zheng	PROPN
ijassa-386	1	35	xie2	xie2	PROPN
ijassa-386	1	36	,	,	PUNCT
ijassa-386	1	37	xianggui	xianggui	PROPN
ijassa-386	1	38	qu3	qu3	NOUN
ijassa-386	1	39	,	,	PUNCT
ijassa-386	1	40	chengli	chengli	PROPN
ijassa-386	1	41	zhao2	zhao2	NOUN
ijassa-386	1	42	and	and	CCONJ
ijassa-386	1	43	chengping	chengpe	VERB
ijassa-386	1	44	hou2	hou2	NOUN
ijassa-386	1	45	1	1	NUM
ijassa-386	1	46	national	national	ADJ
ijassa-386	1	47	key	key	ADJ
ijassa-386	1	48	laboratory	laboratory	NOUN
ijassa-386	1	49	of	of	ADP
ijassa-386	1	50	high	high	ADJ
ijassa-386	1	51	performance	performance	NOUN
ijassa-386	1	52	computing	computing	NOUN
ijassa-386	1	53	,	,	PUNCT
ijassa-386	1	54	changsha	changsha	PROPN
ijassa-386	1	55	,	,	PUNCT
ijassa-386	1	56	hunan	hunan	PROPN
ijassa-386	1	57	,	,	PUNCT
ijassa-386	1	58	410073	410073	NUM
ijassa-386	1	59	,	,	PUNCT
ijassa-386	1	60	china	china	PROPN
ijassa-386	1	61	;	;	PUNCT
ijassa-386	1	62	2	2	NUM
ijassa-386	1	63	department	department	NOUN
ijassa-386	1	64	of	of	ADP
ijassa-386	1	65	mathematics	mathematic	NOUN
ijassa-386	1	66	and	and	CCONJ
ijassa-386	1	67	system	system	NOUN
ijassa-386	1	68	science	science	NOUN
ijassa-386	1	69	,	,	PUNCT
ijassa-386	1	70	national	national	ADJ
ijassa-386	1	71	university	university	PROPN
ijassa-386	1	72	of	of	ADP
ijassa-386	1	73	defense	defense	PROPN
ijassa-386	1	74	technology	technology	PROPN
ijassa-386	1	75	,	,	PUNCT
ijassa-386	1	76	changsha	changsha	PROPN
ijassa-386	1	77	,	,	PUNCT
ijassa-386	1	78	hunan	hunan	PROPN
ijassa-386	1	79	,	,	PUNCT
ijassa-386	1	80	410073	410073	NUM
ijassa-386	1	81	,	,	PUNCT
ijassa-386	1	82	china	china	PROPN
ijassa-386	1	83	;	;	PUNCT
ijassa-386	1	84	3	3	NUM
ijassa-386	1	85	department	department	NOUN
ijassa-386	1	86	of	of	ADP
ijassa-386	1	87	mathematics	mathematic	NOUN
ijassa-386	1	88	and	and	CCONJ
ijassa-386	1	89	statistics	statistic	NOUN
ijassa-386	1	90	,	,	PUNCT
ijassa-386	1	91	oakland	oakland	PROPN
ijassa-386	1	92	university	university	PROPN
ijassa-386	1	93	,	,	PUNCT
ijassa-386	1	94	rochester	rochester	PROPN
ijassa-386	1	95	,	,	PUNCT
ijassa-386	1	96	michigan	michigan	PROPN
ijassa-386	1	97	,	,	PUNCT
ijassa-386	1	98	48309	48309	NUM
ijassa-386	1	99	,	,	PUNCT
ijassa-386	1	100	usa	usa	PROPN
ijassa-386	1	101	.	.	PROPN
ijassa-386	1	102	abstract	abstract	ADJ
ijassa-386	1	103	modeling	modeling	NOUN
ijassa-386	1	104	expression	expression	NOUN
ijassa-386	1	105	of	of	ADP
ijassa-386	1	106	complexity	complexity	NOUN
ijassa-386	1	107	is	be	AUX
ijassa-386	1	108	one	one	NUM
ijassa-386	1	109	of	of	ADP
ijassa-386	1	110	the	the	DET
ijassa-386	1	111	frontier	frontier	NOUN
ijassa-386	1	112	research	research	NOUN
ijassa-386	1	113	fields	field	NOUN
ijassa-386	1	114	in	in	ADP
ijassa-386	1	115	system	system	NOUN
ijassa-386	1	116	science	science	NOUN
ijassa-386	1	117	.	.	PUNCT
ijassa-386	2	1	classical	classical	ADJ
ijassa-386	2	2	graphical	graphical	ADJ
ijassa-386	2	3	models	model	NOUN
ijassa-386	2	4	characterize	characterize	VERB
ijassa-386	2	5	two	two	NUM
ijassa-386	2	6	-	-	PUNCT
ijassa-386	2	7	relations	relation	NOUN
ijassa-386	2	8	but	but	CCONJ
ijassa-386	2	9	lack	lack	NOUN
ijassa-386	2	10	of	of	ADP
ijassa-386	2	11	the	the	DET
ijassa-386	2	12	ability	ability	NOUN
ijassa-386	2	13	of	of	ADP
ijassa-386	2	14	depicting	depict	VERB
ijassa-386	2	15	multi	multi	NOUN
ijassa-386	2	16	-	-	NOUN
ijassa-386	2	17	relations	relation	NOUN
ijassa-386	2	18	among	among	ADP
ijassa-386	2	19	objects	object	NOUN
ijassa-386	2	20	in	in	ADP
ijassa-386	2	21	a	a	DET
ijassa-386	2	22	system	system	NOUN
ijassa-386	2	23	.	.	PUNCT
ijassa-386	3	1	in	in	ADP
ijassa-386	3	2	this	this	DET
ijassa-386	3	3	paper	paper	NOUN
ijassa-386	3	4	,	,	PUNCT
ijassa-386	3	5	a	a	DET
ijassa-386	3	6	multi	multi	ADJ
ijassa-386	3	7	-	-	ADJ
ijassa-386	3	8	relation	relation	ADJ
ijassa-386	3	9	expression	expression	NOUN
ijassa-386	3	10	model	model	NOUN
ijassa-386	3	11	is	be	AUX
ijassa-386	3	12	proposed	propose	VERB
ijassa-386	3	13	based	base	VERB
ijassa-386	3	14	the	the	DET
ijassa-386	3	15	subspaces	subspace	NOUN
ijassa-386	3	16	of	of	ADP
ijassa-386	3	17	the	the	DET
ijassa-386	3	18	attribute	attribute	NOUN
ijassa-386	3	19	space	space	NOUN
ijassa-386	3	20	of	of	ADP
ijassa-386	3	21	objects	object	NOUN
ijassa-386	3	22	in	in	ADP
ijassa-386	3	23	a	a	DET
ijassa-386	3	24	system	system	NOUN
ijassa-386	3	25	.	.	PUNCT
ijassa-386	4	1	properties	property	NOUN
ijassa-386	4	2	of	of	ADP
ijassa-386	4	3	the	the	DET
ijassa-386	4	4	multi	multi	ADJ
ijassa-386	4	5	-	-	ADJ
ijassa-386	4	6	relation	relation	ADJ
ijassa-386	4	7	model	model	NOUN
ijassa-386	4	8	are	be	AUX
ijassa-386	4	9	analyzed	analyze	VERB
ijassa-386	4	10	and	and	CCONJ
ijassa-386	4	11	an	an	DET
ijassa-386	4	12	algorithm	algorithm	NOUN
ijassa-386	4	13	is	be	AUX
ijassa-386	4	14	provided	provide	VERB
ijassa-386	4	15	to	to	PART
ijassa-386	4	16	find	find	VERB
ijassa-386	4	17	the	the	DET
ijassa-386	4	18	multi	multi	ADJ
ijassa-386	4	19	-	-	ADJ
ijassa-386	4	20	relation	relation	NOUN
ijassa-386	4	21	subspaces	subspace	NOUN
ijassa-386	4	22	in	in	ADP
ijassa-386	4	23	a	a	DET
ijassa-386	4	24	data	data	NOUN
ijassa-386	4	25	set	set	VERB
ijassa-386	4	26	.	.	PUNCT
ijassa-386	5	1	the	the	DET
ijassa-386	5	2	relationship	relationship	NOUN
ijassa-386	5	3	between	between	ADP
ijassa-386	5	4	the	the	DET
ijassa-386	5	5	multi	multi	ADJ
ijassa-386	5	6	-	-	ADJ
ijassa-386	5	7	relation	relation	NOUN
ijassa-386	5	8	model	model	NOUN
ijassa-386	5	9	and	and	CCONJ
ijassa-386	5	10	a	a	DET
ijassa-386	5	11	hyper	hyper	ADJ
ijassa-386	5	12	graphical	graphical	ADJ
ijassa-386	5	13	model	model	NOUN
ijassa-386	5	14	is	be	AUX
ijassa-386	5	15	also	also	ADV
ijassa-386	5	16	discussed	discuss	VERB
ijassa-386	5	17	.	.	PUNCT
ijassa-386	6	1	keywords	keyword	VERB
ijassa-386	6	2	complexity	complexity	NOUN
ijassa-386	6	3	;	;	PUNCT
ijassa-386	6	4	relation	relation	NOUN
ijassa-386	6	5	;	;	PUNCT
ijassa-386	6	6	subspace	subspace	NOUN
ijassa-386	6	7	;	;	PUNCT
ijassa-386	6	8	hyper	hyper	NOUN
ijassa-386	6	9	-	-	NOUN
ijassa-386	6	10	graph	graph	NOUN
ijassa-386	6	11	.	.	PUNCT
ijassa-386	7	1	1	1	NUM
ijassa-386	7	2	introduction	introduction	NOUN
ijassa-386	7	3	there	there	PRON
ijassa-386	7	4	are	be	VERB
ijassa-386	7	5	two	two	NUM
ijassa-386	7	6	types	type	NOUN
ijassa-386	7	7	of	of	ADP
ijassa-386	7	8	research	research	NOUN
ijassa-386	7	9	in	in	ADP
ijassa-386	7	10	studying	study	VERB
ijassa-386	7	11	the	the	DET
ijassa-386	7	12	complexity	complexity	NOUN
ijassa-386	7	13	of	of	ADP
ijassa-386	7	14	a	a	DET
ijassa-386	7	15	system	system	NOUN
ijassa-386	7	16	[	[	X
ijassa-386	7	17	1	1	NUM
ijassa-386	7	18	-	-	SYM
ijassa-386	7	19	3	3	NUM
ijassa-386	7	20	]	]	PUNCT
ijassa-386	7	21	,	,	PUNCT
ijassa-386	7	22	one	one	PRON
ijassa-386	7	23	considers	consider	VERB
ijassa-386	7	24	how	how	SCONJ
ijassa-386	7	25	to	to	PART
ijassa-386	7	26	characterize	characterize	VERB
ijassa-386	7	27	and	and	CCONJ
ijassa-386	7	28	compute	compute	VERB
ijassa-386	7	29	the	the	DET
ijassa-386	7	30	overall	overall	ADJ
ijassa-386	7	31	complexity	complexity	NOUN
ijassa-386	7	32	of	of	ADP
ijassa-386	7	33	a	a	DET
ijassa-386	7	34	system	system	NOUN
ijassa-386	7	35	[	[	X
ijassa-386	7	36	4	4	NUM
ijassa-386	7	37	]	]	PUNCT
ijassa-386	7	38	.	.	PUNCT
ijassa-386	8	1	boltzmann	boltzmann	PROPN
ijassa-386	8	2	entropy	entropy	PROPN
ijassa-386	8	3	in	in	ADP
ijassa-386	8	4	statistical	statistical	ADJ
ijassa-386	8	5	physics	physics	NOUN
ijassa-386	8	6	is	be	AUX
ijassa-386	8	7	such	such	DET
ijassa-386	8	8	a	a	DET
ijassa-386	8	9	representative	representative	NOUN
ijassa-386	8	10	which	which	PRON
ijassa-386	8	11	gives	give	VERB
ijassa-386	8	12	an	an	DET
ijassa-386	8	13	overall	overall	ADJ
ijassa-386	8	14	measure	measure	NOUN
ijassa-386	8	15	for	for	ADP
ijassa-386	8	16	the	the	DET
ijassa-386	8	17	system	system	NOUN
ijassa-386	8	18	status	status	NOUN
ijassa-386	8	19	.	.	PUNCT
ijassa-386	9	1	the	the	DET
ijassa-386	9	2	other	other	ADJ
ijassa-386	9	3	type	type	NOUN
ijassa-386	9	4	of	of	ADP
ijassa-386	9	5	research	research	NOUN
ijassa-386	9	6	describes	describe	VERB
ijassa-386	9	7	the	the	DET
ijassa-386	9	8	interactive	interactive	ADJ
ijassa-386	9	9	relationships	relationship	NOUN
ijassa-386	9	10	among	among	ADP
ijassa-386	9	11	various	various	ADJ
ijassa-386	9	12	objects	object	NOUN
ijassa-386	9	13	in	in	ADP
ijassa-386	9	14	a	a	DET
ijassa-386	9	15	system	system	NOUN
ijassa-386	9	16	.	.	PUNCT
ijassa-386	10	1	graphical	graphical	ADJ
ijassa-386	10	2	models	model	NOUN
ijassa-386	10	3	from	from	ADP
ijassa-386	10	4	graph	graph	NOUN
ijassa-386	10	5	theory	theory	NOUN
ijassa-386	10	6	or	or	CCONJ
ijassa-386	10	7	complex	complex	ADJ
ijassa-386	10	8	network	network	NOUN
ijassa-386	10	9	are	be	AUX
ijassa-386	10	10	typical	typical	ADJ
ijassa-386	10	11	representatives	representative	NOUN
ijassa-386	10	12	[	[	X
ijassa-386	10	13	5	5	NUM
ijassa-386	10	14	]	]	PUNCT
ijassa-386	10	15	.	.	PUNCT
ijassa-386	11	1	a	a	DET
ijassa-386	11	2	graphical	graphical	ADJ
ijassa-386	11	3	model	model	NOUN
ijassa-386	11	4	regards	regard	VERB
ijassa-386	11	5	the	the	DET
ijassa-386	11	6	objects	object	NOUN
ijassa-386	11	7	in	in	ADP
ijassa-386	11	8	a	a	DET
ijassa-386	11	9	system	system	NOUN
ijassa-386	11	10	as	as	ADP
ijassa-386	11	11	vertices	vertex	NOUN
ijassa-386	11	12	and	and	CCONJ
ijassa-386	11	13	relationships	relationship	NOUN
ijassa-386	11	14	among	among	ADP
ijassa-386	11	15	objects	object	NOUN
ijassa-386	11	16	as	as	ADP
ijassa-386	11	17	edges	edge	NOUN
ijassa-386	11	18	that	that	PRON
ijassa-386	11	19	can	can	AUX
ijassa-386	11	20	be	be	AUX
ijassa-386	11	21	undirected	undirected	ADJ
ijassa-386	11	22	,	,	PUNCT
ijassa-386	11	23	directed	direct	VERB
ijassa-386	11	24	or	or	CCONJ
ijassa-386	11	25	weighted	weight	VERB
ijassa-386	11	26	.	.	PUNCT
ijassa-386	12	1	graphical	graphical	ADJ
ijassa-386	12	2	models	model	NOUN
ijassa-386	12	3	have	have	VERB
ijassa-386	12	4	a	a	DET
ijassa-386	12	5	lot	lot	NOUN
ijassa-386	12	6	of	of	ADP
ijassa-386	12	7	applications	application	NOUN
ijassa-386	12	8	in	in	ADP
ijassa-386	12	9	the	the	DET
ijassa-386	12	10	analysis	analysis	NOUN
ijassa-386	12	11	of	of	ADP
ijassa-386	12	12	e	e	NOUN
ijassa-386	12	13	-	-	NOUN
ijassa-386	12	14	mail	mail	NOUN
ijassa-386	12	15	data	datum	NOUN
ijassa-386	12	16	,	,	PUNCT
ijassa-386	12	17	communication	communication	NOUN
ijassa-386	12	18	data	datum	NOUN
ijassa-386	12	19	,	,	PUNCT
ijassa-386	12	20	web	web	NOUN
ijassa-386	12	21	data	datum	NOUN
ijassa-386	12	22	,	,	PUNCT
ijassa-386	12	23	biological	biological	ADJ
ijassa-386	12	24	data	datum	NOUN
ijassa-386	12	25	,	,	PUNCT
ijassa-386	12	26	financial	financial	ADJ
ijassa-386	12	27	data	datum	NOUN
ijassa-386	12	28	,	,	PUNCT
ijassa-386	12	29	social	social	ADJ
ijassa-386	12	30	networks	network	NOUN
ijassa-386	12	31	,	,	PUNCT
ijassa-386	12	32	actor	actor	NOUN
ijassa-386	12	33	networks	network	NOUN
ijassa-386	12	34	,	,	PUNCT
ijassa-386	12	35	etc	etc	X
ijassa-386	12	36	.	.	X
ijassa-386	13	1	[	[	X
ijassa-386	13	2	6	6	NUM
ijassa-386	13	3	-	-	SYM
ijassa-386	13	4	8	8	NUM
ijassa-386	13	5	]	]	PUNCT
ijassa-386	13	6	.	.	PUNCT
ijassa-386	14	1	however	however	ADV
ijassa-386	14	2	,	,	PUNCT
ijassa-386	14	3	graphical	graphical	ADJ
ijassa-386	14	4	models	model	NOUN
ijassa-386	14	5	only	only	ADV
ijassa-386	14	6	depict	depict	VERB
ijassa-386	14	7	two	two	NUM
ijassa-386	14	8	-	-	PUNCT
ijassa-386	14	9	relation	relation	NOUN
ijassa-386	14	10	between	between	ADP
ijassa-386	14	11	objects	object	NOUN
ijassa-386	14	12	,	,	PUNCT
ijassa-386	14	13	lack	lack	NOUN
ijassa-386	14	14	of	of	ADP
ijassa-386	14	15	the	the	DET
ijassa-386	14	16	description	description	NOUN
ijassa-386	14	17	of	of	ADP
ijassa-386	14	18	multi	multi	NOUN
ijassa-386	14	19	-	-	NOUN
ijassa-386	14	20	relation	relation	NOUN
ijassa-386	14	21	in	in	ADP
ijassa-386	14	22	a	a	DET
ijassa-386	14	23	system	system	NOUN
ijassa-386	14	24	in	in	ADP
ijassa-386	14	25	practice	practice	NOUN
ijassa-386	14	26	.	.	PUNCT
ijassa-386	15	1	recently	recently	ADV
ijassa-386	15	2	,	,	PUNCT
ijassa-386	15	3	some	some	DET
ijassa-386	15	4	research	research	NOUN
ijassa-386	15	5	articles	article	NOUN
ijassa-386	15	6	discuss	discuss	VERB
ijassa-386	15	7	the	the	DET
ijassa-386	15	8	multi	multi	NOUN
ijassa-386	15	9	-	-	NOUN
ijassa-386	15	10	relation	relation	NOUN
ijassa-386	15	11	using	use	VERB
ijassa-386	15	12	hyper	hyper	ADJ
ijassa-386	15	13	-	-	ADJ
ijassa-386	15	14	graph	graph	NOUN
ijassa-386	15	15	models	model	NOUN
ijassa-386	15	16	[	[	X
ijassa-386	15	17	9	9	NUM
ijassa-386	15	18	-	-	SYM
ijassa-386	15	19	13	13	NUM
ijassa-386	15	20	]	]	PUNCT
ijassa-386	15	21	,	,	PUNCT
ijassa-386	15	22	but	but	CCONJ
ijassa-386	15	23	no	no	DET
ijassa-386	15	24	rigorous	rigorous	ADJ
ijassa-386	15	25	definitions	definition	NOUN
ijassa-386	15	26	and	and	CCONJ
ijassa-386	15	27	generating	generating	NOUN
ijassa-386	15	28	methods	method	NOUN
ijassa-386	15	29	of	of	ADP
ijassa-386	15	30	hyper	hyper	NOUN
ijassa-386	15	31	-	-	NOUN
ijassa-386	15	32	graphs	graph	NOUN
ijassa-386	15	33	from	from	ADP
ijassa-386	15	34	data	datum	NOUN
ijassa-386	15	35	are	be	AUX
ijassa-386	15	36	given	give	VERB
ijassa-386	15	37	.	.	PUNCT
ijassa-386	16	1	in	in	ADP
ijassa-386	16	2	this	this	DET
ijassa-386	16	3	paper	paper	NOUN
ijassa-386	16	4	,	,	PUNCT
ijassa-386	16	5	we	we	PRON
ijassa-386	16	6	propose	propose	VERB
ijassa-386	16	7	a	a	DET
ijassa-386	16	8	subspace	subspace	NOUN
ijassa-386	16	9	multi	multi	ADJ
ijassa-386	16	10	-	-	ADJ
ijassa-386	16	11	relation	relation	ADJ
ijassa-386	16	12	model	model	NOUN
ijassa-386	16	13	to	to	PART
ijassa-386	16	14	characterize	characterize	VERB
ijassa-386	16	15	the	the	DET
ijassa-386	16	16	this	this	DET
ijassa-386	16	17	research	research	NOUN
ijassa-386	16	18	is	be	AUX
ijassa-386	16	19	supported	support	VERB
ijassa-386	16	20	by	by	ADP
ijassa-386	16	21	the	the	DET
ijassa-386	16	22	natural	natural	ADJ
ijassa-386	16	23	science	science	PROPN
ijassa-386	16	24	foundation	foundation	NOUN
ijassa-386	16	25	of	of	ADP
ijassa-386	16	26	china(no.61473302	china(no.61473302	PROPN
ijassa-386	16	27	)	)	PUNCT
ijassa-386	16	28	,	,	PUNCT
ijassa-386	16	29	the	the	DET
ijassa-386	16	30	basic	basic	ADJ
ijassa-386	16	31	research	research	NOUN
ijassa-386	16	32	project	project	NOUN
ijassa-386	16	33	of	of	ADP
ijassa-386	16	34	nudt	nudt	NOUN
ijassa-386	16	35	and	and	CCONJ
ijassa-386	16	36	the	the	DET
ijassa-386	16	37	open	open	ADJ
ijassa-386	16	38	fund	fund	NOUN
ijassa-386	16	39	from	from	ADP
ijassa-386	16	40	hpcl	hpcl	NOUN
ijassa-386	16	41	.	.	PUNCT
ijassa-386	17	1	38	38	NUM
ijassa-386	17	2	dongyun	dongyun	NOUN
ijassa-386	17	3	yi	yi	NOUN
ijassa-386	17	4	:	:	PUNCT
ijassa-386	17	5	a	a	DET
ijassa-386	17	6	subspace	subspace	ADJ
ijassa-386	17	7	multi	multi	ADJ
ijassa-386	17	8	-	-	ADJ
ijassa-386	17	9	relation	relation	ADJ
ijassa-386	17	10	model	model	NOUN
ijassa-386	17	11	for	for	ADP
ijassa-386	17	12	the	the	DET
ijassa-386	17	13	expression	expression	NOUN
ijassa-386	17	14	of	of	ADP
ijassa-386	17	15	system	system	NOUN
ijassa-386	17	16	complexity	complexity	NOUN
ijassa-386	17	17	different	different	ADJ
ijassa-386	17	18	types	type	NOUN
ijassa-386	17	19	of	of	ADP
ijassa-386	17	20	relationships	relationship	NOUN
ijassa-386	17	21	in	in	ADP
ijassa-386	17	22	the	the	DET
ijassa-386	17	23	attribute	attribute	NOUN
ijassa-386	17	24	space	space	NOUN
ijassa-386	17	25	of	of	ADP
ijassa-386	17	26	objects	object	NOUN
ijassa-386	17	27	.	.	PUNCT
ijassa-386	18	1	in	in	ADP
ijassa-386	18	2	this	this	DET
ijassa-386	18	3	model	model	NOUN
ijassa-386	18	4	,	,	PUNCT
ijassa-386	18	5	each	each	DET
ijassa-386	18	6	relationship	relationship	NOUN
ijassa-386	18	7	exists	exist	VERB
ijassa-386	18	8	in	in	ADP
ijassa-386	18	9	its	its	PRON
ijassa-386	18	10	own	own	ADJ
ijassa-386	18	11	subspace	subspace	NOUN
ijassa-386	18	12	,	,	PUNCT
ijassa-386	18	13	which	which	PRON
ijassa-386	18	14	is	be	AUX
ijassa-386	18	15	a	a	DET
ijassa-386	18	16	part	part	NOUN
ijassa-386	18	17	of	of	ADP
ijassa-386	18	18	the	the	DET
ijassa-386	18	19	attribute	attribute	NOUN
ijassa-386	18	20	space	space	NOUN
ijassa-386	18	21	.	.	PUNCT
ijassa-386	19	1	the	the	DET
ijassa-386	19	2	traditional	traditional	ADJ
ijassa-386	19	3	graph	graph	NOUN
ijassa-386	19	4	model	model	NOUN
ijassa-386	19	5	is	be	AUX
ijassa-386	19	6	a	a	DET
ijassa-386	19	7	special	special	ADJ
ijassa-386	19	8	case	case	NOUN
ijassa-386	19	9	of	of	ADP
ijassa-386	19	10	our	our	PRON
ijassa-386	19	11	model	model	NOUN
ijassa-386	19	12	,	,	PUNCT
ijassa-386	19	13	which	which	PRON
ijassa-386	19	14	can	can	AUX
ijassa-386	19	15	be	be	AUX
ijassa-386	19	16	called	call	VERB
ijassa-386	19	17	one	one	NUM
ijassa-386	19	18	-	-	PUNCT
ijassa-386	19	19	dimension	dimension	NOUN
ijassa-386	19	20	relation	relation	NOUN
ijassa-386	19	21	model.based	model.base	VERB
ijassa-386	19	22	on	on	ADP
ijassa-386	19	23	the	the	DET
ijassa-386	19	24	subspace	subspace	NOUN
ijassa-386	19	25	clustering	cluster	VERB
ijassa-386	19	26	principle	principle	NOUN
ijassa-386	19	27	[	[	X
ijassa-386	19	28	14	14	NUM
ijassa-386	19	29	-	-	SYM
ijassa-386	19	30	16	16	NUM
ijassa-386	19	31	]	]	PUNCT
ijassa-386	19	32	,	,	PUNCT
ijassa-386	19	33	we	we	PRON
ijassa-386	19	34	give	give	VERB
ijassa-386	19	35	the	the	DET
ijassa-386	19	36	algorithm	algorithm	NOUN
ijassa-386	19	37	to	to	PART
ijassa-386	19	38	find	find	VERB
ijassa-386	19	39	subspace	subspace	NOUN
ijassa-386	19	40	multi	multi	NOUN
ijassa-386	19	41	-	-	NOUN
ijassa-386	19	42	relation	relation	NOUN
ijassa-386	19	43	from	from	ADP
ijassa-386	19	44	the	the	DET
ijassa-386	19	45	object	object	NOUN
ijassa-386	19	46	attribute	attribute	NOUN
ijassa-386	19	47	space	space	NOUN
ijassa-386	19	48	,	,	PUNCT
ijassa-386	19	49	which	which	PRON
ijassa-386	19	50	is	be	AUX
ijassa-386	19	51	helpful	helpful	ADJ
ijassa-386	19	52	to	to	PART
ijassa-386	19	53	understand	understand	VERB
ijassa-386	19	54	the	the	DET
ijassa-386	19	55	complexity	complexity	NOUN
ijassa-386	19	56	of	of	ADP
ijassa-386	19	57	data	datum	NOUN
ijassa-386	19	58	from	from	ADP
ijassa-386	19	59	multiple	multiple	ADJ
ijassa-386	19	60	perspectives	perspective	NOUN
ijassa-386	19	61	.	.	PUNCT
ijassa-386	20	1	real	real	ADJ
ijassa-386	20	2	data	datum	NOUN
ijassa-386	20	3	are	be	AUX
ijassa-386	20	4	used	use	VERB
ijassa-386	20	5	to	to	PART
ijassa-386	20	6	verify	verify	VERB
ijassa-386	20	7	the	the	DET
ijassa-386	20	8	validity	validity	NOUN
ijassa-386	20	9	of	of	ADP
ijassa-386	20	10	our	our	PRON
ijassa-386	20	11	model	model	NOUN
ijassa-386	20	12	.	.	PUNCT
ijassa-386	21	1	we	we	PRON
ijassa-386	21	2	discuss	discuss	VERB
ijassa-386	21	3	the	the	DET
ijassa-386	21	4	vector	vector	NOUN
ijassa-386	21	5	hyper	hyper	ADJ
ijassa-386	21	6	-	-	ADJ
ijassa-386	21	7	graph	graph	NOUN
ijassa-386	21	8	models	model	NOUN
ijassa-386	21	9	at	at	ADP
ijassa-386	21	10	the	the	DET
ijassa-386	21	11	end	end	NOUN
ijassa-386	21	12	.	.	PUNCT
ijassa-386	22	1	2	2	NUM
ijassa-386	22	2	methods	method	NOUN
ijassa-386	22	3	2.1	2.1	NUM
ijassa-386	22	4	definitions	definition	NOUN
ijassa-386	22	5	of	of	ADP
ijassa-386	22	6	subspace	subspace	NOUN
ijassa-386	22	7	multi	multi	NOUN
ijassa-386	22	8	-	-	NOUN
ijassa-386	22	9	relation	relation	NOUN
ijassa-386	22	10	in	in	ADP
ijassa-386	22	11	this	this	DET
ijassa-386	22	12	section	section	NOUN
ijassa-386	22	13	,	,	PUNCT
ijassa-386	22	14	we	we	PRON
ijassa-386	22	15	define	define	VERB
ijassa-386	22	16	the	the	DET
ijassa-386	22	17	subspace	subspace	NOUN
ijassa-386	22	18	multi	multi	ADJ
ijassa-386	22	19	-	-	ADJ
ijassa-386	22	20	relation	relation	ADJ
ijassa-386	22	21	model	model	NOUN
ijassa-386	22	22	.	.	PUNCT
ijassa-386	23	1	definition	definition	NOUN
ijassa-386	23	2	2.1	2.1	NUM
ijassa-386	23	3	if	if	SCONJ
ijassa-386	23	4	m	m	NOUN
ijassa-386	23	5	objects	object	VERB
ijassa-386	23	6	have	have	VERB
ijassa-386	23	7	a	a	DET
ijassa-386	23	8	common	common	ADJ
ijassa-386	23	9	property	property	NOUN
ijassa-386	23	10	of	of	ADP
ijassa-386	23	11	p	p	NOUN
ijassa-386	23	12	,	,	PUNCT
ijassa-386	23	13	we	we	PRON
ijassa-386	23	14	call	call	VERB
ijassa-386	23	15	the	the	DET
ijassa-386	23	16	m	m	NOUN
ijassa-386	23	17	objects	object	NOUN
ijassa-386	23	18	as	as	ADP
ijassa-386	23	19	m	m	NOUN
ijassa-386	23	20	-	-	NOUN
ijassa-386	23	21	relation	relation	NOUN
ijassa-386	23	22	.	.	PUNCT
ijassa-386	24	1	in	in	ADP
ijassa-386	24	2	the	the	DET
ijassa-386	24	3	examples	example	NOUN
ijassa-386	24	4	provided	provide	VERB
ijassa-386	24	5	by	by	ADP
ijassa-386	24	6	tables	table	NOUN
ijassa-386	24	7	1	1	NUM
ijassa-386	24	8	and	and	CCONJ
ijassa-386	24	9	2	2	NUM
ijassa-386	24	10	,	,	PUNCT
ijassa-386	24	11	there	there	PRON
ijassa-386	24	12	are	be	VERB
ijassa-386	24	13	three	three	NUM
ijassa-386	24	14	events	event	NOUN
ijassa-386	24	15	and	and	CCONJ
ijassa-386	24	16	three	three	NUM
ijassa-386	24	17	individuals	individual	NOUN
ijassa-386	24	18	.	.	PUNCT
ijassa-386	25	1	property	property	NOUN
ijassa-386	25	2	p	p	PROPN
ijassa-386	25	3	means	mean	VERB
ijassa-386	25	4	that	that	SCONJ
ijassa-386	25	5	there	there	PRON
ijassa-386	25	6	are	be	VERB
ijassa-386	25	7	individuals	individual	NOUN
ijassa-386	25	8	appearing	appear	VERB
ijassa-386	25	9	in	in	ADP
ijassa-386	25	10	the	the	DET
ijassa-386	25	11	same	same	ADJ
ijassa-386	25	12	event	event	NOUN
ijassa-386	25	13	.	.	PUNCT
ijassa-386	26	1	in	in	ADP
ijassa-386	26	2	table	table	NOUN
ijassa-386	26	3	1	1	NUM
ijassa-386	26	4	,	,	PUNCT
ijassa-386	26	5	any	any	DET
ijassa-386	26	6	two	two	NUM
ijassa-386	26	7	individuals	individual	NOUN
ijassa-386	26	8	appear	appear	VERB
ijassa-386	26	9	simultaneously	simultaneously	ADV
ijassa-386	26	10	in	in	ADP
ijassa-386	26	11	one	one	NUM
ijassa-386	26	12	event	event	NOUN
ijassa-386	26	13	,	,	PUNCT
ijassa-386	26	14	and	and	CCONJ
ijassa-386	26	15	therefore	therefore	ADV
ijassa-386	26	16	there	there	PRON
ijassa-386	26	17	exists	exist	VERB
ijassa-386	26	18	a	a	DET
ijassa-386	26	19	two	two	NUM
ijassa-386	26	20	-	-	PUNCT
ijassa-386	26	21	relation	relation	NOUN
ijassa-386	26	22	between	between	ADP
ijassa-386	26	23	any	any	DET
ijassa-386	26	24	two	two	NUM
ijassa-386	26	25	individuals	individual	NOUN
ijassa-386	26	26	,	,	PUNCT
ijassa-386	26	27	which	which	PRON
ijassa-386	26	28	can	can	AUX
ijassa-386	26	29	be	be	AUX
ijassa-386	26	30	expressed	express	VERB
ijassa-386	26	31	by	by	ADP
ijassa-386	26	32	the	the	DET
ijassa-386	26	33	fully	fully	ADV
ijassa-386	26	34	connected	connected	ADJ
ijassa-386	26	35	network	network	NOUN
ijassa-386	26	36	model	model	NOUN
ijassa-386	26	37	.	.	PUNCT
ijassa-386	27	1	in	in	ADP
ijassa-386	27	2	table	table	NOUN
ijassa-386	27	3	2	2	NUM
ijassa-386	27	4	,	,	PUNCT
ijassa-386	27	5	we	we	PRON
ijassa-386	27	6	notice	notice	VERB
ijassa-386	27	7	that	that	SCONJ
ijassa-386	27	8	three	three	NUM
ijassa-386	27	9	individuals	individual	NOUN
ijassa-386	27	10	simultaneously	simultaneously	ADV
ijassa-386	27	11	appear	appear	VERB
ijassa-386	27	12	in	in	ADP
ijassa-386	27	13	the	the	DET
ijassa-386	27	14	event	event	NOUN
ijassa-386	27	15	a.	a.	NOUN
ijassa-386	27	16	individuals	individual	NOUN
ijassa-386	27	17	1	1	NUM
ijassa-386	27	18	,	,	PUNCT
ijassa-386	27	19	3	3	NUM
ijassa-386	27	20	appear	appear	VERB
ijassa-386	27	21	in	in	ADP
ijassa-386	27	22	the	the	DET
ijassa-386	27	23	event	event	NOUN
ijassa-386	27	24	b	b	NOUN
ijassa-386	27	25	and	and	CCONJ
ijassa-386	27	26	individuals	individual	NOUN
ijassa-386	27	27	2	2	NUM
ijassa-386	27	28	,	,	PUNCT
ijassa-386	27	29	3	3	NUM
ijassa-386	27	30	appear	appear	VERB
ijassa-386	27	31	in	in	ADP
ijassa-386	27	32	the	the	DET
ijassa-386	27	33	event	event	NOUN
ijassa-386	27	34	c.	c.	NOUN
ijassa-386	27	35	thus	thus	ADV
ijassa-386	27	36	there	there	PRON
ijassa-386	27	37	are	be	VERB
ijassa-386	27	38	one	one	NUM
ijassa-386	27	39	threerelation	threerelation	NOUN
ijassa-386	27	40	and	and	CCONJ
ijassa-386	27	41	two	two	NUM
ijassa-386	27	42	two	two	NUM
ijassa-386	27	43	-	-	PUNCT
ijassa-386	27	44	relations	relation	NOUN
ijassa-386	27	45	by	by	ADP
ijassa-386	27	46	definition	definition	NOUN
ijassa-386	27	47	2.1	2.1	NUM
ijassa-386	27	48	.	.	PUNCT
ijassa-386	28	1	the	the	DET
ijassa-386	28	2	difference	difference	NOUN
ijassa-386	28	3	between	between	ADP
ijassa-386	28	4	table	table	NOUN
ijassa-386	28	5	2	2	NUM
ijassa-386	28	6	and	and	CCONJ
ijassa-386	28	7	table	table	NOUN
ijassa-386	28	8	1	1	NUM
ijassa-386	28	9	shows	show	VERB
ijassa-386	28	10	that	that	SCONJ
ijassa-386	28	11	:	:	PUNCT
ijassa-386	28	12	firstly	firstly	ADV
ijassa-386	28	13	,	,	PUNCT
ijassa-386	28	14	three	three	NUM
ijassa-386	28	15	-	-	PUNCT
ijassa-386	28	16	relation	relation	NOUN
ijassa-386	28	17	can	can	AUX
ijassa-386	28	18	not	not	PART
ijassa-386	28	19	be	be	AUX
ijassa-386	28	20	obtained	obtain	VERB
ijassa-386	28	21	from	from	ADP
ijassa-386	28	22	tworelation	tworelation	NOUN
ijassa-386	28	23	;	;	PUNCT
ijassa-386	28	24	secondly	secondly	ADV
ijassa-386	28	25	,	,	PUNCT
ijassa-386	28	26	the	the	DET
ijassa-386	28	27	definition	definition	NOUN
ijassa-386	28	28	of	of	ADP
ijassa-386	28	29	the	the	DET
ijassa-386	28	30	multi	multi	NOUN
ijassa-386	28	31	-	-	NOUN
ijassa-386	28	32	relation	relation	NOUN
ijassa-386	28	33	needs	need	NOUN
ijassa-386	28	34	consider	consider	VERB
ijassa-386	28	35	the	the	DET
ijassa-386	28	36	subspace	subspace	NOUN
ijassa-386	28	37	arising	arise	VERB
ijassa-386	28	38	relation	relation	NOUN
ijassa-386	28	39	.	.	PUNCT
ijassa-386	29	1	thus	thus	ADV
ijassa-386	29	2	we	we	PRON
ijassa-386	29	3	should	should	AUX
ijassa-386	29	4	make	make	VERB
ijassa-386	29	5	some	some	DET
ijassa-386	29	6	modification	modification	NOUN
ijassa-386	29	7	to	to	ADP
ijassa-386	29	8	definition	definition	NOUN
ijassa-386	29	9	2.1	2.1	NUM
ijassa-386	29	10	.	.	PUNCT
ijassa-386	29	11	table	table	NOUN
ijassa-386	29	12	1	1	NUM
ijassa-386	29	13	any	any	DET
ijassa-386	29	14	two	two	NUM
ijassa-386	29	15	individuals	individual	NOUN
ijassa-386	29	16	appear	appear	VERB
ijassa-386	29	17	simultaneously	simultaneously	ADV
ijassa-386	29	18	in	in	ADP
ijassa-386	29	19	one	one	NUM
ijassa-386	29	20	event	event	NOUN
ijassa-386	29	21	,	,	PUNCT
ijassa-386	29	22	and	and	CCONJ
ijassa-386	29	23	hence	hence	ADV
ijassa-386	29	24	,	,	PUNCT
ijassa-386	29	25	two	two	NUM
ijassa-386	29	26	-	-	PUNCT
ijassa-386	29	27	relations	relation	NOUN
ijassa-386	29	28	between	between	ADP
ijassa-386	29	29	any	any	DET
ijassa-386	29	30	two	two	NUM
ijassa-386	29	31	of	of	ADP
ijassa-386	29	32	them	they	PRON
ijassa-386	29	33	exist	exist	VERB
ijassa-386	29	34	.	.	PUNCT
ijassa-386	30	1	event	event	NOUN
ijassa-386	30	2	a	a	DET
ijassa-386	30	3	event	event	NOUN
ijassa-386	30	4	b	b	PROPN
ijassa-386	30	5	event	event	NOUN
ijassa-386	30	6	c	c	PROPN
ijassa-386	30	7	individual	individual	ADJ
ijassa-386	30	8	1	1	NUM
ijassa-386	30	9	1	1	NUM
ijassa-386	30	10	1	1	NUM
ijassa-386	30	11	0	0	NUM
ijassa-386	30	12	individual	individual	NOUN
ijassa-386	30	13	2	2	NUM
ijassa-386	30	14	1	1	NUM
ijassa-386	30	15	0	0	NUM
ijassa-386	30	16	1	1	NUM
ijassa-386	30	17	individual	individual	NOUN
ijassa-386	30	18	3	3	NUM
ijassa-386	30	19	0	0	NUM
ijassa-386	30	20	1	1	NUM
ijassa-386	30	21	1	1	NUM
ijassa-386	30	22	table	table	NOUN
ijassa-386	30	23	2	2	NUM
ijassa-386	30	24	there	there	PRON
ijassa-386	30	25	are	be	VERB
ijassa-386	30	26	three	three	NUM
ijassa-386	30	27	individuals	individual	NOUN
ijassa-386	30	28	appearing	appear	VERB
ijassa-386	30	29	in	in	ADP
ijassa-386	30	30	the	the	DET
ijassa-386	30	31	event	event	NOUN
ijassa-386	30	32	a	a	PRON
ijassa-386	30	33	at	at	ADP
ijassa-386	30	34	the	the	DET
ijassa-386	30	35	same	same	ADJ
ijassa-386	30	36	time	time	NOUN
ijassa-386	30	37	,	,	PUNCT
ijassa-386	30	38	which	which	PRON
ijassa-386	30	39	indicates	indicate	VERB
ijassa-386	30	40	that	that	SCONJ
ijassa-386	30	41	a	a	DET
ijassa-386	30	42	three	three	NUM
ijassa-386	30	43	-	-	PUNCT
ijassa-386	30	44	relation	relation	NOUN
ijassa-386	30	45	exists	exist	VERB
ijassa-386	30	46	.	.	PUNCT
ijassa-386	31	1	event	event	NOUN
ijassa-386	31	2	a	a	DET
ijassa-386	31	3	event	event	NOUN
ijassa-386	31	4	b	b	PROPN
ijassa-386	31	5	event	event	NOUN
ijassa-386	31	6	c	c	PROPN
ijassa-386	31	7	individual	individual	ADJ
ijassa-386	31	8	1	1	NUM
ijassa-386	31	9	1	1	NUM
ijassa-386	31	10	1	1	NUM
ijassa-386	31	11	0	0	NUM
ijassa-386	31	12	individual	individual	NOUN
ijassa-386	31	13	2	2	NUM
ijassa-386	31	14	1	1	NUM
ijassa-386	31	15	0	0	NUM
ijassa-386	31	16	1	1	NUM
ijassa-386	31	17	individual	individual	NOUN
ijassa-386	31	18	3	3	NUM
ijassa-386	31	19	1	1	NUM
ijassa-386	31	20	1	1	NUM
ijassa-386	31	21	1	1	NUM
ijassa-386	31	22	establishing	establish	VERB
ijassa-386	31	23	relations	relation	NOUN
ijassa-386	31	24	among	among	ADP
ijassa-386	31	25	objects	object	NOUN
ijassa-386	31	26	needs	need	NOUN
ijassa-386	31	27	to	to	PART
ijassa-386	31	28	consider	consider	VERB
ijassa-386	31	29	the	the	DET
ijassa-386	31	30	object	object	NOUN
ijassa-386	31	31	attribute	attribute	NOUN
ijassa-386	31	32	space	space	NOUN
ijassa-386	31	33	.	.	PUNCT
ijassa-386	32	1	for	for	ADP
ijassa-386	32	2	example	example	NOUN
ijassa-386	32	3	,	,	PUNCT
ijassa-386	32	4	a	a	DET
ijassa-386	32	5	person	person	NOUN
ijassa-386	32	6	can	can	AUX
ijassa-386	32	7	be	be	AUX
ijassa-386	32	8	described	describe	VERB
ijassa-386	32	9	by	by	ADP
ijassa-386	32	10	an	an	DET
ijassa-386	32	11	attribute	attribute	NOUN
ijassa-386	32	12	space	space	NOUN
ijassa-386	32	13	including	include	VERB
ijassa-386	32	14	gender	gender	NOUN
ijassa-386	32	15	,	,	PUNCT
ijassa-386	32	16	age	age	NOUN
ijassa-386	32	17	,	,	PUNCT
ijassa-386	32	18	education	education	NOUN
ijassa-386	32	19	,	,	PUNCT
ijassa-386	32	20	hobby	hobby	NOUN
ijassa-386	32	21	,	,	PUNCT
ijassa-386	32	22	strength	strength	NOUN
ijassa-386	32	23	,	,	PUNCT
ijassa-386	32	24	event	event	NOUN
ijassa-386	32	25	,	,	PUNCT
ijassa-386	32	26	and	and	CCONJ
ijassa-386	32	27	so	so	ADV
ijassa-386	32	28	on	on	ADV
ijassa-386	32	29	;	;	PUNCT
ijassa-386	32	30	an	an	DET
ijassa-386	32	31	email	email	NOUN
ijassa-386	32	32	attribute	attribute	NOUN
ijassa-386	32	33	space	space	NOUN
ijassa-386	32	34	includes	include	VERB
ijassa-386	32	35	sender	sender	NOUN
ijassa-386	32	36	,	,	PUNCT
ijassa-386	32	37	recipient	recipient	NOUN
ijassa-386	32	38	,	,	PUNCT
ijassa-386	32	39	delivery	delivery	NOUN
ijassa-386	32	40	time	time	NOUN
ijassa-386	32	41	,	,	PUNCT
ijassa-386	32	42	subject	subject	ADJ
ijassa-386	32	43	,	,	PUNCT
ijassa-386	32	44	body	body	NOUN
ijassa-386	32	45	,	,	PUNCT
ijassa-386	32	46	attachments	attachment	NOUN
ijassa-386	32	47	,	,	PUNCT
ijassa-386	32	48	and	and	CCONJ
ijassa-386	32	49	people	people	NOUN
ijassa-386	32	50	names	name	NOUN
ijassa-386	32	51	that	that	PRON
ijassa-386	32	52	appear	appear	VERB
ijassa-386	32	53	in	in	ADP
ijassa-386	32	54	the	the	DET
ijassa-386	32	55	mail	mail	NOUN
ijassa-386	32	56	,	,	PUNCT
ijassa-386	32	57	and	and	CCONJ
ijassa-386	32	58	so	so	ADV
ijassa-386	32	59	on	on	ADV
ijassa-386	32	60	.	.	PUNCT
ijassa-386	33	1	hence	hence	ADV
ijassa-386	33	2	each	each	DET
ijassa-386	33	3	object	object	NOUN
ijassa-386	33	4	can	can	AUX
ijassa-386	33	5	be	be	AUX
ijassa-386	33	6	expressed	express	VERB
ijassa-386	33	7	by	by	ADP
ijassa-386	33	8	a	a	DET
ijassa-386	33	9	numerical	numerical	ADJ
ijassa-386	33	10	vector	vector	NOUN
ijassa-386	33	11	in	in	ADP
ijassa-386	33	12	its	its	PRON
ijassa-386	33	13	attribute	attribute	NOUN
ijassa-386	33	14	space	space	NOUN
ijassa-386	33	15	.	.	PUNCT
ijassa-386	34	1	assuming	assume	VERB
ijassa-386	34	2	there	there	PRON
ijassa-386	34	3	are	be	VERB
ijassa-386	34	4	m	m	VERB
ijassa-386	34	5	objects	object	NOUN
ijassa-386	34	6	denoted	denote	VERB
ijassa-386	34	7	by	by	ADP
ijassa-386	34	8	xi	xi	PROPN
ijassa-386	34	9	,	,	PUNCT
ijassa-386	34	10	i	i	PRON
ijassa-386	34	11	=	=	NOUN
ijassa-386	34	12	1	1	NUM
ijassa-386	34	13	,	,	PUNCT
ijassa-386	34	14	2	2	NUM
ijassa-386	34	15	,	,	PUNCT
ijassa-386	34	16	·	·	PUNCT
ijassa-386	34	17	·	·	PUNCT
ijassa-386	34	18	·	·	PUNCT
ijassa-386	34	19	,	,	PUNCT
ijassa-386	34	20	m	m	PROPN
ijassa-386	34	21	,	,	PUNCT
ijassa-386	34	22	of	of	ADP
ijassa-386	34	23	which	which	PRON
ijassa-386	34	24	attribute	attribute	NOUN
ijassa-386	34	25	space	space	NOUN
ijassa-386	34	26	is	be	AUX
ijassa-386	34	27	n	n	ADV
ijassa-386	34	28	-	-	PUNCT
ijassa-386	34	29	dimensional	dimensional	ADJ
ijassa-386	34	30	.	.	PUNCT
ijassa-386	35	1	then	then	ADV
ijassa-386	35	2	each	each	DET
ijassa-386	35	3	object	object	NOUN
ijassa-386	35	4	can	can	AUX
ijassa-386	35	5	be	be	AUX
ijassa-386	35	6	represented	represent	VERB
ijassa-386	35	7	as	as	ADP
ijassa-386	35	8	a	a	DET
ijassa-386	35	9	n	n	ADV
ijassa-386	35	10	-	-	PUNCT
ijassa-386	35	11	dimensional	dimensional	ADJ
ijassa-386	35	12	vector	vector	NOUN
ijassa-386	35	13	xi	xi	X
ijassa-386	35	14	=	=	SYM
ijassa-386	35	15	(	(	PUNCT
ijassa-386	35	16	xi1	xi1	PROPN
ijassa-386	35	17	,	,	PUNCT
ijassa-386	35	18	·	·	PUNCT
ijassa-386	35	19	·	·	PUNCT
ijassa-386	35	20	·	·	PUNCT
ijassa-386	35	21	,	,	PUNCT
ijassa-386	35	22	xin)t	xin)t	PROPN
ijassa-386	35	23	∈	∈	PROPN
ijassa-386	35	24	rn	rn	PROPN
ijassa-386	35	25	,	,	PUNCT
ijassa-386	35	26	i	i	PRON
ijassa-386	35	27	=	=	NOUN
ijassa-386	35	28	advances	advance	NOUN
ijassa-386	35	29	in	in	ADP
ijassa-386	35	30	systems	system	NOUN
ijassa-386	35	31	science	science	NOUN
ijassa-386	35	32	and	and	CCONJ
ijassa-386	35	33	application(2015	application(2015	ADJ
ijassa-386	35	34	)	)	PUNCT
ijassa-386	35	35	vol.15	vol.15	NOUN
ijassa-386	35	36	no.1	no.1	VERB
ijassa-386	35	37	39	39	NUM
ijassa-386	35	38	1	1	NUM
ijassa-386	35	39	,	,	PUNCT
ijassa-386	35	40	2	2	NUM
ijassa-386	35	41	,	,	PUNCT
ijassa-386	35	42	·	·	PUNCT
ijassa-386	35	43	·	·	PUNCT
ijassa-386	35	44	·	·	PUNCT
ijassa-386	35	45	,	,	PUNCT
ijassa-386	35	46	m.	m.	NOUN
ijassa-386	35	47	in	in	ADP
ijassa-386	35	48	order	order	NOUN
ijassa-386	35	49	to	to	PART
ijassa-386	35	50	be	be	AUX
ijassa-386	35	51	able	able	ADJ
ijassa-386	35	52	to	to	PART
ijassa-386	35	53	obtain	obtain	VERB
ijassa-386	35	54	the	the	DET
ijassa-386	35	55	multi	multi	NOUN
ijassa-386	35	56	-	-	NOUN
ijassa-386	35	57	relations	relation	NOUN
ijassa-386	35	58	among	among	ADP
ijassa-386	35	59	objects	object	NOUN
ijassa-386	35	60	from	from	ADP
ijassa-386	35	61	the	the	DET
ijassa-386	35	62	attribute	attribute	NOUN
ijassa-386	35	63	space	space	NOUN
ijassa-386	35	64	,	,	PUNCT
ijassa-386	35	65	we	we	PRON
ijassa-386	35	66	give	give	VERB
ijassa-386	35	67	the	the	DET
ijassa-386	35	68	definition	definition	NOUN
ijassa-386	35	69	of	of	ADP
ijassa-386	35	70	subspace	subspace	PROPN
ijassa-386	35	71	multi	multi	NOUN
ijassa-386	35	72	-	-	NOUN
ijassa-386	35	73	relation	relation	NOUN
ijassa-386	35	74	.	.	PUNCT
ijassa-386	36	1	definition	definition	NOUN
ijassa-386	36	2	2.2	2.2	NUM
ijassa-386	36	3	suppose	suppose	VERB
ijassa-386	36	4	that	that	SCONJ
ijassa-386	36	5	rn	rn	PROPN
ijassa-386	36	6	=	=	SYM
ijassa-386	37	1	x1	x1	PROPN
ijassa-386	37	2	×	×	NOUN
ijassa-386	38	1	x2	x2	NOUN
ijassa-386	38	2	×	×	PROPN
ijassa-386	38	3	·	·	PUNCT
ijassa-386	38	4	·	·	PUNCT
ijassa-386	38	5	·	·	PUNCT
ijassa-386	38	6	×	×	NOUN
ijassa-386	38	7	xn	xn	INTJ
ijassa-386	38	8	,	,	PUNCT
ijassa-386	38	9	and	and	CCONJ
ijassa-386	38	10	if	if	SCONJ
ijassa-386	38	11	there	there	PRON
ijassa-386	38	12	exists	exist	VERB
ijassa-386	38	13	a	a	DET
ijassa-386	38	14	sub	sub	ADJ
ijassa-386	38	15	-	-	NOUN
ijassa-386	38	16	sequence	sequence	NOUN
ijassa-386	38	17	denoted	denote	VERB
ijassa-386	38	18	by	by	ADP
ijassa-386	38	19	i1	i1	PROPN
ijassa-386	38	20	<	<	X
ijassa-386	38	21	i2	i2	PROPN
ijassa-386	38	22	<	<	X
ijassa-386	38	23	·	·	PUNCT
ijassa-386	38	24	·	·	PUNCT
ijassa-386	38	25	·	·	PUNCT
ijassa-386	39	1	<	<	X
ijassa-386	39	2	ik	ik	PROPN
ijassa-386	39	3	,	,	PUNCT
ijassa-386	39	4	aij	aij	PROPN
ijassa-386	39	5	⊂	⊂	PROPN
ijassa-386	39	6	xij	xij	PROPN
ijassa-386	39	7	is	be	AUX
ijassa-386	39	8	a	a	DET
ijassa-386	39	9	subset	subset	NOUN
ijassa-386	39	10	of	of	ADP
ijassa-386	39	11	xij	xij	PROPN
ijassa-386	39	12	,	,	PUNCT
ijassa-386	39	13	j	j	PROPN
ijassa-386	39	14	=	=	SYM
ijassa-386	39	15	1	1	NUM
ijassa-386	39	16	,	,	PUNCT
ijassa-386	39	17	2	2	NUM
ijassa-386	39	18	,	,	PUNCT
ijassa-386	39	19	·	·	PUNCT
ijassa-386	39	20	·	·	PUNCT
ijassa-386	39	21	·	·	PUNCT
ijassa-386	39	22	,	,	PUNCT
ijassa-386	39	23	k	k	X
ijassa-386	39	24	,	,	PUNCT
ijassa-386	39	25	which	which	PRON
ijassa-386	39	26	makes	make	VERB
ijassa-386	39	27	the	the	DET
ijassa-386	39	28	subset	subset	NOUN
ijassa-386	39	29	b	b	NOUN
ijassa-386	39	30	=	=	PUNCT
ijassa-386	39	31	ai1	ai1	VERB
ijassa-386	39	32	×	×	NOUN
ijassa-386	39	33	ai2	ai2	NOUN
ijassa-386	39	34	×	×	NOUN
ijassa-386	39	35	·	·	PUNCT
ijassa-386	39	36	·	·	PUNCT
ijassa-386	39	37	·	·	PUNCT
ijassa-386	39	38	×	×	NOUN
ijassa-386	39	39	aik	aik	NOUN
ijassa-386	39	40	in	in	ADP
ijassa-386	39	41	the	the	DET
ijassa-386	39	42	k	k	ADJ
ijassa-386	39	43	-	-	ADJ
ijassa-386	39	44	dimension	dimension	NOUN
ijassa-386	39	45	subspace	subspace	NOUN
ijassa-386	39	46	xi1	xi1	PROPN
ijassa-386	39	47	×xi2	×xi2	PROPN
ijassa-386	39	48	×	×	PROPN
ijassa-386	39	49	·	·	PUNCT
ijassa-386	39	50	·	·	PUNCT
ijassa-386	39	51	·	·	PUNCT
ijassa-386	40	1	×xik	×xik	PRON
ijassa-386	40	2	has	have	VERB
ijassa-386	40	3	a	a	DET
ijassa-386	40	4	common	common	ADJ
ijassa-386	40	5	property	property	NOUN
ijassa-386	40	6	denoted	denote	VERB
ijassa-386	40	7	by	by	ADP
ijassa-386	40	8	p	p	PROPN
ijassa-386	40	9	.	.	PUNCT
ijassa-386	41	1	then	then	ADV
ijassa-386	41	2	we	we	PRON
ijassa-386	41	3	call	call	VERB
ijassa-386	41	4	set	set	VERB
ijassa-386	41	5	b	b	NOUN
ijassa-386	41	6	as	as	ADP
ijassa-386	41	7	the	the	DET
ijassa-386	41	8	k	k	ADJ
ijassa-386	41	9	-	-	ADJ
ijassa-386	41	10	dimension	dimension	NOUN
ijassa-386	41	11	subspace	subspace	NOUN
ijassa-386	41	12	m	m	PROPN
ijassa-386	41	13	-	-	PUNCT
ijassa-386	41	14	relation	relation	NOUN
ijassa-386	41	15	,	,	PUNCT
ijassa-386	41	16	where	where	SCONJ
ijassa-386	41	17	m	m	NOUN
ijassa-386	41	18	is	be	AUX
ijassa-386	41	19	number	number	NOUN
ijassa-386	41	20	of	of	ADP
ijassa-386	41	21	element	element	NOUN
ijassa-386	41	22	in	in	ADP
ijassa-386	41	23	set	set	PROPN
ijassa-386	41	24	b.	b.	PROPN
ijassa-386	41	25	definition	definition	NOUN
ijassa-386	41	26	2.2	2.2	NUM
ijassa-386	41	27	shows	show	VERB
ijassa-386	41	28	that	that	SCONJ
ijassa-386	41	29	the	the	DET
ijassa-386	41	30	relation	relation	NOUN
ijassa-386	41	31	not	not	PART
ijassa-386	41	32	only	only	ADV
ijassa-386	41	33	means	mean	VERB
ijassa-386	41	34	that	that	SCONJ
ijassa-386	41	35	the	the	DET
ijassa-386	41	36	objects	object	NOUN
ijassa-386	41	37	in	in	ADP
ijassa-386	41	38	set	set	NOUN
ijassa-386	41	39	b	b	PART
ijassa-386	41	40	have	have	VERB
ijassa-386	41	41	a	a	DET
ijassa-386	41	42	common	common	ADJ
ijassa-386	41	43	property	property	NOUN
ijassa-386	41	44	,	,	PUNCT
ijassa-386	41	45	but	but	CCONJ
ijassa-386	41	46	also	also	ADV
ijassa-386	41	47	tells	tell	VERB
ijassa-386	41	48	us	we	PRON
ijassa-386	41	49	that	that	SCONJ
ijassa-386	41	50	the	the	DET
ijassa-386	41	51	relation	relation	NOUN
ijassa-386	41	52	occurs	occur	VERB
ijassa-386	41	53	in	in	ADP
ijassa-386	41	54	which	which	PRON
ijassa-386	41	55	attribute	attribute	NOUN
ijassa-386	41	56	space	space	NOUN
ijassa-386	41	57	.	.	PUNCT
ijassa-386	42	1	as	as	SCONJ
ijassa-386	42	2	defined	define	VERB
ijassa-386	42	3	,	,	PUNCT
ijassa-386	42	4	the	the	DET
ijassa-386	42	5	multi	multi	NOUN
ijassa-386	42	6	-	-	NOUN
ijassa-386	42	7	relation	relation	NOUN
ijassa-386	42	8	in	in	ADP
ijassa-386	42	9	table	table	NOUN
ijassa-386	42	10	1	1	NUM
ijassa-386	42	11	can	can	AUX
ijassa-386	42	12	be	be	AUX
ijassa-386	42	13	written	write	VERB
ijassa-386	42	14	as	as	ADP
ijassa-386	42	15	(	(	PUNCT
ijassa-386	42	16	x1	x1	PROPN
ijassa-386	42	17	,	,	PUNCT
ijassa-386	42	18	x2;a	x2;a	PROPN
ijassa-386	42	19	)	)	PUNCT
ijassa-386	42	20	,	,	PUNCT
ijassa-386	42	21	(	(	PUNCT
ijassa-386	42	22	x1	x1	PROPN
ijassa-386	42	23	,	,	PUNCT
ijassa-386	42	24	x3;b	x3;b	PROPN
ijassa-386	42	25	)	)	PUNCT
ijassa-386	42	26	,	,	PUNCT
ijassa-386	42	27	(	(	PUNCT
ijassa-386	42	28	x2	x2	NOUN
ijassa-386	42	29	,	,	PUNCT
ijassa-386	42	30	x3;c	x3;c	PROPN
ijassa-386	42	31	)	)	PUNCT
ijassa-386	42	32	,	,	PUNCT
ijassa-386	42	33	and	and	CCONJ
ijassa-386	42	34	the	the	DET
ijassa-386	42	35	multi	multi	NOUN
ijassa-386	42	36	-	-	NOUN
ijassa-386	42	37	relation	relation	NOUN
ijassa-386	42	38	in	in	ADP
ijassa-386	42	39	table	table	NOUN
ijassa-386	42	40	2	2	NUM
ijassa-386	42	41	can	can	AUX
ijassa-386	42	42	be	be	AUX
ijassa-386	42	43	written	write	VERB
ijassa-386	42	44	as	as	ADP
ijassa-386	42	45	(	(	PUNCT
ijassa-386	42	46	x1	x1	PROPN
ijassa-386	42	47	,	,	PUNCT
ijassa-386	42	48	x2	x2	PROPN
ijassa-386	42	49	,	,	PUNCT
ijassa-386	42	50	x3;a	x3;a	PROPN
ijassa-386	42	51	)	)	PUNCT
ijassa-386	42	52	,	,	PUNCT
ijassa-386	42	53	(	(	PUNCT
ijassa-386	42	54	x1	x1	PROPN
ijassa-386	42	55	,	,	PUNCT
ijassa-386	42	56	x3;b	x3;b	PROPN
ijassa-386	42	57	)	)	PUNCT
ijassa-386	42	58	,	,	PUNCT
ijassa-386	42	59	(	(	PUNCT
ijassa-386	42	60	x2	x2	NOUN
ijassa-386	42	61	,	,	PUNCT
ijassa-386	42	62	x3;c	x3;c	PROPN
ijassa-386	42	63	)	)	PUNCT
ijassa-386	42	64	.	.	PUNCT
ijassa-386	43	1	therefore	therefore	ADV
ijassa-386	43	2	there	there	PRON
ijassa-386	43	3	are	be	VERB
ijassa-386	43	4	three	three	NUM
ijassa-386	43	5	one	one	NUM
ijassa-386	43	6	-	-	PUNCT
ijassa-386	43	7	dimension	dimension	NOUN
ijassa-386	43	8	subspace	subspace	NOUN
ijassa-386	43	9	two	two	NUM
ijassa-386	43	10	-	-	PUNCT
ijassa-386	43	11	relations	relation	NOUN
ijassa-386	43	12	in	in	ADP
ijassa-386	43	13	table	table	NOUN
ijassa-386	43	14	1	1	NUM
ijassa-386	43	15	,	,	PUNCT
ijassa-386	43	16	and	and	CCONJ
ijassa-386	43	17	two	two	NUM
ijassa-386	43	18	one	one	NUM
ijassa-386	43	19	-	-	PUNCT
ijassa-386	43	20	dimension	dimension	NOUN
ijassa-386	43	21	subspace	subspace	NOUN
ijassa-386	43	22	two	two	NUM
ijassa-386	43	23	-	-	PUNCT
ijassa-386	43	24	relations	relation	NOUN
ijassa-386	43	25	and	and	CCONJ
ijassa-386	43	26	one	one	NUM
ijassa-386	43	27	one	one	NUM
ijassa-386	43	28	-	-	PUNCT
ijassa-386	43	29	dimension	dimension	NOUN
ijassa-386	43	30	subspace	subspace	NOUN
ijassa-386	43	31	three	three	NUM
ijassa-386	43	32	-	-	PUNCT
ijassa-386	43	33	relation	relation	NOUN
ijassa-386	43	34	in	in	ADP
ijassa-386	43	35	table	table	NOUN
ijassa-386	43	36	2	2	NUM
ijassa-386	43	37	.	.	PUNCT
ijassa-386	44	1	we	we	PRON
ijassa-386	44	2	have	have	AUX
ijassa-386	44	3	defined	define	VERB
ijassa-386	44	4	the	the	DET
ijassa-386	44	5	kdimension	kdimension	PROPN
ijassa-386	44	6	subspace	subspace	PROPN
ijassa-386	44	7	multi	multi	PROPN
ijassa-386	44	8	-	-	NOUN
ijassa-386	44	9	relation	relation	NOUN
ijassa-386	44	10	.	.	PUNCT
ijassa-386	45	1	how	how	SCONJ
ijassa-386	45	2	can	can	AUX
ijassa-386	45	3	we	we	PRON
ijassa-386	45	4	compute	compute	VERB
ijassa-386	45	5	subspace	subspace	NOUN
ijassa-386	45	6	multi	multi	NOUN
ijassa-386	45	7	-	-	NOUN
ijassa-386	45	8	relations	relation	NOUN
ijassa-386	45	9	in	in	ADP
ijassa-386	45	10	real	real	ADJ
ijassa-386	45	11	data	datum	NOUN
ijassa-386	45	12	?	?	PUNCT
ijassa-386	46	1	the	the	DET
ijassa-386	46	2	following	follow	VERB
ijassa-386	46	3	definition	definition	NOUN
ijassa-386	46	4	2.3	2.3	NUM
ijassa-386	46	5	provides	provide	VERB
ijassa-386	46	6	a	a	DET
ijassa-386	46	7	solution	solution	NOUN
ijassa-386	46	8	.	.	PUNCT
ijassa-386	47	1	definition	definition	NOUN
ijassa-386	47	2	2.3	2.3	NUM
ijassa-386	47	3	given	give	VERB
ijassa-386	47	4	ϵ	ϵ	PROPN
ijassa-386	47	5	>	>	X
ijassa-386	47	6	0	0	NUM
ijassa-386	47	7	,	,	PUNCT
ijassa-386	47	8	let	let	VERB
ijassa-386	47	9	rn	rn	PROPN
ijassa-386	47	10	=	=	SYM
ijassa-386	48	1	x1	x1	PROPN
ijassa-386	48	2	×	×	NOUN
ijassa-386	49	1	x2	x2	NOUN
ijassa-386	49	2	×	×	PROPN
ijassa-386	49	3	·	·	PUNCT
ijassa-386	49	4	·	·	PUNCT
ijassa-386	49	5	·	·	PUNCT
ijassa-386	50	1	×	×	NOUN
ijassa-386	50	2	xn	xn	INTJ
ijassa-386	50	3	,	,	PUNCT
ijassa-386	50	4	if	if	SCONJ
ijassa-386	50	5	there	there	PRON
ijassa-386	50	6	is	be	VERB
ijassa-386	50	7	a	a	DET
ijassa-386	50	8	subsequence	subsequence	NOUN
ijassa-386	50	9	of	of	ADP
ijassa-386	50	10	1	1	NUM
ijassa-386	50	11	,	,	PUNCT
ijassa-386	50	12	2	2	NUM
ijassa-386	50	13	,	,	PUNCT
ijassa-386	50	14	·	·	PUNCT
ijassa-386	50	15	·	·	PUNCT
ijassa-386	50	16	·	·	PUNCT
ijassa-386	50	17	,	,	PUNCT
ijassa-386	50	18	n	n	CCONJ
ijassa-386	50	19	denoted	denote	VERB
ijassa-386	50	20	by	by	ADP
ijassa-386	50	21	i1	i1	PROPN
ijassa-386	50	22	,	,	PUNCT
ijassa-386	50	23	i2	i2	PROPN
ijassa-386	50	24	<	<	X
ijassa-386	50	25	·	·	PUNCT
ijassa-386	50	26	·	·	PUNCT
ijassa-386	50	27	·	·	PUNCT
ijassa-386	50	28	<	<	X
ijassa-386	50	29	ik	ik	PROPN
ijassa-386	50	30	,	,	PUNCT
ijassa-386	50	31	aij	aij	PROPN
ijassa-386	50	32	⊂	⊂	PROPN
ijassa-386	50	33	xij	xij	PROPN
ijassa-386	50	34	is	be	AUX
ijassa-386	50	35	a	a	DET
ijassa-386	50	36	point	point	NOUN
ijassa-386	50	37	set	set	NOUN
ijassa-386	50	38	of	of	ADP
ijassa-386	50	39	xij	xij	PROPN
ijassa-386	50	40	,	,	PUNCT
ijassa-386	50	41	which	which	PRON
ijassa-386	50	42	makes	make	VERB
ijassa-386	50	43	the	the	DET
ijassa-386	50	44	subset	subset	NOUN
ijassa-386	50	45	b	b	NOUN
ijassa-386	50	46	=	=	PUNCT
ijassa-386	50	47	ai1	ai1	VERB
ijassa-386	50	48	×	×	NOUN
ijassa-386	50	49	ai2	ai2	NOUN
ijassa-386	50	50	×	×	NOUN
ijassa-386	50	51	·	·	PUNCT
ijassa-386	50	52	·	·	PUNCT
ijassa-386	50	53	·	·	PUNCT
ijassa-386	51	1	×	×	INTJ
ijassa-386	51	2	aik	aik	NOUN
ijassa-386	51	3	in	in	ADP
ijassa-386	51	4	xi1	xi1	PROPN
ijassa-386	51	5	×xi2	×xi2	PROPN
ijassa-386	51	6	×	×	PROPN
ijassa-386	51	7	·	·	PUNCT
ijassa-386	51	8	·	·	PUNCT
ijassa-386	51	9	·	·	PUNCT
ijassa-386	52	1	×xik	×xik	PRON
ijassa-386	52	2	be	be	AUX
ijassa-386	52	3	covered	cover	VERB
ijassa-386	52	4	by	by	ADP
ijassa-386	52	5	the	the	DET
ijassa-386	52	6	hypercube	hypercube	NOUN
ijassa-386	52	7	u(ϵ	u(ϵ	PROPN
ijassa-386	52	8	)	)	PUNCT
ijassa-386	52	9	,	,	PUNCT
ijassa-386	52	10	ϵ	ϵ	X
ijassa-386	52	11	>	>	X
ijassa-386	52	12	0	0	PUNCT
ijassa-386	53	1	in	in	ADP
ijassa-386	53	2	rk	rk	NOUN
ijassa-386	53	3	,	,	PUNCT
ijassa-386	53	4	then	then	ADV
ijassa-386	53	5	the	the	DET
ijassa-386	53	6	subset	subset	PROPN
ijassa-386	53	7	b	b	PROPN
ijassa-386	53	8	is	be	AUX
ijassa-386	53	9	called	call	VERB
ijassa-386	53	10	the	the	DET
ijassa-386	53	11	k	k	ADJ
ijassa-386	53	12	-	-	ADJ
ijassa-386	53	13	dimension	dimension	NOUN
ijassa-386	53	14	subspace	subspace	NOUN
ijassa-386	53	15	m	m	NOUN
ijassa-386	53	16	-	-	PUNCT
ijassa-386	53	17	object	object	NOUN
ijassa-386	53	18	relation	relation	NOUN
ijassa-386	53	19	,	,	PUNCT
ijassa-386	53	20	m	m	VERB
ijassa-386	53	21	is	be	AUX
ijassa-386	53	22	the	the	DET
ijassa-386	53	23	number	number	NOUN
ijassa-386	53	24	of	of	ADP
ijassa-386	53	25	element	element	NOUN
ijassa-386	53	26	in	in	ADP
ijassa-386	53	27	subset	subset	PROPN
ijassa-386	53	28	b.	b.	PROPN
ijassa-386	53	29	note	note	PROPN
ijassa-386	53	30	:	:	PUNCT
ijassa-386	53	31	in	in	ADP
ijassa-386	53	32	definition	definition	NOUN
ijassa-386	53	33	2.3	2.3	NUM
ijassa-386	53	34	,	,	PUNCT
ijassa-386	53	35	u(ϵ	u(ϵ	PROPN
ijassa-386	53	36	)	)	PUNCT
ijassa-386	53	37	refers	refer	VERB
ijassa-386	53	38	to	to	ADP
ijassa-386	53	39	the	the	DET
ijassa-386	53	40	k	k	ADJ
ijassa-386	53	41	-	-	ADJ
ijassa-386	53	42	dimensional	dimensional	ADJ
ijassa-386	53	43	hypercube	hypercube	NOUN
ijassa-386	53	44	of	of	ADP
ijassa-386	53	45	side	side	NOUN
ijassa-386	53	46	length	length	NOUN
ijassa-386	53	47	2ϵ	2ϵ	NUM
ijassa-386	53	48	in	in	ADP
ijassa-386	53	49	rk	rk	NOUN
ijassa-386	53	50	,	,	PUNCT
ijassa-386	53	51	where	where	SCONJ
ijassa-386	53	52	ϵ	ϵ	X
ijassa-386	53	53	>	>	X
ijassa-386	53	54	0	0	NUM
ijassa-386	53	55	depends	depend	VERB
ijassa-386	53	56	on	on	ADP
ijassa-386	53	57	the	the	DET
ijassa-386	53	58	specific	specific	ADJ
ijassa-386	53	59	situation	situation	NOUN
ijassa-386	53	60	.	.	PUNCT
ijassa-386	54	1	for	for	ADP
ijassa-386	54	2	example	example	NOUN
ijassa-386	54	3	,	,	PUNCT
ijassa-386	54	4	if	if	SCONJ
ijassa-386	54	5	we	we	PRON
ijassa-386	54	6	define	define	VERB
ijassa-386	54	7	u(ϵ	u(ϵ	NOUN
ijassa-386	54	8	)	)	PUNCT
ijassa-386	54	9	=	=	PRON
ijassa-386	54	10	(	(	PUNCT
ijassa-386	54	11	−ϵ	−ϵ	PROPN
ijassa-386	54	12	,	,	PUNCT
ijassa-386	54	13	ϵ	ϵ	NOUN
ijassa-386	54	14	)	)	PUNCT
ijassa-386	54	15	,	,	PUNCT
ijassa-386	54	16	∀ϵ	∀ϵ	NOUN
ijassa-386	54	17	>	>	X
ijassa-386	54	18	0	0	PUNCT
ijassa-386	55	1	in	in	ADP
ijassa-386	55	2	the	the	DET
ijassa-386	55	3	space	space	NOUN
ijassa-386	55	4	of	of	ADP
ijassa-386	55	5	r1	r1	PROPN
ijassa-386	55	6	,	,	PUNCT
ijassa-386	55	7	then	then	ADV
ijassa-386	55	8	,	,	PUNCT
ijassa-386	55	9	there	there	PRON
ijassa-386	55	10	are	be	VERB
ijassa-386	55	11	one	one	NUM
ijassa-386	55	12	one	one	NUM
ijassa-386	55	13	-	-	PUNCT
ijassa-386	55	14	dimension	dimension	NOUN
ijassa-386	55	15	subspace	subspace	NOUN
ijassa-386	55	16	three	three	NUM
ijassa-386	55	17	-	-	PUNCT
ijassa-386	55	18	relation	relation	NOUN
ijassa-386	55	19	and	and	CCONJ
ijassa-386	55	20	two	two	NUM
ijassa-386	55	21	one	one	NUM
ijassa-386	55	22	-	-	PUNCT
ijassa-386	55	23	dimension	dimension	NOUN
ijassa-386	55	24	subspace	subspace	NOUN
ijassa-386	55	25	two	two	NUM
ijassa-386	55	26	-	-	PUNCT
ijassa-386	55	27	relations	relation	NOUN
ijassa-386	55	28	in	in	ADP
ijassa-386	55	29	table	table	NOUN
ijassa-386	55	30	2	2	NUM
ijassa-386	55	31	by	by	ADP
ijassa-386	55	32	simple	simple	ADJ
ijassa-386	55	33	calculation	calculation	NOUN
ijassa-386	55	34	.	.	PUNCT
ijassa-386	56	1	2.2	2.2	NUM
ijassa-386	56	2	properties	property	NOUN
ijassa-386	56	3	of	of	ADP
ijassa-386	56	4	subspace	subspace	NOUN
ijassa-386	56	5	multi	multi	PROPN
ijassa-386	56	6	-	-	ADJ
ijassa-386	56	7	relation	relation	NOUN
ijassa-386	56	8	theorem	theorem	VERB
ijassa-386	56	9	2.1	2.1	NUM
ijassa-386	56	10	subspace	subspace	NOUN
ijassa-386	56	11	multi	multi	NOUN
ijassa-386	56	12	-	-	NOUN
ijassa-386	56	13	relation	relation	NOUN
ijassa-386	56	14	is	be	AUX
ijassa-386	56	15	of	of	ADP
ijassa-386	56	16	downward	downward	ADJ
ijassa-386	56	17	compatibility	compatibility	NOUN
ijassa-386	56	18	.	.	PUNCT
ijassa-386	57	1	that	that	PRON
ijassa-386	57	2	is	be	AUX
ijassa-386	57	3	to	to	PART
ijassa-386	57	4	say	say	VERB
ijassa-386	57	5	,	,	PUNCT
ijassa-386	57	6	if	if	SCONJ
ijassa-386	57	7	b	b	PROPN
ijassa-386	57	8	is	be	AUX
ijassa-386	57	9	a	a	DET
ijassa-386	57	10	k	k	ADJ
ijassa-386	57	11	-	-	ADJ
ijassa-386	57	12	dimension	dimension	NOUN
ijassa-386	57	13	subspace	subspace	NOUN
ijassa-386	57	14	m	m	PROPN
ijassa-386	57	15	-	-	PUNCT
ijassa-386	57	16	relation	relation	NOUN
ijassa-386	57	17	,	,	PUNCT
ijassa-386	57	18	then	then	ADV
ijassa-386	57	19	for	for	ADP
ijassa-386	57	20	any	any	DET
ijassa-386	57	21	k1,m1	k1,m1	PROPN
ijassa-386	57	22	,	,	PUNCT
ijassa-386	57	23	0	0	PUNCT
ijassa-386	57	24	<	<	X
ijassa-386	57	25	k1	k1	X
ijassa-386	57	26	<	<	X
ijassa-386	57	27	k	k	PROPN
ijassa-386	57	28	,	,	PUNCT
ijassa-386	57	29	0	0	PUNCT
ijassa-386	57	30	<	<	X
ijassa-386	57	31	m1	m1	PROPN
ijassa-386	57	32	<	<	X
ijassa-386	57	33	m	m	PROPN
ijassa-386	57	34	,	,	PUNCT
ijassa-386	57	35	b	b	PROPN
ijassa-386	57	36	is	be	AUX
ijassa-386	57	37	also	also	ADV
ijassa-386	57	38	k1	k1	ADJ
ijassa-386	57	39	-	-	PUNCT
ijassa-386	57	40	dimension	dimension	NOUN
ijassa-386	57	41	subspace	subspace	NOUN
ijassa-386	57	42	m1	m1	NOUN
ijassa-386	57	43	-	-	PUNCT
ijassa-386	57	44	relation	relation	NOUN
ijassa-386	57	45	.	.	PUNCT
ijassa-386	58	1	proof	proof	NOUN
ijassa-386	58	2	.	.	PUNCT
ijassa-386	59	1	let	let	VERB
ijassa-386	59	2	b	b	NOUN
ijassa-386	59	3	=	=	PRON
ijassa-386	59	4	{	{	PUNCT
ijassa-386	59	5	xi|i	xi|i	X
ijassa-386	59	6	=	=	SYM
ijassa-386	59	7	1	1	NUM
ijassa-386	59	8	,	,	PUNCT
ijassa-386	59	9	2	2	NUM
ijassa-386	59	10	,	,	PUNCT
ijassa-386	59	11	·	·	PUNCT
ijassa-386	59	12	·	·	PUNCT
ijassa-386	59	13	·	·	PUNCT
ijassa-386	59	14	,	,	PUNCT
ijassa-386	59	15	m	m	AUX
ijassa-386	59	16	}	}	PUNCT
ijassa-386	59	17	has	have	VERB
ijassa-386	59	18	the	the	DET
ijassa-386	59	19	k	k	ADJ
ijassa-386	59	20	-	-	ADJ
ijassa-386	59	21	dimension	dimension	ADJ
ijassa-386	59	22	m	m	NOUN
ijassa-386	59	23	-	-	NOUN
ijassa-386	59	24	relation	relation	NOUN
ijassa-386	59	25	.	.	PUNCT
ijassa-386	60	1	given	give	VERB
ijassa-386	60	2	ϵ	ϵ	ADP
ijassa-386	60	3	>	>	X
ijassa-386	60	4	0	0	NUM
ijassa-386	60	5	,	,	PUNCT
ijassa-386	60	6	then	then	ADV
ijassa-386	60	7	there	there	PRON
ijassa-386	60	8	exists	exist	VERB
ijassa-386	60	9	a	a	DET
ijassa-386	60	10	positive	positive	ADJ
ijassa-386	60	11	integer	integer	NOUN
ijassa-386	60	12	k	k	NOUN
ijassa-386	60	13	,	,	PUNCT
ijassa-386	60	14	rk	rk	PROPN
ijassa-386	60	15	⊂	⊂	PROPN
ijassa-386	60	16	rn	rn	PROPN
ijassa-386	60	17	,	,	PUNCT
ijassa-386	60	18	which	which	PRON
ijassa-386	60	19	makes	make	VERB
ijassa-386	60	20	the	the	DET
ijassa-386	60	21	projection	projection	NOUN
ijassa-386	60	22	xi|rk	xi|rk	PROPN
ijassa-386	61	1	=	=	PRON
ijassa-386	61	2	(	(	PUNCT
ijassa-386	61	3	xi1	xi1	PROPN
ijassa-386	61	4	,	,	PUNCT
ijassa-386	61	5	xi2	xi2	PROPN
ijassa-386	61	6	,	,	PUNCT
ijassa-386	61	7	·	·	PUNCT
ijassa-386	61	8	·	·	PUNCT
ijassa-386	61	9	·	·	PUNCT
ijassa-386	61	10	,	,	PUNCT
ijassa-386	61	11	xik)t	xik)t	PROPN
ijassa-386	61	12	of	of	ADP
ijassa-386	61	13	xi	xi	PRON
ijassa-386	61	14	covered	cover	VERB
ijassa-386	61	15	by	by	ADP
ijassa-386	61	16	the	the	DET
ijassa-386	61	17	hypercube	hypercube	NOUN
ijassa-386	61	18	of	of	ADP
ijassa-386	61	19	u(ϵ	u(ϵ	PROPN
ijassa-386	61	20	)	)	PUNCT
ijassa-386	61	21	,	,	PUNCT
ijassa-386	62	1	ϵ	ϵ	X
ijassa-386	62	2	>	>	X
ijassa-386	62	3	0	0	NUM
ijassa-386	62	4	.	.	PUNCT
ijassa-386	63	1	thus	thus	ADV
ijassa-386	63	2	for	for	ADP
ijassa-386	63	3	any	any	DET
ijassa-386	63	4	subspace	subspace	NOUN
ijassa-386	63	5	rk	rk	NOUN
ijassa-386	63	6	1	1	NUM
ijassa-386	63	7	with	with	ADP
ijassa-386	63	8	rk	rk	PROPN
ijassa-386	63	9	1	1	NUM
ijassa-386	63	10	⊂	⊂	NOUN
ijassa-386	63	11	rk	rk	NOUN
ijassa-386	63	12	,	,	PUNCT
ijassa-386	63	13	and	and	CCONJ
ijassa-386	63	14	any	any	DET
ijassa-386	63	15	subset	subset	NOUN
ijassa-386	63	16	{	{	PUNCT
ijassa-386	63	17	xi|i	xi|i	PROPN
ijassa-386	63	18	=	=	SYM
ijassa-386	63	19	i1	i1	PROPN
ijassa-386	63	20	,	,	PUNCT
ijassa-386	63	21	·	·	PUNCT
ijassa-386	63	22	·	·	PUNCT
ijassa-386	63	23	·	·	PUNCT
ijassa-386	63	24	,	,	PUNCT
ijassa-386	63	25	im1	im1	PROPN
ijassa-386	63	26	}	}	PUNCT
ijassa-386	63	27	,	,	PUNCT
ijassa-386	63	28	∥	∥	PROPN
ijassa-386	63	29	xi	xi	X
ijassa-386	63	30	−	−	PROPN
ijassa-386	63	31	xj	xj	PROPN
ijassa-386	63	32	∥rk1≤∥	∥rk1≤∥	PROPN
ijassa-386	63	33	xi	xi	PUNCT
ijassa-386	63	34	−	−	PROPN
ijassa-386	64	1	xj	xj	PROPN
ijassa-386	64	2	∥rk	∥rk	PROPN
ijassa-386	64	3	<	<	X
ijassa-386	64	4	ϵ.	ϵ.	NOUN
ijassa-386	65	1	so	so	ADV
ijassa-386	65	2	b	b	PROPN
ijassa-386	65	3	is	be	AUX
ijassa-386	65	4	k1	k1	NOUN
ijassa-386	65	5	-	-	PUNCT
ijassa-386	65	6	dimension	dimension	NOUN
ijassa-386	65	7	subspace	subspace	NOUN
ijassa-386	65	8	m1	m1	NOUN
ijassa-386	65	9	-	-	PUNCT
ijassa-386	65	10	relation	relation	NOUN
ijassa-386	65	11	.	.	PUNCT
ijassa-386	66	1	40	40	NUM
ijassa-386	66	2	dongyun	dongyun	NOUN
ijassa-386	66	3	yi	yi	NOUN
ijassa-386	66	4	:	:	PUNCT
ijassa-386	66	5	a	a	DET
ijassa-386	66	6	subspace	subspace	ADJ
ijassa-386	66	7	multi	multi	ADJ
ijassa-386	66	8	-	-	ADJ
ijassa-386	66	9	relation	relation	ADJ
ijassa-386	66	10	model	model	NOUN
ijassa-386	66	11	for	for	ADP
ijassa-386	66	12	the	the	DET
ijassa-386	66	13	expression	expression	NOUN
ijassa-386	66	14	of	of	ADP
ijassa-386	66	15	system	system	NOUN
ijassa-386	66	16	complexity	complexity	NOUN
ijassa-386	66	17	theorem	theorem	VERB
ijassa-386	66	18	2.2	2.2	NUM
ijassa-386	66	19	subspace	subspace	NOUN
ijassa-386	66	20	multi	multi	NOUN
ijassa-386	66	21	-	-	NOUN
ijassa-386	66	22	relation	relation	NOUN
ijassa-386	66	23	is	be	AUX
ijassa-386	66	24	of	of	ADP
ijassa-386	66	25	upward	upward	ADJ
ijassa-386	66	26	aggregation	aggregation	NOUN
ijassa-386	66	27	.	.	PUNCT
ijassa-386	67	1	assuming	assume	VERB
ijassa-386	67	2	that	that	SCONJ
ijassa-386	67	3	all	all	DET
ijassa-386	67	4	one	one	NUM
ijassa-386	67	5	-	-	PUNCT
ijassa-386	67	6	dimension	dimension	NOUN
ijassa-386	67	7	subspace	subspace	NOUN
ijassa-386	67	8	multi	multi	NOUN
ijassa-386	67	9	-	-	NOUN
ijassa-386	67	10	relation	relation	NOUN
ijassa-386	67	11	in	in	ADP
ijassa-386	67	12	the	the	DET
ijassa-386	67	13	set	set	NOUN
ijassa-386	67	14	of	of	ADP
ijassa-386	67	15	objects	object	NOUN
ijassa-386	67	16	s	s	AUX
ijassa-386	67	17	denoted	denote	VERB
ijassa-386	67	18	by	by	ADP
ijassa-386	67	19	si	si	PROPN
ijassa-386	67	20	,	,	PUNCT
ijassa-386	67	21	i	i	NOUN
ijassa-386	67	22	=	=	NOUN
ijassa-386	67	23	1	1	NUM
ijassa-386	67	24	,	,	PUNCT
ijassa-386	67	25	2	2	NUM
ijassa-386	67	26	,	,	PUNCT
ijassa-386	67	27	·	·	PUNCT
ijassa-386	67	28	·	·	PUNCT
ijassa-386	67	29	·	·	PUNCT
ijassa-386	67	30	,	,	PUNCT
ijassa-386	67	31	m	m	NOUN
ijassa-386	67	32	.	.	PUNCT
ijassa-386	68	1	if	if	SCONJ
ijassa-386	68	2	si1i2···ik	si1i2···ik	PROPN
ijassa-386	68	3	=	=	SYM
ijassa-386	68	4	si1	si1	PROPN
ijassa-386	68	5	∩si2	∩si2	NOUN
ijassa-386	68	6	∩	∩	PROPN
ijassa-386	68	7	·	·	PUNCT
ijassa-386	68	8	·	·	PUNCT
ijassa-386	68	9	·	·	PUNCT
ijassa-386	68	10	∩sik	∩sik	PROPN
ijassa-386	68	11	̸=	̸=	PROPN
ijassa-386	68	12	∅	∅	NOUN
ijassa-386	68	13	,	,	PUNCT
ijassa-386	68	14	1	1	NUM
ijassa-386	68	15	≤	≤	PROPN
ijassa-386	68	16	i1	i1	PROPN
ijassa-386	68	17	<	<	X
ijassa-386	68	18	i2	i2	PROPN
ijassa-386	68	19	<	<	X
ijassa-386	68	20	·	·	PUNCT
ijassa-386	68	21	·	·	PUNCT
ijassa-386	68	22	·	·	PUNCT
ijassa-386	68	23	<	<	X
ijassa-386	68	24	ik	ik	PROPN
ijassa-386	68	25	≤	≤	PROPN
ijassa-386	68	26	m	m	VERB
ijassa-386	68	27	,	,	PUNCT
ijassa-386	68	28	then	then	ADV
ijassa-386	68	29	si1i2···ik	si1i2···ik	PROPN
ijassa-386	68	30	is	be	AUX
ijassa-386	68	31	k	k	ADJ
ijassa-386	68	32	-	-	ADJ
ijassa-386	68	33	dimension	dimension	ADJ
ijassa-386	68	34	subspace	subspace	NOUN
ijassa-386	68	35	mi1i2···ik	mi1i2···ik	NOUN
ijassa-386	68	36	-	-	PUNCT
ijassa-386	68	37	relation	relation	NOUN
ijassa-386	68	38	,	,	PUNCT
ijassa-386	68	39	where	where	SCONJ
ijassa-386	68	40	mi1i2···ik	mi1i2···ik	PROPN
ijassa-386	68	41	is	be	AUX
ijassa-386	68	42	the	the	DET
ijassa-386	68	43	number	number	NOUN
ijassa-386	68	44	of	of	ADP
ijassa-386	68	45	element	element	NOUN
ijassa-386	68	46	in	in	ADP
ijassa-386	68	47	set	set	NOUN
ijassa-386	68	48	(	(	PUNCT
ijassa-386	68	49	si1i2···ik	si1i2···ik	PROPN
ijassa-386	68	50	.	.	PUNCT
ijassa-386	69	1	proof	proof	NOUN
ijassa-386	69	2	.	.	PUNCT
ijassa-386	70	1	for	for	ADP
ijassa-386	70	2	any	any	DET
ijassa-386	70	3	xi	xi	PROPN
ijassa-386	70	4	,	,	PUNCT
ijassa-386	70	5	xj	xj	PROPN
ijassa-386	70	6	∈	∈	PROPN
ijassa-386	70	7	si1i2···ik	si1i2···ik	PROPN
ijassa-386	70	8	,	,	PUNCT
ijassa-386	70	9	xi	xi	PROPN
ijassa-386	70	10	=	=	PUNCT
ijassa-386	70	11	(	(	PUNCT
ijassa-386	70	12	xi1	xi1	PROPN
ijassa-386	70	13	,	,	PUNCT
ijassa-386	70	14	·	·	PUNCT
ijassa-386	70	15	·	·	PUNCT
ijassa-386	70	16	·	·	PUNCT
ijassa-386	70	17	,	,	PUNCT
ijassa-386	70	18	xik	xik	PROPN
ijassa-386	70	19	)	)	PUNCT
ijassa-386	70	20	,	,	PUNCT
ijassa-386	70	21	xj	xj	PROPN
ijassa-386	70	22	=	=	SYM
ijassa-386	70	23	(	(	PUNCT
ijassa-386	70	24	xj1	xj1	PROPN
ijassa-386	70	25	,	,	PUNCT
ijassa-386	70	26	·	·	PUNCT
ijassa-386	70	27	·	·	PUNCT
ijassa-386	70	28	·	·	PUNCT
ijassa-386	70	29	,	,	PUNCT
ijassa-386	70	30	xjk	xjk	PROPN
ijassa-386	70	31	)	)	PUNCT
ijassa-386	70	32	,	,	PUNCT
ijassa-386	70	33	to	to	PART
ijassa-386	70	34	eliminate	eliminate	VERB
ijassa-386	70	35	the	the	DET
ijassa-386	70	36	influence	influence	NOUN
ijassa-386	70	37	of	of	ADP
ijassa-386	70	38	the	the	DET
ijassa-386	70	39	different	different	ADJ
ijassa-386	70	40	subspace	subspace	NOUN
ijassa-386	70	41	calculation	calculation	NOUN
ijassa-386	70	42	,	,	PUNCT
ijassa-386	70	43	we	we	PRON
ijassa-386	70	44	use	use	VERB
ijassa-386	70	45	the	the	DET
ijassa-386	70	46	manhattan	manhattan	PROPN
ijassa-386	70	47	distance	distance	NOUN
ijassa-386	70	48	which	which	PRON
ijassa-386	70	49	is	be	AUX
ijassa-386	70	50	normalized	normalize	VERB
ijassa-386	70	51	on	on	ADP
ijassa-386	70	52	dimension	dimension	NOUN
ijassa-386	70	53	as	as	ADP
ijassa-386	70	54	following	follow	VERB
ijassa-386	70	55	:	:	PUNCT
ijassa-386	70	56	drk(xi	drk(xi	NUM
ijassa-386	70	57	,	,	PUNCT
ijassa-386	70	58	xj	xj	PROPN
ijassa-386	70	59	)	)	PUNCT
ijassa-386	70	60	=	=	SYM
ijassa-386	71	1	k∑	k∑	VERB
ijassa-386	72	1	s=1	s=1	X
ijassa-386	72	2	|xis	|xis	X
ijassa-386	72	3	−	−	PUNCT
ijassa-386	72	4	xjs	xjs	PROPN
ijassa-386	72	5	|/k	|/k	PROPN
ijassa-386	72	6	as	as	ADP
ijassa-386	72	7	xi	xi	PROPN
ijassa-386	72	8	,	,	PUNCT
ijassa-386	72	9	xj	xj	PROPN
ijassa-386	72	10	∈	∈	PROPN
ijassa-386	72	11	si1i2···ik	si1i2···ik	PROPN
ijassa-386	72	12	,	,	PUNCT
ijassa-386	72	13	then	then	ADV
ijassa-386	72	14	|xis	|xis	VERB
ijassa-386	72	15	−	−	PROPN
ijassa-386	72	16	xjs	xjs	NOUN
ijassa-386	73	1	|	|	ADV
ijassa-386	73	2	<	<	X
ijassa-386	73	3	ϵ,thus	ϵ,thus	X
ijassa-386	73	4	drk(xi	drk(xi	NOUN
ijassa-386	73	5	,	,	PUNCT
ijassa-386	73	6	xj	xj	PROPN
ijassa-386	73	7	)	)	PUNCT
ijassa-386	73	8	=	=	SYM
ijassa-386	74	1	∑k	∑k	PROPN
ijassa-386	74	2	s=1	s=1	PUNCT
ijassa-386	74	3	|xis	|xis	X
ijassa-386	74	4	−	−	PUNCT
ijassa-386	74	5	xjs	xjs	PROPN
ijassa-386	74	6	|/k	|/k	NOUN
ijassa-386	74	7	<	<	X
ijassa-386	74	8	ϵ	ϵ	X
ijassa-386	74	9	note	note	NOUN
ijassa-386	74	10	:	:	PUNCT
ijassa-386	74	11	here	here	ADV
ijassa-386	74	12	we	we	PRON
ijassa-386	74	13	assume	assume	VERB
ijassa-386	74	14	that	that	SCONJ
ijassa-386	74	15	the	the	DET
ijassa-386	74	16	ϵ	ϵ	X
ijassa-386	74	17	>	>	X
ijassa-386	74	18	0	0	NUM
ijassa-386	74	19	is	be	AUX
ijassa-386	74	20	uniform	uniform	ADJ
ijassa-386	74	21	on	on	ADP
ijassa-386	74	22	different	different	ADJ
ijassa-386	74	23	subspace	subspace	NOUN
ijassa-386	74	24	in	in	ADP
ijassa-386	74	25	the	the	DET
ijassa-386	74	26	proof	proof	NOUN
ijassa-386	74	27	,	,	PUNCT
ijassa-386	74	28	but	but	CCONJ
ijassa-386	74	29	the	the	DET
ijassa-386	74	30	ϵ	ϵ	X
ijassa-386	74	31	>	>	SYM
ijassa-386	74	32	0	0	NUM
ijassa-386	74	33	can	can	AUX
ijassa-386	74	34	be	be	AUX
ijassa-386	74	35	different	different	ADJ
ijassa-386	74	36	according	accord	VERB
ijassa-386	74	37	to	to	ADP
ijassa-386	74	38	the	the	DET
ijassa-386	74	39	actual	actual	ADJ
ijassa-386	74	40	problems	problem	NOUN
ijassa-386	74	41	.	.	PUNCT
ijassa-386	75	1	3	3	NUM
ijassa-386	75	2	algorithm	algorithm	NOUN
ijassa-386	75	3	we	we	PRON
ijassa-386	75	4	have	have	AUX
ijassa-386	75	5	given	give	VERB
ijassa-386	75	6	the	the	DET
ijassa-386	75	7	definitions	definition	NOUN
ijassa-386	75	8	of	of	ADP
ijassa-386	75	9	subspace	subspace	NOUN
ijassa-386	75	10	multi	multi	NOUN
ijassa-386	75	11	-	-	NOUN
ijassa-386	75	12	relation	relation	NOUN
ijassa-386	75	13	and	and	CCONJ
ijassa-386	75	14	discussed	discuss	VERB
ijassa-386	75	15	its	its	PRON
ijassa-386	75	16	properties	property	NOUN
ijassa-386	75	17	.	.	PUNCT
ijassa-386	76	1	in	in	ADP
ijassa-386	76	2	this	this	DET
ijassa-386	76	3	section	section	NOUN
ijassa-386	76	4	we	we	PRON
ijassa-386	76	5	will	will	AUX
ijassa-386	76	6	discuss	discuss	VERB
ijassa-386	76	7	the	the	DET
ijassa-386	76	8	searching	search	VERB
ijassa-386	76	9	algorithm	algorithm	NOUN
ijassa-386	76	10	of	of	ADP
ijassa-386	76	11	subspace	subspace	NOUN
ijassa-386	76	12	multirelation	multirelation	NOUN
ijassa-386	76	13	and	and	CCONJ
ijassa-386	76	14	give	give	VERB
ijassa-386	76	15	some	some	DET
ijassa-386	76	16	practical	practical	ADJ
ijassa-386	76	17	examples	example	NOUN
ijassa-386	76	18	.	.	PUNCT
ijassa-386	77	1	the	the	DET
ijassa-386	77	2	subspace	subspace	PROPN
ijassa-386	77	3	multi	multi	PROPN
ijassa-386	77	4	-	-	NOUN
ijassa-386	77	5	relation	relation	NOUN
ijassa-386	77	6	is	be	AUX
ijassa-386	77	7	downward	downward	ADJ
ijassa-386	77	8	compatibility	compatibility	NOUN
ijassa-386	77	9	and	and	CCONJ
ijassa-386	77	10	upward	upward	ADJ
ijassa-386	77	11	aggregation	aggregation	NOUN
ijassa-386	77	12	,	,	PUNCT
ijassa-386	77	13	which	which	PRON
ijassa-386	77	14	allows	allow	VERB
ijassa-386	77	15	us	we	PRON
ijassa-386	77	16	to	to	PART
ijassa-386	77	17	adopt	adopt	VERB
ijassa-386	77	18	a	a	DET
ijassa-386	77	19	bottom	bottom	NOUN
ijassa-386	77	20	-	-	PUNCT
ijassa-386	77	21	up	up	ADP
ijassa-386	77	22	searching	search	VERB
ijassa-386	77	23	algorithm	algorithm	NOUN
ijassa-386	77	24	to	to	PART
ijassa-386	77	25	obtain	obtain	VERB
ijassa-386	77	26	subspace	subspace	NOUN
ijassa-386	77	27	multi	multi	NOUN
ijassa-386	77	28	-	-	NOUN
ijassa-386	77	29	relation	relation	NOUN
ijassa-386	77	30	from	from	ADP
ijassa-386	77	31	low	low	ADJ
ijassa-386	77	32	-	-	PUNCT
ijassa-386	77	33	dimension	dimension	NOUN
ijassa-386	77	34	to	to	ADP
ijassa-386	77	35	high	high	ADJ
ijassa-386	77	36	-	-	PUNCT
ijassa-386	77	37	dimension	dimension	NOUN
ijassa-386	77	38	.	.	PUNCT
ijassa-386	78	1	firstly	firstly	ADV
ijassa-386	78	2	,	,	PUNCT
ijassa-386	78	3	multirelation	multirelation	NOUN
ijassa-386	78	4	is	be	AUX
ijassa-386	78	5	searched	search	VERB
ijassa-386	78	6	in	in	ADP
ijassa-386	78	7	one	one	NUM
ijassa-386	78	8	-	-	PUNCT
ijassa-386	78	9	dimension	dimension	NOUN
ijassa-386	78	10	subspace	subspace	NOUN
ijassa-386	78	11	.	.	PUNCT
ijassa-386	79	1	secondly	secondly	ADV
ijassa-386	79	2	any	any	DET
ijassa-386	79	3	two	two	NUM
ijassa-386	79	4	of	of	ADP
ijassa-386	79	5	one	one	NUM
ijassa-386	79	6	-	-	PUNCT
ijassa-386	79	7	dimension	dimension	NOUN
ijassa-386	79	8	subspace	subspace	NOUN
ijassa-386	79	9	multi	multi	NOUN
ijassa-386	79	10	-	-	NOUN
ijassa-386	79	11	relation	relation	NOUN
ijassa-386	79	12	are	be	AUX
ijassa-386	79	13	used	use	VERB
ijassa-386	79	14	to	to	PART
ijassa-386	79	15	compute	compute	VERB
ijassa-386	79	16	intersection	intersection	NOUN
ijassa-386	79	17	,	,	PUNCT
ijassa-386	79	18	and	and	CCONJ
ijassa-386	79	19	which	which	PRON
ijassa-386	79	20	being	be	AUX
ijassa-386	79	21	not	not	PART
ijassa-386	79	22	empty	empty	ADJ
ijassa-386	79	23	is	be	AUX
ijassa-386	79	24	to	to	PART
ijassa-386	79	25	form	form	VERB
ijassa-386	79	26	two	two	NUM
ijassa-386	79	27	-	-	PUNCT
ijassa-386	79	28	dimension	dimension	NOUN
ijassa-386	79	29	subspace	subspace	NOUN
ijassa-386	79	30	multi	multi	NOUN
ijassa-386	79	31	-	-	NOUN
ijassa-386	79	32	relation	relation	NOUN
ijassa-386	79	33	.	.	PUNCT
ijassa-386	80	1	thirdly	thirdly	ADV
ijassa-386	80	2	,	,	PUNCT
ijassa-386	80	3	three	three	NUM
ijassa-386	80	4	-	-	PUNCT
ijassa-386	80	5	dimension	dimension	NOUN
ijassa-386	80	6	subspace	subspace	NOUN
ijassa-386	80	7	multi	multi	NOUN
ijassa-386	80	8	-	-	NOUN
ijassa-386	80	9	relation	relation	NOUN
ijassa-386	80	10	could	could	AUX
ijassa-386	80	11	be	be	AUX
ijassa-386	80	12	found	find	VERB
ijassa-386	80	13	by	by	ADP
ijassa-386	80	14	computing	compute	VERB
ijassa-386	80	15	the	the	DET
ijassa-386	80	16	intersection	intersection	NOUN
ijassa-386	80	17	of	of	ADP
ijassa-386	80	18	any	any	DET
ijassa-386	80	19	two	two	NUM
ijassa-386	80	20	of	of	ADP
ijassa-386	80	21	two	two	NUM
ijassa-386	80	22	-	-	PUNCT
ijassa-386	80	23	dimension	dimension	NOUN
ijassa-386	80	24	subspace	subspace	NOUN
ijassa-386	80	25	relations	relation	NOUN
ijassa-386	80	26	.	.	PUNCT
ijassa-386	81	1	finally	finally	ADV
ijassa-386	81	2	,	,	PUNCT
ijassa-386	81	3	based	base	VERB
ijassa-386	81	4	on	on	ADP
ijassa-386	81	5	this	this	DET
ijassa-386	81	6	process	process	NOUN
ijassa-386	81	7	all	all	DET
ijassa-386	81	8	the	the	DET
ijassa-386	81	9	existing	exist	VERB
ijassa-386	81	10	subspace	subspace	NOUN
ijassa-386	81	11	multi	multi	NOUN
ijassa-386	81	12	-	-	NOUN
ijassa-386	81	13	relations	relation	NOUN
ijassa-386	81	14	in	in	ADP
ijassa-386	81	15	attribute	attribute	NOUN
ijassa-386	81	16	space	space	NOUN
ijassa-386	81	17	will	will	AUX
ijassa-386	81	18	be	be	AUX
ijassa-386	81	19	found	find	VERB
ijassa-386	81	20	.	.	PUNCT
ijassa-386	82	1	this	this	DET
ijassa-386	82	2	method	method	NOUN
ijassa-386	82	3	is	be	AUX
ijassa-386	82	4	capable	capable	ADJ
ijassa-386	82	5	of	of	ADP
ijassa-386	82	6	avoiding	avoid	VERB
ijassa-386	82	7	the	the	DET
ijassa-386	82	8	effect	effect	NOUN
ijassa-386	82	9	of	of	ADP
ijassa-386	82	10	the	the	DET
ijassa-386	82	11	high	high	ADJ
ijassa-386	82	12	-	-	PUNCT
ijassa-386	82	13	dimension	dimension	NOUN
ijassa-386	82	14	disaster	disaster	NOUN
ijassa-386	82	15	problem	problem	NOUN
ijassa-386	82	16	which	which	PRON
ijassa-386	82	17	is	be	AUX
ijassa-386	82	18	encountered	encounter	VERB
ijassa-386	82	19	during	during	ADP
ijassa-386	82	20	the	the	DET
ijassa-386	82	21	direct	direct	ADJ
ijassa-386	82	22	search	search	NOUN
ijassa-386	82	23	in	in	ADP
ijassa-386	82	24	the	the	DET
ijassa-386	82	25	high	high	ADJ
ijassa-386	82	26	-	-	PUNCT
ijassa-386	82	27	dimension	dimension	NOUN
ijassa-386	82	28	space	space	NOUN
ijassa-386	82	29	,	,	PUNCT
ijassa-386	82	30	and	and	CCONJ
ijassa-386	82	31	hence	hence	ADV
ijassa-386	82	32	can	can	AUX
ijassa-386	82	33	greatly	greatly	ADV
ijassa-386	82	34	improve	improve	VERB
ijassa-386	82	35	the	the	DET
ijassa-386	82	36	computational	computational	ADJ
ijassa-386	82	37	efficiency	efficiency	NOUN
ijassa-386	82	38	.	.	PUNCT
ijassa-386	83	1	assume	assume	VERB
ijassa-386	83	2	that	that	SCONJ
ijassa-386	83	3	there	there	PRON
ijassa-386	83	4	are	be	VERB
ijassa-386	83	5	m	m	NOUN
ijassa-386	83	6	objects	object	NOUN
ijassa-386	83	7	xi	xi	ADP
ijassa-386	83	8	,	,	PUNCT
ijassa-386	83	9	i	i	PRON
ijassa-386	83	10	=	=	NOUN
ijassa-386	83	11	1	1	NUM
ijassa-386	83	12	,	,	PUNCT
ijassa-386	83	13	2	2	NUM
ijassa-386	83	14	,	,	PUNCT
ijassa-386	83	15	·	·	PUNCT
ijassa-386	83	16	·	·	PUNCT
ijassa-386	83	17	·	·	PUNCT
ijassa-386	83	18	,	,	PUNCT
ijassa-386	83	19	m	m	PROPN
ijassa-386	83	20	,	,	PUNCT
ijassa-386	83	21	which	which	PRON
ijassa-386	83	22	are	be	AUX
ijassa-386	83	23	expressed	express	VERB
ijassa-386	83	24	as	as	ADP
ijassa-386	83	25	xi	xi	X
ijassa-386	83	26	=	=	PUNCT
ijassa-386	83	27	(	(	PUNCT
ijassa-386	83	28	xi1	xi1	PROPN
ijassa-386	83	29	,	,	PUNCT
ijassa-386	83	30	·	·	PUNCT
ijassa-386	83	31	·	·	PUNCT
ijassa-386	83	32	·	·	PUNCT
ijassa-386	83	33	,	,	PUNCT
ijassa-386	83	34	xin)t	xin)t	PROPN
ijassa-386	83	35	∈	∈	PROPN
ijassa-386	83	36	rn	rn	PROPN
ijassa-386	83	37	,	,	PUNCT
ijassa-386	83	38	i	i	NOUN
ijassa-386	83	39	=	=	NOUN
ijassa-386	83	40	1	1	NUM
ijassa-386	83	41	,	,	PUNCT
ijassa-386	83	42	2	2	NUM
ijassa-386	83	43	,	,	PUNCT
ijassa-386	83	44	·	·	PUNCT
ijassa-386	83	45	·	·	PUNCT
ijassa-386	83	46	·	·	PUNCT
ijassa-386	83	47	,	,	PUNCT
ijassa-386	83	48	m	m	VERB
ijassa-386	83	49	in	in	ADP
ijassa-386	83	50	the	the	DET
ijassa-386	83	51	attribute	attribute	NOUN
ijassa-386	83	52	space	space	NOUN
ijassa-386	83	53	.	.	PUNCT
ijassa-386	84	1	here	here	ADV
ijassa-386	84	2	we	we	PRON
ijassa-386	84	3	want	want	VERB
ijassa-386	84	4	to	to	PART
ijassa-386	84	5	find	find	VERB
ijassa-386	84	6	the	the	DET
ijassa-386	84	7	complex	complex	ADJ
ijassa-386	84	8	relations	relation	NOUN
ijassa-386	84	9	among	among	ADP
ijassa-386	84	10	the	the	DET
ijassa-386	84	11	objects	object	NOUN
ijassa-386	84	12	in	in	ADP
ijassa-386	84	13	attribute	attribute	NOUN
ijassa-386	84	14	space	space	NOUN
ijassa-386	84	15	based	base	VERB
ijassa-386	84	16	on	on	ADP
ijassa-386	84	17	subspace	subspace	PROPN
ijassa-386	84	18	multi	multi	PROPN
ijassa-386	84	19	-	-	ADJ
ijassa-386	84	20	relation	relation	ADJ
ijassa-386	84	21	model	model	NOUN
ijassa-386	84	22	.	.	PUNCT
ijassa-386	85	1	the	the	DET
ijassa-386	85	2	main	main	ADJ
ijassa-386	85	3	steps	step	NOUN
ijassa-386	85	4	of	of	ADP
ijassa-386	85	5	subspace	subspace	NOUN
ijassa-386	85	6	multi	multi	ADJ
ijassa-386	85	7	-	-	ADJ
ijassa-386	85	8	relation	relation	ADJ
ijassa-386	85	9	searching	searching	NOUN
ijassa-386	85	10	algorithm	algorithm	NOUN
ijassa-386	85	11	are	be	AUX
ijassa-386	85	12	given	give	VERB
ijassa-386	85	13	as	as	ADP
ijassa-386	85	14	follow	follow	NOUN
ijassa-386	85	15	:	:	PUNCT
ijassa-386	85	16	step	step	NOUN
ijassa-386	85	17	1	1	NUM
ijassa-386	85	18	:	:	PUNCT
ijassa-386	85	19	search	search	VERB
ijassa-386	85	20	one	one	NUM
ijassa-386	85	21	-	-	PUNCT
ijassa-386	85	22	dimension	dimension	NOUN
ijassa-386	85	23	subspace	subspace	NOUN
ijassa-386	85	24	multi	multi	NOUN
ijassa-386	85	25	-	-	NOUN
ijassa-386	85	26	relation	relation	NOUN
ijassa-386	85	27	.	.	PUNCT
ijassa-386	86	1	let	let	VERB
ijassa-386	86	2	j	j	NOUN
ijassa-386	86	3	=	=	NOUN
ijassa-386	86	4	1	1	NUM
ijassa-386	86	5	,	,	PUNCT
ijassa-386	86	6	according	accord	VERB
ijassa-386	86	7	to	to	ADP
ijassa-386	86	8	some	some	DET
ijassa-386	86	9	clustering	clustering	ADJ
ijassa-386	86	10	methods	method	NOUN
ijassa-386	86	11	,	,	PUNCT
ijassa-386	86	12	we	we	PRON
ijassa-386	86	13	cluster	cluster	VERB
ijassa-386	86	14	the	the	DET
ijassa-386	86	15	projection	projection	NOUN
ijassa-386	86	16	{	{	PUNCT
ijassa-386	86	17	xij	xij	PROPN
ijassa-386	86	18	,	,	PUNCT
ijassa-386	86	19	i	i	PRON
ijassa-386	86	20	=	=	NOUN
ijassa-386	86	21	1	1	NUM
ijassa-386	86	22	,	,	PUNCT
ijassa-386	86	23	2	2	NUM
ijassa-386	86	24	,	,	PUNCT
ijassa-386	86	25	·	·	PUNCT
ijassa-386	86	26	·	·	PUNCT
ijassa-386	86	27	·	·	PUNCT
ijassa-386	86	28	,	,	PUNCT
ijassa-386	86	29	m	m	VERB
ijassa-386	86	30	}	}	PUNCT
ijassa-386	86	31	in	in	ADP
ijassa-386	86	32	advances	advance	NOUN
ijassa-386	86	33	in	in	ADP
ijassa-386	86	34	systems	system	NOUN
ijassa-386	86	35	science	science	NOUN
ijassa-386	86	36	and	and	CCONJ
ijassa-386	86	37	application(2015	application(2015	ADJ
ijassa-386	86	38	)	)	PUNCT
ijassa-386	86	39	vol.15	vol.15	NOUN
ijassa-386	86	40	no.1	no.1	VERB
ijassa-386	86	41	41	41	NUM
ijassa-386	86	42	one	one	NUM
ijassa-386	86	43	-	-	PUNCT
ijassa-386	86	44	dimension	dimension	NOUN
ijassa-386	86	45	subspace	subspace	NOUN
ijassa-386	86	46	rj	rj	PROPN
ijassa-386	86	47	with	with	ADP
ijassa-386	86	48	each	each	DET
ijassa-386	86	49	cluster	cluster	NOUN
ijassa-386	86	50	covered	cover	VERB
ijassa-386	86	51	by	by	ADP
ijassa-386	86	52	an	an	DET
ijassa-386	86	53	interval	interval	NOUN
ijassa-386	86	54	of	of	ADP
ijassa-386	86	55	length	length	NOUN
ijassa-386	86	56	2ϵ.	2ϵ.	NOUN
ijassa-386	86	57	the	the	DET
ijassa-386	86	58	result	result	NOUN
ijassa-386	86	59	is	be	AUX
ijassa-386	86	60	denoted	denote	VERB
ijassa-386	86	61	by	by	ADP
ijassa-386	86	62	cj(i	cj(i	PROPN
ijassa-386	86	63	)	)	PUNCT
ijassa-386	86	64	,	,	PUNCT
ijassa-386	87	1	i	i	PRON
ijassa-386	87	2	=	=	NOUN
ijassa-386	87	3	1	1	NUM
ijassa-386	87	4	,	,	PUNCT
ijassa-386	87	5	2	2	NUM
ijassa-386	87	6	,	,	PUNCT
ijassa-386	87	7	·	·	PUNCT
ijassa-386	87	8	·	·	PUNCT
ijassa-386	87	9	·	·	PUNCT
ijassa-386	87	10	,	,	PUNCT
ijassa-386	87	11	mj	mj	INTJ
ijassa-386	87	12	,	,	PUNCT
ijassa-386	87	13	and	and	CCONJ
ijassa-386	87	14	let	let	VERB
ijassa-386	87	15	sj(i	sj(i	NUM
ijassa-386	87	16	)	)	PUNCT
ijassa-386	87	17	=	=	PRON
ijassa-386	87	18	{	{	PUNCT
ijassa-386	88	1	x	x	X
ijassa-386	88	2	:	:	PUNCT
ijassa-386	88	3	xij	xij	PROPN
ijassa-386	88	4	∈	∈	PROPN
ijassa-386	88	5	cj(i	cj(i	PROPN
ijassa-386	88	6	)	)	PUNCT
ijassa-386	88	7	}	}	PUNCT
ijassa-386	88	8	,	,	PUNCT
ijassa-386	88	9	i	i	PRON
ijassa-386	88	10	=	=	NOUN
ijassa-386	88	11	1	1	NUM
ijassa-386	88	12	,	,	PUNCT
ijassa-386	88	13	2	2	NUM
ijassa-386	88	14	,	,	PUNCT
ijassa-386	88	15	·	·	PUNCT
ijassa-386	88	16	·	·	PUNCT
ijassa-386	88	17	·	·	PUNCT
ijassa-386	88	18	,	,	PUNCT
ijassa-386	88	19	mj	mj	INTJ
ijassa-386	88	20	,	,	PUNCT
ijassa-386	88	21	which	which	PRON
ijassa-386	88	22	is	be	AUX
ijassa-386	88	23	belong	belong	VERB
ijassa-386	88	24	to	to	ADP
ijassa-386	88	25	rn	rn	PROPN
ijassa-386	88	26	.	.	PUNCT
ijassa-386	89	1	j	j	PROPN
ijassa-386	89	2	=	=	SYM
ijassa-386	89	3	j	j	PROPN
ijassa-386	90	1	+	+	CCONJ
ijassa-386	90	2	1	1	NUM
ijassa-386	90	3	until	until	SCONJ
ijassa-386	90	4	j	j	PROPN
ijassa-386	90	5	=	=	SYM
ijassa-386	90	6	n.	n.	PROPN
ijassa-386	90	7	step	step	NOUN
ijassa-386	90	8	2	2	NUM
ijassa-386	90	9	:	:	PUNCT
ijassa-386	90	10	search	search	VERB
ijassa-386	90	11	two	two	NUM
ijassa-386	90	12	-	-	PUNCT
ijassa-386	90	13	dimension	dimension	NOUN
ijassa-386	90	14	subspace	subspace	NOUN
ijassa-386	90	15	multi	multi	NOUN
ijassa-386	90	16	-	-	NOUN
ijassa-386	90	17	relation	relation	NOUN
ijassa-386	90	18	.	.	PUNCT
ijassa-386	91	1	if	if	SCONJ
ijassa-386	91	2	sj1j2(i1i2	sj1j2(i1i2	PROPN
ijassa-386	91	3	)	)	PUNCT
ijassa-386	91	4	=	=	PUNCT
ijassa-386	92	1	sj1i1	sj1i1	PROPN
ijassa-386	92	2	∩	∩	NOUN
ijassa-386	92	3	sj2i2	sj2i2	PROPN
ijassa-386	92	4	̸=	̸=	PROPN
ijassa-386	92	5	∅	∅	NOUN
ijassa-386	92	6	let	let	VERB
ijassa-386	92	7	mj1j2	mj1j2	PROPN
ijassa-386	92	8	(	(	PUNCT
ijassa-386	92	9	i1i2	i1i2	NOUN
ijassa-386	92	10	)	)	PUNCT
ijassa-386	92	11	=	=	SYM
ijassa-386	92	12	num(sj1i1	num(sj1i1	NOUN
ijassa-386	92	13	∩	∩	NOUN
ijassa-386	92	14	sj2i2	sj2i2	PROPN
ijassa-386	92	15	)	)	PUNCT
ijassa-386	92	16	then	then	ADV
ijassa-386	92	17	there	there	PRON
ijassa-386	92	18	exists	exist	VERB
ijassa-386	92	19	a	a	DET
ijassa-386	92	20	two	two	NUM
ijassa-386	92	21	dimension	dimension	NOUN
ijassa-386	92	22	mj1j2	mj1j2	PROPN
ijassa-386	92	23	(	(	PUNCT
ijassa-386	92	24	i1i2	i1i2	NOUN
ijassa-386	92	25	)	)	PUNCT
ijassa-386	93	1	-relation,1	-relation,1	NUM
ijassa-386	93	2	≤	≤	NUM
ijassa-386	93	3	j1	j1	PROPN
ijassa-386	93	4	<	<	X
ijassa-386	93	5	j2	j2	PROPN
ijassa-386	93	6	≤	≤	PROPN
ijassa-386	93	7	n	n	CCONJ
ijassa-386	93	8	,	,	PUNCT
ijassa-386	93	9	1	1	NUM
ijassa-386	93	10	≤	≤	PROPN
ijassa-386	93	11	i1	i1	PROPN
ijassa-386	93	12	≤	≤	PROPN
ijassa-386	93	13	mj1	mj1	PROPN
ijassa-386	93	14	,	,	PUNCT
ijassa-386	93	15	1	1	NUM
ijassa-386	93	16	≤	≤	PROPN
ijassa-386	93	17	i2	i2	PROPN
ijassa-386	93	18	≤	≤	PROPN
ijassa-386	93	19	mj2	mj2	PROPN
ijassa-386	93	20	,	,	PUNCT
ijassa-386	93	21	i1	i1	PROPN
ijassa-386	93	22	<	<	X
ijassa-386	93	23	i2	i2	PROPN
ijassa-386	93	24	.	.	PUNCT
ijassa-386	94	1	step	step	NOUN
ijassa-386	94	2	3	3	NUM
ijassa-386	94	3	:	:	PUNCT
ijassa-386	94	4	similarly	similarly	ADV
ijassa-386	94	5	,	,	PUNCT
ijassa-386	94	6	we	we	PRON
ijassa-386	94	7	can	can	AUX
ijassa-386	94	8	search	search	VERB
ijassa-386	94	9	for	for	ADP
ijassa-386	94	10	higher	high	ADJ
ijassa-386	94	11	dimension	dimension	NOUN
ijassa-386	94	12	subspace	subspace	PROPN
ijassa-386	94	13	multi	multi	NOUN
ijassa-386	94	14	-	-	NOUN
ijassa-386	94	15	relations	relation	NOUN
ijassa-386	94	16	.	.	PUNCT
ijassa-386	95	1	k=3	k=3	X
ijassa-386	95	2	;	;	PUNCT
ijassa-386	95	3	if	if	SCONJ
ijassa-386	95	4	sj1j2	sj1j2	PROPN
ijassa-386	95	5	...	...	PUNCT
ijassa-386	95	6	jki1i2	jki1i2	PROPN
ijassa-386	95	7	...	...	PUNCT
ijassa-386	95	8	ik	ik	PROPN
ijassa-386	95	9	=	=	SYM
ijassa-386	95	10	sj1i1	sj1i1	PROPN
ijassa-386	95	11	∩	∩	NOUN
ijassa-386	95	12	sj2i2	sj2i2	PROPN
ijassa-386	95	13	∩	∩	NOUN
ijassa-386	95	14	...	...	PUNCT
ijassa-386	95	15	∩	∩	ADJ
ijassa-386	95	16	sjkik	sjkik	ADJ
ijassa-386	95	17	̸=	̸=	PROPN
ijassa-386	95	18	∅	∅	ADP
ijassa-386	95	19	1	1	NUM
ijassa-386	95	20	<	<	X
ijassa-386	95	21	i1	i1	PROPN
ijassa-386	95	22	<	<	X
ijassa-386	95	23	i2	i2	PROPN
ijassa-386	95	24	<	<	X
ijassa-386	95	25	·	·	PUNCT
ijassa-386	95	26	·	·	PUNCT
ijassa-386	95	27	·	·	PUNCT
ijassa-386	95	28	<	<	X
ijassa-386	95	29	ik	ik	PROPN
ijassa-386	95	30	≤	≤	PROPN
ijassa-386	95	31	m	m	PROPN
ijassa-386	95	32	,	,	PUNCT
ijassa-386	95	33	1	1	NUM
ijassa-386	95	34	≤	≤	NUM
ijassa-386	95	35	it	it	PRON
ijassa-386	95	36	≤	≤	PROPN
ijassa-386	95	37	mi	mi	PROPN
ijassa-386	95	38	,	,	PUNCT
ijassa-386	95	39	t	t	NOUN
ijassa-386	95	40	=	=	SYM
ijassa-386	95	41	1	1	NUM
ijassa-386	95	42	,	,	PUNCT
ijassa-386	95	43	2	2	NUM
ijassa-386	95	44	·	·	PUNCT
ijassa-386	95	45	·	·	PUNCT
ijassa-386	95	46	·	·	PUNCT
ijassa-386	95	47	,	,	PUNCT
ijassa-386	95	48	k	k	PROPN
ijassa-386	95	49	then	then	ADV
ijassa-386	95	50	we	we	PRON
ijassa-386	95	51	say	say	VERB
ijassa-386	95	52	sj1j2···jk(i1i2···ik	sj1j2···jk(i1i2···ik	ADV
ijassa-386	95	53	)	)	PUNCT
ijassa-386	95	54	=	=	PUNCT
ijassa-386	96	1	sj1i1	sj1i1	PROPN
ijassa-386	96	2	∩	∩	NOUN
ijassa-386	96	3	sj2i2	sj2i2	PROPN
ijassa-386	96	4	∩	∩	X
ijassa-386	96	5	·	·	PUNCT
ijassa-386	96	6	·	·	PUNCT
ijassa-386	96	7	·	·	PUNCT
ijassa-386	96	8	∩	∩	X
ijassa-386	96	9	sjkik	sjkik	NOUN
ijassa-386	96	10	has	have	VERB
ijassa-386	96	11	k	k	ADJ
ijassa-386	96	12	-	-	ADJ
ijassa-386	96	13	dimension	dimension	ADJ
ijassa-386	96	14	mi1i2···ik	mi1i2···ik	PROPN
ijassa-386	96	15	-relation	-relation	NOUN
ijassa-386	96	16	,	,	PUNCT
ijassa-386	96	17	where	where	SCONJ
ijassa-386	96	18	mi1i2···ik	mi1i2···ik	PROPN
ijassa-386	96	19	=	=	SYM
ijassa-386	96	20	num(sj1j2···jk(i1i2···ik	num(sj1j2···jk(i1i2···ik	NUM
ijassa-386	96	21	)	)	PUNCT
ijassa-386	96	22	)	)	PUNCT
ijassa-386	97	1	k	k	X
ijassa-386	97	2	=	=	SYM
ijassa-386	97	3	k+1,if	k+1,if	X
ijassa-386	97	4	all	all	PRON
ijassa-386	97	5	of	of	ADP
ijassa-386	97	6	the	the	DET
ijassa-386	97	7	intersection	intersection	NOUN
ijassa-386	97	8	is	be	AUX
ijassa-386	97	9	empty	empty	ADJ
ijassa-386	97	10	,	,	PUNCT
ijassa-386	97	11	then	then	ADV
ijassa-386	97	12	stop	stop	VERB
ijassa-386	97	13	searching	search	VERB
ijassa-386	97	14	.	.	PUNCT
ijassa-386	98	1	note	note	VERB
ijassa-386	98	2	1	1	NUM
ijassa-386	98	3	:	:	PUNCT
ijassa-386	98	4	the	the	DET
ijassa-386	98	5	clustering	clustering	ADJ
ijassa-386	98	6	method	method	NOUN
ijassa-386	98	7	of	of	ADP
ijassa-386	98	8	one	one	NUM
ijassa-386	98	9	-	-	PUNCT
ijassa-386	98	10	dimension	dimension	NOUN
ijassa-386	98	11	space	space	NOUN
ijassa-386	98	12	above	above	ADV
ijassa-386	98	13	can	can	AUX
ijassa-386	98	14	be	be	AUX
ijassa-386	98	15	suitably	suitably	ADV
ijassa-386	98	16	selected	select	VERB
ijassa-386	98	17	according	accord	VERB
ijassa-386	98	18	to	to	ADP
ijassa-386	98	19	actual	actual	ADJ
ijassa-386	98	20	data	datum	NOUN
ijassa-386	98	21	such	such	ADJ
ijassa-386	98	22	as	as	ADP
ijassa-386	98	23	k	k	NOUN
ijassa-386	98	24	-	-	PUNCT
ijassa-386	98	25	means	mean	VERB
ijassa-386	98	26	method	method	NOUN
ijassa-386	98	27	or	or	CCONJ
ijassa-386	98	28	hierarchical	hierarchical	ADJ
ijassa-386	98	29	clustering	clustering	NOUN
ijassa-386	98	30	method	method	NOUN
ijassa-386	98	31	;	;	PUNCT
ijassa-386	98	32	note	note	NOUN
ijassa-386	98	33	2	2	NUM
ijassa-386	98	34	:	:	PUNCT
ijassa-386	98	35	when	when	SCONJ
ijassa-386	98	36	dealing	deal	VERB
ijassa-386	98	37	with	with	ADP
ijassa-386	98	38	big	big	ADJ
ijassa-386	98	39	data	datum	NOUN
ijassa-386	98	40	,	,	PUNCT
ijassa-386	98	41	in	in	ADP
ijassa-386	98	42	order	order	NOUN
ijassa-386	98	43	to	to	PART
ijassa-386	98	44	control	control	VERB
ijassa-386	98	45	the	the	DET
ijassa-386	98	46	number	number	NOUN
ijassa-386	98	47	of	of	ADP
ijassa-386	98	48	subspace	subspace	NOUN
ijassa-386	98	49	multi	multi	NOUN
ijassa-386	98	50	-	-	NOUN
ijassa-386	98	51	relation	relation	NOUN
ijassa-386	98	52	,	,	PUNCT
ijassa-386	98	53	the	the	DET
ijassa-386	98	54	number	number	NOUN
ijassa-386	98	55	n	n	ADP
ijassa-386	98	56	of	of	ADP
ijassa-386	98	57	objects	object	NOUN
ijassa-386	98	58	in	in	ADP
ijassa-386	98	59	which	which	PRON
ijassa-386	98	60	is	be	AUX
ijassa-386	98	61	asked	ask	VERB
ijassa-386	98	62	to	to	PART
ijassa-386	98	63	be	be	AUX
ijassa-386	98	64	greater	great	ADJ
ijassa-386	98	65	than	than	ADP
ijassa-386	98	66	a	a	DET
ijassa-386	98	67	given	give	VERB
ijassa-386	98	68	positive	positive	ADJ
ijassa-386	98	69	integer	integer	NOUN
ijassa-386	98	70	that	that	PRON
ijassa-386	98	71	is	be	AUX
ijassa-386	98	72	used	use	VERB
ijassa-386	98	73	to	to	PART
ijassa-386	98	74	characterize	characterize	VERB
ijassa-386	98	75	how	how	SCONJ
ijassa-386	98	76	many	many	ADJ
ijassa-386	98	77	objects	object	NOUN
ijassa-386	98	78	are	be	AUX
ijassa-386	98	79	interesting	interesting	ADJ
ijassa-386	98	80	,	,	PUNCT
ijassa-386	98	81	and	and	CCONJ
ijassa-386	98	82	parameter	parameter	PROPN
ijassa-386	98	83	ϵ	ϵ	PROPN
ijassa-386	98	84	refers	refer	VERB
ijassa-386	98	85	to	to	ADP
ijassa-386	98	86	the	the	DET
ijassa-386	98	87	tightness	tightness	NOUN
ijassa-386	98	88	of	of	ADP
ijassa-386	98	89	relation	relation	NOUN
ijassa-386	98	90	.	.	PUNCT
ijassa-386	99	1	4	4	NUM
ijassa-386	99	2	examples	example	NOUN
ijassa-386	99	3	4.1	4.1	NUM
ijassa-386	99	4	experiment	experiment	NOUN
ijassa-386	99	5	1	1	NUM
ijassa-386	99	6	in	in	ADP
ijassa-386	99	7	the	the	DET
ijassa-386	99	8	department	department	NOUN
ijassa-386	99	9	of	of	ADP
ijassa-386	99	10	mathematics	mathematic	NOUN
ijassa-386	99	11	of	of	ADP
ijassa-386	99	12	some	some	DET
ijassa-386	99	13	college	college	NOUN
ijassa-386	99	14	,	,	PUNCT
ijassa-386	99	15	the	the	DET
ijassa-386	99	16	data	datum	NOUN
ijassa-386	99	17	set	set	VERB
ijassa-386	99	18	consists	consist	VERB
ijassa-386	99	19	of	of	ADP
ijassa-386	99	20	84	84	NUM
ijassa-386	99	21	staff	staff	NOUN
ijassa-386	99	22	vertices	vertex	NOUN
ijassa-386	99	23	,	,	PUNCT
ijassa-386	99	24	where	where	SCONJ
ijassa-386	99	25	each	each	DET
ijassa-386	99	26	vertex	vertex	NOUN
ijassa-386	99	27	has	have	VERB
ijassa-386	99	28	a	a	DET
ijassa-386	99	29	total	total	NOUN
ijassa-386	99	30	of	of	ADP
ijassa-386	99	31	52	52	NUM
ijassa-386	99	32	attributes	attribute	NOUN
ijassa-386	99	33	including	include	VERB
ijassa-386	99	34	gender	gender	NOUN
ijassa-386	99	35	,	,	PUNCT
ijassa-386	99	36	education	education	NOUN
ijassa-386	99	37	,	,	PUNCT
ijassa-386	99	38	job	job	NOUN
ijassa-386	99	39	title	title	NOUN
ijassa-386	99	40	,	,	PUNCT
ijassa-386	99	41	hobby	hobby	NOUN
ijassa-386	99	42	,	,	PUNCT
ijassa-386	99	43	physical	physical	ADJ
ijassa-386	99	44	health	health	NOUN
ijassa-386	99	45	,	,	PUNCT
ijassa-386	99	46	etc	etc	X
ijassa-386	99	47	.	.	X
ijassa-386	100	1	the	the	DET
ijassa-386	100	2	searching	search	VERB
ijassa-386	100	3	algorithm	algorithm	NOUN
ijassa-386	100	4	given	give	VERB
ijassa-386	100	5	above	above	ADV
ijassa-386	100	6	is	be	AUX
ijassa-386	100	7	used	use	VERB
ijassa-386	100	8	to	to	PART
ijassa-386	100	9	find	find	VERB
ijassa-386	100	10	subspace	subspace	NOUN
ijassa-386	100	11	multi	multi	NOUN
ijassa-386	100	12	-	-	NOUN
ijassa-386	100	13	relation	relation	NOUN
ijassa-386	100	14	in	in	ADP
ijassa-386	100	15	data	datum	NOUN
ijassa-386	100	16	.	.	PUNCT
ijassa-386	101	1	the	the	DET
ijassa-386	101	2	parameters	parameter	NOUN
ijassa-386	101	3	ϵ	ϵ	VERB
ijassa-386	101	4	is	be	AUX
ijassa-386	101	5	set	set	VERB
ijassa-386	101	6	to	to	ADP
ijassa-386	101	7	0.5	0.5	NUM
ijassa-386	101	8	and	and	CCONJ
ijassa-386	101	9	n	n	CCONJ
ijassa-386	101	10	(	(	PUNCT
ijassa-386	101	11	the	the	DET
ijassa-386	101	12	number	number	NOUN
ijassa-386	101	13	of	of	ADP
ijassa-386	101	14	staffs	staff	NOUN
ijassa-386	101	15	in	in	ADP
ijassa-386	101	16	subspace	subspace	PROPN
ijassa-386	101	17	multi	multi	NOUN
ijassa-386	101	18	-	-	NOUN
ijassa-386	101	19	relation	relation	NOUN
ijassa-386	101	20	)	)	PUNCT
ijassa-386	101	21	is	be	AUX
ijassa-386	101	22	5	5	NUM
ijassa-386	101	23	.	.	PUNCT
ijassa-386	102	1	the	the	DET
ijassa-386	102	2	total	total	ADJ
ijassa-386	102	3	125	125	NUM
ijassa-386	102	4	subspace	subspace	NOUN
ijassa-386	102	5	multi	multi	NOUN
ijassa-386	102	6	-	-	NOUN
ijassa-386	102	7	relations	relation	NOUN
ijassa-386	102	8	are	be	AUX
ijassa-386	102	9	found	find	VERB
ijassa-386	102	10	.	.	PUNCT
ijassa-386	103	1	by	by	ADP
ijassa-386	103	2	use	use	NOUN
ijassa-386	103	3	of	of	ADP
ijassa-386	103	4	traditional	traditional	ADJ
ijassa-386	103	5	graph	graph	NOUN
ijassa-386	103	6	model	model	NOUN
ijassa-386	103	7	we	we	PRON
ijassa-386	103	8	can	can	AUX
ijassa-386	103	9	only	only	ADV
ijassa-386	103	10	obtain	obtain	VERB
ijassa-386	103	11	fully	fully	ADV
ijassa-386	103	12	connective	connective	ADJ
ijassa-386	103	13	graph	graph	NOUN
ijassa-386	103	14	which	which	PRON
ijassa-386	103	15	lost	lose	VERB
ijassa-386	103	16	a	a	DET
ijassa-386	103	17	lot	lot	NOUN
ijassa-386	103	18	of	of	ADP
ijassa-386	103	19	information	information	NOUN
ijassa-386	103	20	42	42	NUM
ijassa-386	103	21	dongyun	dongyun	NOUN
ijassa-386	103	22	yi	yi	NOUN
ijassa-386	103	23	:	:	PUNCT
ijassa-386	103	24	a	a	DET
ijassa-386	103	25	subspace	subspace	ADJ
ijassa-386	103	26	multi	multi	ADJ
ijassa-386	103	27	-	-	ADJ
ijassa-386	103	28	relation	relation	ADJ
ijassa-386	103	29	model	model	NOUN
ijassa-386	103	30	for	for	ADP
ijassa-386	103	31	the	the	DET
ijassa-386	103	32	expression	expression	NOUN
ijassa-386	103	33	of	of	ADP
ijassa-386	103	34	system	system	NOUN
ijassa-386	103	35	complexity	complexity	NOUN
ijassa-386	103	36	in	in	ADP
ijassa-386	103	37	data	datum	NOUN
ijassa-386	103	38	.	.	PUNCT
ijassa-386	104	1	that	that	PRON
ijassa-386	104	2	is	be	AUX
ijassa-386	104	3	because	because	SCONJ
ijassa-386	104	4	classical	classical	ADJ
ijassa-386	104	5	two	two	NUM
ijassa-386	104	6	-	-	PUNCT
ijassa-386	104	7	relation	relation	NOUN
ijassa-386	104	8	just	just	ADV
ijassa-386	104	9	indicate	indicate	VERB
ijassa-386	104	10	whether	whether	SCONJ
ijassa-386	104	11	two	two	NUM
ijassa-386	104	12	objects	object	NOUN
ijassa-386	104	13	have	have	VERB
ijassa-386	104	14	relation	relation	NOUN
ijassa-386	104	15	,	,	PUNCT
ijassa-386	104	16	but	but	CCONJ
ijassa-386	104	17	do	do	AUX
ijassa-386	104	18	pay	pay	VERB
ijassa-386	104	19	attention	attention	NOUN
ijassa-386	104	20	to	to	ADP
ijassa-386	104	21	neither	neither	CCONJ
ijassa-386	104	22	the	the	DET
ijassa-386	104	23	simultaneously	simultaneously	ADV
ijassa-386	104	24	relation	relation	NOUN
ijassa-386	104	25	of	of	ADP
ijassa-386	104	26	how	how	SCONJ
ijassa-386	104	27	many	many	ADJ
ijassa-386	104	28	objects	object	NOUN
ijassa-386	104	29	nor	nor	CCONJ
ijassa-386	104	30	in	in	ADP
ijassa-386	104	31	which	which	DET
ijassa-386	104	32	subspace	subspace	NOUN
ijassa-386	104	33	the	the	DET
ijassa-386	104	34	relation	relation	NOUN
ijassa-386	104	35	happened	happen	VERB
ijassa-386	104	36	.	.	PUNCT
ijassa-386	105	1	the	the	DET
ijassa-386	105	2	more	more	ADV
ijassa-386	105	3	complex	complex	ADJ
ijassa-386	105	4	relation	relation	NOUN
ijassa-386	105	5	that	that	PRON
ijassa-386	105	6	exists	exist	VERB
ijassa-386	105	7	in	in	ADP
ijassa-386	105	8	actual	actual	ADJ
ijassa-386	105	9	data	datum	NOUN
ijassa-386	105	10	can	can	AUX
ijassa-386	105	11	be	be	AUX
ijassa-386	105	12	expressed	express	VERB
ijassa-386	105	13	by	by	ADP
ijassa-386	105	14	the	the	DET
ijassa-386	105	15	subspace	subspace	NOUN
ijassa-386	105	16	multi	multi	ADJ
ijassa-386	105	17	-	-	ADJ
ijassa-386	105	18	relation	relation	ADJ
ijassa-386	105	19	model	model	NOUN
ijassa-386	105	20	,	,	PUNCT
ijassa-386	105	21	which	which	PRON
ijassa-386	105	22	can	can	AUX
ijassa-386	105	23	not	not	PART
ijassa-386	105	24	only	only	ADV
ijassa-386	105	25	tell	tell	VERB
ijassa-386	105	26	us	we	PRON
ijassa-386	105	27	how	how	SCONJ
ijassa-386	105	28	many	many	ADJ
ijassa-386	105	29	objects	object	NOUN
ijassa-386	105	30	have	have	VERB
ijassa-386	105	31	relation	relation	NOUN
ijassa-386	105	32	but	but	CCONJ
ijassa-386	105	33	also	also	ADV
ijassa-386	105	34	point	point	VERB
ijassa-386	105	35	out	out	ADP
ijassa-386	105	36	the	the	DET
ijassa-386	105	37	attribute	attribute	NOUN
ijassa-386	105	38	space	space	NOUN
ijassa-386	105	39	which	which	PRON
ijassa-386	105	40	the	the	DET
ijassa-386	105	41	relation	relation	NOUN
ijassa-386	105	42	exists	exist	VERB
ijassa-386	105	43	in	in	ADP
ijassa-386	105	44	.	.	PUNCT
ijassa-386	106	1	in	in	ADP
ijassa-386	106	2	example	example	NOUN
ijassa-386	106	3	given	give	VERB
ijassa-386	106	4	above	above	ADV
ijassa-386	106	5	,	,	PUNCT
ijassa-386	106	6	staffs	staff	NOUN
ijassa-386	106	7	link	link	VERB
ijassa-386	106	8	together	together	ADV
ijassa-386	106	9	differently	differently	ADV
ijassa-386	106	10	because	because	SCONJ
ijassa-386	106	11	of	of	ADP
ijassa-386	106	12	schoolfellows	schoolfellow	NOUN
ijassa-386	106	13	,	,	PUNCT
ijassa-386	106	14	countrymen	countryman	NOUN
ijassa-386	106	15	,	,	PUNCT
ijassa-386	106	16	or	or	CCONJ
ijassa-386	106	17	the	the	DET
ijassa-386	106	18	same	same	ADJ
ijassa-386	106	19	research	research	NOUN
ijassa-386	106	20	field	field	NOUN
ijassa-386	106	21	and	and	CCONJ
ijassa-386	106	22	so	so	ADV
ijassa-386	106	23	on	on	ADV
ijassa-386	106	24	.	.	PUNCT
ijassa-386	107	1	4.2	4.2	NUM
ijassa-386	107	2	experiment	experiment	NOUN
ijassa-386	107	3	2	2	NUM
ijassa-386	107	4	enron	enron	PROPN
ijassa-386	107	5	was	be	AUX
ijassa-386	107	6	one	one	NUM
ijassa-386	107	7	of	of	ADP
ijassa-386	107	8	the	the	DET
ijassa-386	107	9	most	most	ADV
ijassa-386	107	10	important	important	ADJ
ijassa-386	107	11	companies	company	NOUN
ijassa-386	107	12	in	in	ADP
ijassa-386	107	13	the	the	DET
ijassa-386	107	14	u.s	u.s	PROPN
ijassa-386	107	15	.	.	PROPN
ijassa-386	107	16	energy	energy	NOUN
ijassa-386	107	17	industry	industry	NOUN
ijassa-386	107	18	.	.	PUNCT
ijassa-386	108	1	in	in	ADP
ijassa-386	108	2	2001	2001	NUM
ijassa-386	108	3	,	,	PUNCT
ijassa-386	108	4	the	the	DET
ijassa-386	108	5	accounting	accounting	NOUN
ijassa-386	108	6	fraud	fraud	NOUN
ijassa-386	108	7	scandal	scandal	NOUN
ijassa-386	108	8	of	of	ADP
ijassa-386	108	9	the	the	DET
ijassa-386	108	10	enron	enron	PROPN
ijassa-386	108	11	was	be	AUX
ijassa-386	108	12	exposed	expose	VERB
ijassa-386	108	13	.	.	PUNCT
ijassa-386	109	1	then	then	ADV
ijassa-386	109	2	the	the	DET
ijassa-386	109	3	federal	federal	ADJ
ijassa-386	109	4	energy	energy	NOUN
ijassa-386	109	5	planning	planning	NOUN
ijassa-386	109	6	board	board	NOUN
ijassa-386	109	7	took	take	VERB
ijassa-386	109	8	e	e	NOUN
ijassa-386	109	9	-	-	NOUN
ijassa-386	109	10	mail	mail	NOUN
ijassa-386	109	11	communications	communication	NOUN
ijassa-386	109	12	between	between	ADP
ijassa-386	109	13	enron	enron	PROPN
ijassa-386	109	14	employees	employee	NOUN
ijassa-386	109	15	posted	post	VERB
ijassa-386	109	16	online	online	ADV
ijassa-386	109	17	[	[	X
ijassa-386	109	18	17	17	NUM
ijassa-386	109	19	]	]	PUNCT
ijassa-386	109	20	for	for	ADP
ijassa-386	109	21	publicity	publicity	NOUN
ijassa-386	109	22	and	and	CCONJ
ijassa-386	109	23	academic	academic	ADJ
ijassa-386	109	24	research	research	NOUN
ijassa-386	109	25	.	.	PUNCT
ijassa-386	110	1	here	here	ADV
ijassa-386	110	2	,	,	PUNCT
ijassa-386	110	3	we	we	PRON
ijassa-386	110	4	want	want	VERB
ijassa-386	110	5	to	to	PART
ijassa-386	110	6	discover	discover	VERB
ijassa-386	110	7	some	some	DET
ijassa-386	110	8	interesting	interesting	ADJ
ijassa-386	110	9	groups	group	NOUN
ijassa-386	110	10	based	base	VERB
ijassa-386	110	11	on	on	ADP
ijassa-386	110	12	these	these	DET
ijassa-386	110	13	email	email	NOUN
ijassa-386	110	14	.	.	PUNCT
ijassa-386	111	1	from	from	ADP
ijassa-386	111	2	the	the	DET
ijassa-386	111	3	body	body	NOUN
ijassa-386	111	4	content	content	NOUN
ijassa-386	111	5	of	of	ADP
ijassa-386	111	6	those	those	DET
ijassa-386	111	7	emails	email	NOUN
ijassa-386	111	8	which	which	PRON
ijassa-386	111	9	happened	happen	VERB
ijassa-386	111	10	before	before	ADP
ijassa-386	111	11	the	the	DET
ijassa-386	111	12	fraud	fraud	NOUN
ijassa-386	111	13	scandal	scandal	NOUN
ijassa-386	111	14	we	we	PRON
ijassa-386	111	15	extract	extract	VERB
ijassa-386	111	16	2062	2062	NUM
ijassa-386	111	17	different	different	ADJ
ijassa-386	111	18	people	people	NOUN
ijassa-386	111	19	as	as	ADP
ijassa-386	111	20	vertices	vertex	NOUN
ijassa-386	111	21	and	and	CCONJ
ijassa-386	111	22	set	set	VERB
ijassa-386	111	23	144	144	NUM
ijassa-386	111	24	staff	staff	NOUN
ijassa-386	111	25	’s	’s	PART
ijassa-386	111	26	mailbox	mailbox	NOUN
ijassa-386	111	27	as	as	ADP
ijassa-386	111	28	the	the	DET
ijassa-386	111	29	attributes	attribute	NOUN
ijassa-386	111	30	of	of	ADP
ijassa-386	111	31	vertices	vertex	NOUN
ijassa-386	111	32	.	.	PUNCT
ijassa-386	112	1	let	let	VERB
ijassa-386	112	2	ϵ	ϵ	PRON
ijassa-386	112	3	be	be	AUX
ijassa-386	112	4	0.5	0.5	NUM
ijassa-386	112	5	and	and	CCONJ
ijassa-386	112	6	n	n	PRON
ijassa-386	112	7	be	be	VERB
ijassa-386	112	8	60	60	NUM
ijassa-386	112	9	,	,	PUNCT
ijassa-386	112	10	we	we	PRON
ijassa-386	112	11	finally	finally	ADV
ijassa-386	112	12	find	find	VERB
ijassa-386	112	13	275	275	NUM
ijassa-386	112	14	subspace	subspace	NOUN
ijassa-386	112	15	multi	multi	NOUN
ijassa-386	112	16	-	-	NOUN
ijassa-386	112	17	relations	relation	NOUN
ijassa-386	112	18	by	by	ADP
ijassa-386	112	19	our	our	PRON
ijassa-386	112	20	searching	searching	NOUN
ijassa-386	112	21	algorithm	algorithm	NOUN
ijassa-386	112	22	.	.	PUNCT
ijassa-386	113	1	it	it	PRON
ijassa-386	113	2	is	be	AUX
ijassa-386	113	3	very	very	ADV
ijassa-386	113	4	interesting	interesting	ADJ
ijassa-386	113	5	that	that	SCONJ
ijassa-386	113	6	the	the	DET
ijassa-386	113	7	highest	high	ADJ
ijassa-386	113	8	dimension	dimension	NOUN
ijassa-386	113	9	of	of	ADP
ijassa-386	113	10	subspace	subspace	NOUN
ijassa-386	113	11	in	in	ADP
ijassa-386	113	12	all	all	DET
ijassa-386	113	13	subspace	subspace	NOUN
ijassa-386	113	14	multi	multi	NOUN
ijassa-386	113	15	-	-	NOUN
ijassa-386	113	16	relation	relation	NOUN
ijassa-386	113	17	is	be	AUX
ijassa-386	113	18	8	8	NUM
ijassa-386	113	19	with	with	ADP
ijassa-386	113	20	86	86	NUM
ijassa-386	113	21	mailboxes	mailbox	NOUN
ijassa-386	113	22	,	,	PUNCT
ijassa-386	113	23	referring	refer	VERB
ijassa-386	113	24	to	to	ADP
ijassa-386	113	25	8	8	NUM
ijassa-386	113	26	people	people	NOUN
ijassa-386	113	27	including	include	VERB
ijassa-386	113	28	chief	chief	ADJ
ijassa-386	113	29	operating	operating	NOUN
ijassa-386	113	30	officer	officer	NOUN
ijassa-386	113	31	,	,	PUNCT
ijassa-386	113	32	director	director	NOUN
ijassa-386	113	33	of	of	ADP
ijassa-386	113	34	risk	risk	NOUN
ijassa-386	113	35	management	management	NOUN
ijassa-386	113	36	,	,	PUNCT
ijassa-386	113	37	vice	vice	NOUN
ijassa-386	113	38	president	president	NOUN
ijassa-386	113	39	and	and	CCONJ
ijassa-386	113	40	chief	chief	NOUN
ijassa-386	113	41	,	,	PUNCT
ijassa-386	113	42	online	online	ADJ
ijassa-386	113	43	president	president	NOUN
ijassa-386	113	44	of	of	ADP
ijassa-386	113	45	enron	enron	PROPN
ijassa-386	113	46	,	,	PUNCT
ijassa-386	113	47	enron	enron	PROPN
ijassa-386	113	48	ceo	ceo	PROPN
ijassa-386	113	49	in	in	ADP
ijassa-386	113	50	north	north	PROPN
ijassa-386	113	51	america	america	PROPN
ijassa-386	113	52	,	,	PUNCT
ijassa-386	113	53	and	and	CCONJ
ijassa-386	113	54	other	other	ADJ
ijassa-386	113	55	two	two	NUM
ijassa-386	113	56	important	important	ADJ
ijassa-386	113	57	figures	figure	NOUN
ijassa-386	113	58	,	,	PUNCT
ijassa-386	113	59	who	who	PRON
ijassa-386	113	60	all	all	PRON
ijassa-386	113	61	are	be	AUX
ijassa-386	113	62	suspected	suspect	VERB
ijassa-386	113	63	of	of	ADP
ijassa-386	113	64	fraud	fraud	NOUN
ijassa-386	113	65	,	,	PUNCT
ijassa-386	113	66	which	which	PRON
ijassa-386	113	67	tell	tell	VERB
ijassa-386	113	68	us	we	PRON
ijassa-386	113	69	maybe	maybe	ADV
ijassa-386	113	70	the	the	DET
ijassa-386	113	71	event	event	NOUN
ijassa-386	113	72	come	come	VERB
ijassa-386	113	73	from	from	ADP
ijassa-386	113	74	people	people	NOUN
ijassa-386	113	75	’s	’s	PART
ijassa-386	113	76	talking	talk	VERB
ijassa-386	113	77	.	.	PUNCT
ijassa-386	114	1	5	5	NUM
ijassa-386	114	2	subspace	subspace	PROPN
ijassa-386	114	3	multi	multi	NOUN
ijassa-386	114	4	-	-	NOUN
ijassa-386	114	5	relation	relation	NOUN
ijassa-386	114	6	and	and	CCONJ
ijassa-386	114	7	vector	vector	NOUN
ijassa-386	114	8	hyper	hyper	NOUN
ijassa-386	114	9	-	-	NOUN
ijassa-386	114	10	graph	graph	NOUN
ijassa-386	114	11	as	as	ADP
ijassa-386	114	12	two	two	NUM
ijassa-386	114	13	-	-	PUNCT
ijassa-386	114	14	dimension	dimension	NOUN
ijassa-386	114	15	relation	relation	NOUN
ijassa-386	114	16	corresponds	correspond	VERB
ijassa-386	114	17	to	to	ADP
ijassa-386	114	18	the	the	DET
ijassa-386	114	19	graph	graph	NOUN
ijassa-386	114	20	model	model	NOUN
ijassa-386	114	21	,	,	PUNCT
ijassa-386	114	22	subspace	subspace	NOUN
ijassa-386	114	23	multirelation	multirelation	NOUN
ijassa-386	114	24	corresponds	correspond	VERB
ijassa-386	114	25	to	to	ADP
ijassa-386	114	26	the	the	DET
ijassa-386	114	27	hyper	hyper	NOUN
ijassa-386	114	28	-	-	ADJ
ijassa-386	114	29	graph	graph	NOUN
ijassa-386	114	30	model	model	NOUN
ijassa-386	114	31	.	.	PUNCT
ijassa-386	115	1	recently	recently	ADV
ijassa-386	115	2	studies	study	NOUN
ijassa-386	115	3	on	on	ADP
ijassa-386	115	4	hyper	hyper	ADJ
ijassa-386	115	5	-	-	ADJ
ijassa-386	115	6	graph	graph	NOUN
ijassa-386	115	7	model	model	NOUN
ijassa-386	115	8	have	have	AUX
ijassa-386	115	9	mainly	mainly	ADV
ijassa-386	115	10	focused	focus	VERB
ijassa-386	115	11	on	on	ADP
ijassa-386	115	12	how	how	SCONJ
ijassa-386	115	13	to	to	PART
ijassa-386	115	14	expand	expand	VERB
ijassa-386	115	15	the	the	DET
ijassa-386	115	16	existed	exist	VERB
ijassa-386	115	17	properties	property	NOUN
ijassa-386	115	18	in	in	ADP
ijassa-386	115	19	graph	graph	NOUN
ijassa-386	115	20	theory	theory	NOUN
ijassa-386	115	21	into	into	ADP
ijassa-386	115	22	hyper	hyper	NOUN
ijassa-386	115	23	-	-	NOUN
ijassa-386	115	24	graph	graph	NOUN
ijassa-386	115	25	,	,	PUNCT
ijassa-386	115	26	such	such	ADJ
ijassa-386	115	27	as	as	ADP
ijassa-386	115	28	hyper	hyper	NOUN
ijassa-386	115	29	-	-	NOUN
ijassa-386	115	30	path	path	NOUN
ijassa-386	115	31	,	,	PUNCT
ijassa-386	115	32	hyper	hyper	NOUN
ijassa-386	115	33	-	-	NOUN
ijassa-386	115	34	chain	chain	NOUN
ijassa-386	115	35	,	,	PUNCT
ijassa-386	115	36	graph	graph	NOUN
ijassa-386	115	37	partitioning	partitioning	NOUN
ijassa-386	115	38	and	and	CCONJ
ijassa-386	115	39	so	so	ADV
ijassa-386	115	40	on	on	ADP
ijassa-386	115	41	[	[	PUNCT
ijassa-386	115	42	9	9	NUM
ijassa-386	115	43	-	-	SYM
ijassa-386	115	44	13	13	NUM
ijassa-386	115	45	]	]	PUNCT
ijassa-386	115	46	.	.	PUNCT
ijassa-386	116	1	furthermore	furthermore	ADV
ijassa-386	116	2	,	,	PUNCT
ijassa-386	116	3	hyper	hyper	ADJ
ijassa-386	116	4	-	-	ADJ
ijassa-386	116	5	graph	graph	NOUN
ijassa-386	116	6	models	model	NOUN
ijassa-386	116	7	do	do	AUX
ijassa-386	116	8	not	not	PART
ijassa-386	116	9	indicate	indicate	VERB
ijassa-386	116	10	that	that	SCONJ
ijassa-386	116	11	the	the	DET
ijassa-386	116	12	multi	multi	NOUN
ijassa-386	116	13	-	-	NOUN
ijassa-386	116	14	relation	relation	NOUN
ijassa-386	116	15	exists	exist	VERB
ijassa-386	116	16	in	in	ADP
ijassa-386	116	17	different	different	ADJ
ijassa-386	116	18	subspaces	subspace	NOUN
ijassa-386	116	19	.	.	PUNCT
ijassa-386	117	1	here	here	ADV
ijassa-386	117	2	we	we	PRON
ijassa-386	117	3	propose	propose	VERB
ijassa-386	117	4	the	the	DET
ijassa-386	117	5	concept	concept	NOUN
ijassa-386	117	6	of	of	ADP
ijassa-386	117	7	vector	vector	NOUN
ijassa-386	117	8	hyper	hyper	NOUN
ijassa-386	117	9	-	-	NOUN
ijassa-386	117	10	graph	graph	NOUN
ijassa-386	117	11	corresponding	correspond	VERB
ijassa-386	117	12	to	to	AUX
ijassa-386	117	13	subspace	subspace	VERB
ijassa-386	117	14	multi	multi	NOUN
ijassa-386	117	15	-	-	NOUN
ijassa-386	117	16	relation	relation	NOUN
ijassa-386	117	17	.	.	PUNCT
ijassa-386	118	1	definition	definition	NOUN
ijassa-386	118	2	5.1	5.1	NUM
ijassa-386	118	3	let	let	VERB
ijassa-386	118	4	x	x	PUNCT
ijassa-386	118	5	=	=	PRON
ijassa-386	118	6	{	{	PUNCT
ijassa-386	118	7	x1	x1	PROPN
ijassa-386	118	8	,	,	PUNCT
ijassa-386	118	9	x2	x2	PROPN
ijassa-386	118	10	,	,	PUNCT
ijassa-386	118	11	·	·	PUNCT
ijassa-386	118	12	·	·	PUNCT
ijassa-386	118	13	·	·	PUNCT
ijassa-386	118	14	,	,	PUNCT
ijassa-386	118	15	xs	xs	PROPN
ijassa-386	118	16	}	}	PUNCT
ijassa-386	118	17	,	,	PUNCT
ijassa-386	118	18	xi	xi	PROPN
ijassa-386	118	19	∈	∈	PROPN
ijassa-386	118	20	rn	rn	AUX
ijassa-386	118	21	be	be	AUX
ijassa-386	118	22	a	a	DET
ijassa-386	118	23	finite	finite	ADJ
ijassa-386	118	24	set	set	NOUN
ijassa-386	118	25	.	.	PUNCT
ijassa-386	119	1	a	a	DET
ijassa-386	119	2	vector	vector	NOUN
ijassa-386	119	3	hypergraph	hypergraph	NOUN
ijassa-386	119	4	of	of	ADP
ijassa-386	119	5	x	x	PROPN
ijassa-386	119	6	is	be	AUX
ijassa-386	119	7	denoted	denote	VERB
ijassa-386	119	8	by	by	ADP
ijassa-386	119	9	g	g	PROPN
ijassa-386	119	10	=	=	SYM
ijassa-386	119	11	(	(	PUNCT
ijassa-386	119	12	e1,rk1	e1,rk1	X
ijassa-386	119	13	)	)	PUNCT
ijassa-386	119	14	,	,	PUNCT
ijassa-386	119	15	·	·	PUNCT
ijassa-386	119	16	·	·	PUNCT
ijassa-386	119	17	·	·	PUNCT
ijassa-386	119	18	,	,	PUNCT
ijassa-386	119	19	(	(	PUNCT
ijassa-386	119	20	ep	ep	PROPN
ijassa-386	119	21	,	,	PUNCT
ijassa-386	119	22	rkp	rkp	PROPN
ijassa-386	119	23	)	)	PUNCT
ijassa-386	119	24	where	where	SCONJ
ijassa-386	119	25	ei	ei	NOUN
ijassa-386	119	26	is	be	AUX
ijassa-386	119	27	the	the	DET
ijassa-386	119	28	finite	finite	ADJ
ijassa-386	119	29	collection	collection	NOUN
ijassa-386	119	30	of	of	ADP
ijassa-386	119	31	subset	subset	NOUN
ijassa-386	119	32	of	of	ADP
ijassa-386	119	33	x	x	PRON
ijassa-386	119	34	,	,	PUNCT
ijassa-386	119	35	such	such	ADJ
ijassa-386	119	36	that	that	SCONJ
ijassa-386	119	37	:	:	PUNCT
ijassa-386	119	38	(	(	PUNCT
ijassa-386	119	39	1)ei	1)ei	NUM
ijassa-386	119	40	̸=	̸=	PROPN
ijassa-386	119	41	θ	θ	PROPN
ijassa-386	119	42	,	,	PUNCT
ijassa-386	119	43	i	i	PRON
ijassa-386	119	44	=	=	NOUN
ijassa-386	119	45	1	1	NUM
ijassa-386	119	46	,	,	PUNCT
ijassa-386	119	47	2	2	NUM
ijassa-386	119	48	·	·	PUNCT
ijassa-386	119	49	·	·	PUNCT
ijassa-386	119	50	·	·	PUNCT
ijassa-386	119	51	,	,	PUNCT
ijassa-386	119	52	p	p	NOUN
ijassa-386	119	53	advances	advance	VERB
ijassa-386	119	54	in	in	ADP
ijassa-386	119	55	systems	system	NOUN
ijassa-386	119	56	science	science	NOUN
ijassa-386	119	57	and	and	CCONJ
ijassa-386	119	58	application(2015	application(2015	ADJ
ijassa-386	119	59	)	)	PUNCT
ijassa-386	119	60	vol.15	vol.15	NOUN
ijassa-386	119	61	no.1	no.1	VERB
ijassa-386	119	62	43	43	NUM
ijassa-386	119	63	(	(	PUNCT
ijassa-386	119	64	2	2	NUM
ijassa-386	119	65	)	)	PUNCT
ijassa-386	119	66	p	p	NOUN
ijassa-386	119	67	∪	∪	NOUN
ijassa-386	119	68	i=1	i=1	X
ijassa-386	119	69	ei	ei	X
ijassa-386	119	70	=	=	SYM
ijassa-386	119	71	x	x	PROPN
ijassa-386	119	72	,	,	PUNCT
ijassa-386	119	73	rki	rki	PROPN
ijassa-386	119	74	<	<	X
ijassa-386	119	75	rn	rn	PROPN
ijassa-386	119	76	,	,	PUNCT
ijassa-386	119	77	1	1	NUM
ijassa-386	119	78	≤	≤	NUM
ijassa-386	119	79	ki	ki	PROPN
ijassa-386	119	80	≤	≤	PROPN
ijassa-386	119	81	n	n	CCONJ
ijassa-386	119	82	,	,	PUNCT
ijassa-386	119	83	i	i	PRON
ijassa-386	119	84	=	=	NOUN
ijassa-386	119	85	1	1	NUM
ijassa-386	119	86	,	,	PUNCT
ijassa-386	119	87	2	2	NUM
ijassa-386	119	88	·	·	PUNCT
ijassa-386	119	89	·	·	PUNCT
ijassa-386	119	90	·	·	PUNCT
ijassa-386	120	1	p	p	NOUN
ijassa-386	120	2	in	in	ADP
ijassa-386	120	3	the	the	DET
ijassa-386	120	4	vector	vector	NOUN
ijassa-386	120	5	hyper	hyper	NOUN
ijassa-386	120	6	-	-	NOUN
ijassa-386	120	7	graph	graph	NOUN
ijassa-386	120	8	g	g	NOUN
ijassa-386	120	9	,	,	PUNCT
ijassa-386	120	10	xi	xi	X
ijassa-386	120	11	is	be	AUX
ijassa-386	120	12	called	call	VERB
ijassa-386	120	13	a	a	DET
ijassa-386	120	14	vertex	vertex	NOUN
ijassa-386	120	15	,	,	PUNCT
ijassa-386	120	16	(	(	PUNCT
ijassa-386	120	17	ei	ei	NOUN
ijassa-386	120	18	,	,	PUNCT
ijassa-386	120	19	rk	rk	NOUN
ijassa-386	120	20	i	i	PRON
ijassa-386	120	21	)	)	PUNCT
ijassa-386	120	22	is	be	AUX
ijassa-386	120	23	called	call	VERB
ijassa-386	120	24	vector	vector	NOUN
ijassa-386	120	25	hyperedge	hyperedge	NOUN
ijassa-386	120	26	.	.	PUNCT
ijassa-386	121	1	there	there	PRON
ijassa-386	121	2	exists	exist	VERB
ijassa-386	121	3	a	a	DET
ijassa-386	121	4	natural	natural	ADJ
ijassa-386	121	5	connection	connection	NOUN
ijassa-386	121	6	between	between	ADP
ijassa-386	121	7	the	the	DET
ijassa-386	121	8	vector	vector	NOUN
ijassa-386	121	9	hyper	hyper	NOUN
ijassa-386	121	10	-	-	NOUN
ijassa-386	121	11	graph	graph	NOUN
ijassa-386	121	12	and	and	CCONJ
ijassa-386	121	13	subspace	subspace	NOUN
ijassa-386	121	14	multi	multi	NOUN
ijassa-386	121	15	-	-	NOUN
ijassa-386	121	16	relation	relation	NOUN
ijassa-386	121	17	.	.	PUNCT
ijassa-386	122	1	assume	assume	VERB
ijassa-386	122	2	that	that	SCONJ
ijassa-386	122	3	a	a	DET
ijassa-386	122	4	vector	vector	NOUN
ijassa-386	122	5	hyper	hyper	NOUN
ijassa-386	122	6	-	-	NOUN
ijassa-386	122	7	graph	graph	NOUN
ijassa-386	122	8	x	x	PUNCT
ijassa-386	122	9	has	have	VERB
ijassa-386	122	10	a	a	DET
ijassa-386	122	11	vector	vector	NOUN
ijassa-386	122	12	hyperedge	hyperedge	NOUN
ijassa-386	122	13	(	(	PUNCT
ijassa-386	122	14	ei	ei	PROPN
ijassa-386	122	15	,	,	PUNCT
ijassa-386	122	16	rki	rki	PROPN
ijassa-386	122	17	)	)	PUNCT
ijassa-386	122	18	=	=	PUNCT
ijassa-386	123	1	(	(	PUNCT
ijassa-386	123	2	xi1	xi1	PROPN
ijassa-386	123	3	,	,	PUNCT
ijassa-386	123	4	xi2	xi2	PROPN
ijassa-386	123	5	,	,	PUNCT
ijassa-386	123	6	·	·	PUNCT
ijassa-386	123	7	·	·	PUNCT
ijassa-386	123	8	·	·	PUNCT
ijassa-386	123	9	,	,	PUNCT
ijassa-386	123	10	ximi	ximi	PROPN
ijassa-386	123	11	,	,	PUNCT
ijassa-386	123	12	rki	rki	PROPN
ijassa-386	123	13	)	)	PUNCT
ijassa-386	123	14	,	,	PUNCT
ijassa-386	123	15	then	then	ADV
ijassa-386	123	16	the	the	DET
ijassa-386	123	17	objects	object	NOUN
ijassa-386	123	18	xi1	xi1	PROPN
ijassa-386	123	19	,	,	PUNCT
ijassa-386	123	20	xi2	xi2	PROPN
ijassa-386	123	21	,	,	PUNCT
ijassa-386	123	22	·	·	PUNCT
ijassa-386	123	23	·	·	PUNCT
ijassa-386	123	24	·	·	PUNCT
ijassa-386	123	25	,	,	PUNCT
ijassa-386	123	26	ximi	ximi	PROPN
ijassa-386	123	27	has	have	VERB
ijassa-386	123	28	multi	multi	NOUN
ijassa-386	123	29	-	-	NOUN
ijassa-386	123	30	relation	relation	NOUN
ijassa-386	123	31	on	on	ADP
ijassa-386	123	32	subspace	subspace	PROPN
ijassa-386	123	33	rki	rki	PROPN
ijassa-386	123	34	,	,	PUNCT
ijassa-386	123	35	which	which	PRON
ijassa-386	123	36	means	mean	VERB
ijassa-386	123	37	ki	ki	PROPN
ijassa-386	123	38	-	-	PUNCT
ijassa-386	123	39	dimension	dimension	PROPN
ijassa-386	123	40	mi	mi	PROPN
ijassa-386	123	41	-	-	NOUN
ijassa-386	123	42	relation	relation	NOUN
ijassa-386	123	43	,	,	PUNCT
ijassa-386	123	44	and	and	CCONJ
ijassa-386	123	45	vice	vice	ADV
ijassa-386	123	46	versa	versa	ADV
ijassa-386	123	47	.	.	PUNCT
ijassa-386	124	1	hence	hence	ADV
ijassa-386	124	2	we	we	PRON
ijassa-386	124	3	can	can	AUX
ijassa-386	124	4	use	use	VERB
ijassa-386	124	5	the	the	DET
ijassa-386	124	6	vector	vector	NOUN
ijassa-386	124	7	hyper	hyper	NOUN
ijassa-386	124	8	-	-	NOUN
ijassa-386	124	9	graph	graph	NOUN
ijassa-386	124	10	to	to	PART
ijassa-386	124	11	express	express	VERB
ijassa-386	124	12	subspace	subspace	NOUN
ijassa-386	124	13	multi	multi	ADJ
ijassa-386	124	14	-	-	NOUN
ijassa-386	124	15	relation	relation	NOUN
ijassa-386	124	16	and	and	CCONJ
ijassa-386	124	17	study	study	VERB
ijassa-386	124	18	the	the	DET
ijassa-386	124	19	complex	complex	ADJ
ijassa-386	124	20	relation	relation	NOUN
ijassa-386	124	21	in	in	ADP
ijassa-386	124	22	system	system	NOUN
ijassa-386	124	23	.	.	PUNCT
ijassa-386	125	1	6	6	NUM
ijassa-386	125	2	conclusions	conclusion	NOUN
ijassa-386	125	3	we	we	PRON
ijassa-386	125	4	discuss	discuss	VERB
ijassa-386	125	5	the	the	DET
ijassa-386	125	6	method	method	NOUN
ijassa-386	125	7	to	to	PART
ijassa-386	125	8	express	express	VERB
ijassa-386	125	9	the	the	DET
ijassa-386	125	10	complexity	complexity	NOUN
ijassa-386	125	11	of	of	ADP
ijassa-386	125	12	a	a	DET
ijassa-386	125	13	system	system	NOUN
ijassa-386	125	14	by	by	ADP
ijassa-386	125	15	a	a	DET
ijassa-386	125	16	subspace	subspace	NOUN
ijassa-386	125	17	multi	multi	ADJ
ijassa-386	125	18	-	-	ADJ
ijassa-386	125	19	relation	relation	ADJ
ijassa-386	125	20	model	model	NOUN
ijassa-386	125	21	.	.	PUNCT
ijassa-386	126	1	based	base	VERB
ijassa-386	126	2	on	on	ADP
ijassa-386	126	3	the	the	DET
ijassa-386	126	4	attribute	attribute	NOUN
ijassa-386	126	5	space	space	NOUN
ijassa-386	126	6	of	of	ADP
ijassa-386	126	7	objects	object	NOUN
ijassa-386	126	8	,	,	PUNCT
ijassa-386	126	9	we	we	PRON
ijassa-386	126	10	establish	establish	VERB
ijassa-386	126	11	the	the	DET
ijassa-386	126	12	rigorous	rigorous	ADJ
ijassa-386	126	13	definition	definition	NOUN
ijassa-386	126	14	of	of	ADP
ijassa-386	126	15	subspace	subspace	PROPN
ijassa-386	126	16	multi	multi	NOUN
ijassa-386	126	17	-	-	NOUN
ijassa-386	126	18	relation	relation	NOUN
ijassa-386	126	19	.	.	PUNCT
ijassa-386	127	1	the	the	DET
ijassa-386	127	2	traditional	traditional	ADJ
ijassa-386	127	3	graph	graph	NOUN
ijassa-386	127	4	model	model	NOUN
ijassa-386	127	5	or	or	CCONJ
ijassa-386	127	6	complex	complex	ADJ
ijassa-386	127	7	network	network	NOUN
ijassa-386	127	8	is	be	AUX
ijassa-386	127	9	a	a	DET
ijassa-386	127	10	special	special	ADJ
ijassa-386	127	11	case	case	NOUN
ijassa-386	127	12	which	which	PRON
ijassa-386	127	13	is	be	AUX
ijassa-386	127	14	equivalent	equivalent	ADJ
ijassa-386	127	15	to	to	ADP
ijassa-386	127	16	the	the	DET
ijassa-386	127	17	one	one	NUM
ijassa-386	127	18	-	-	PUNCT
ijassa-386	127	19	dimension	dimension	NOUN
ijassa-386	127	20	tworelation	tworelation	NOUN
ijassa-386	127	21	.	.	PUNCT
ijassa-386	128	1	moreover	moreover	ADV
ijassa-386	128	2	,	,	PUNCT
ijassa-386	128	3	an	an	DET
ijassa-386	128	4	algorithm	algorithm	NOUN
ijassa-386	128	5	is	be	AUX
ijassa-386	128	6	given	give	VERB
ijassa-386	128	7	to	to	PART
ijassa-386	128	8	search	search	VERB
ijassa-386	128	9	for	for	ADP
ijassa-386	128	10	the	the	DET
ijassa-386	128	11	subspace	subspace	NOUN
ijassa-386	128	12	multi	multi	NOUN
ijassa-386	128	13	-	-	NOUN
ijassa-386	128	14	relation	relation	NOUN
ijassa-386	128	15	and	and	CCONJ
ijassa-386	128	16	its	its	PRON
ijassa-386	128	17	effectiveness	effectiveness	NOUN
ijassa-386	128	18	is	be	AUX
ijassa-386	128	19	verified	verify	VERB
ijassa-386	128	20	by	by	ADP
ijassa-386	128	21	real	real	ADJ
ijassa-386	128	22	data	datum	NOUN
ijassa-386	128	23	.	.	PUNCT
ijassa-386	129	1	finally	finally	ADV
ijassa-386	129	2	,	,	PUNCT
ijassa-386	129	3	vector	vector	NOUN
ijassa-386	129	4	hyper	hyper	NOUN
ijassa-386	129	5	-	-	PUNCT
ijassa-386	129	6	graphs	graph	NOUN
ijassa-386	129	7	related	relate	VERB
ijassa-386	129	8	to	to	ADP
ijassa-386	129	9	multi	multi	ADJ
ijassa-386	129	10	-	-	ADJ
ijassa-386	129	11	relation	relation	NOUN
ijassa-386	129	12	models	model	NOUN
ijassa-386	129	13	are	be	AUX
ijassa-386	129	14	discussed	discuss	VERB
ijassa-386	129	15	.	.	PUNCT
ijassa-386	130	1	the	the	DET
ijassa-386	130	2	equivalence	equivalence	NOUN
ijassa-386	130	3	of	of	ADP
ijassa-386	130	4	the	the	DET
ijassa-386	130	5	subspace	subspace	NOUN
ijassa-386	130	6	multirelation	multirelation	NOUN
ijassa-386	130	7	and	and	CCONJ
ijassa-386	130	8	the	the	DET
ijassa-386	130	9	vector	vector	NOUN
ijassa-386	130	10	hyper	hyper	NOUN
ijassa-386	130	11	-	-	NOUN
ijassa-386	130	12	graph	graph	NOUN
ijassa-386	130	13	is	be	AUX
ijassa-386	130	14	pointed	point	VERB
ijassa-386	130	15	out	out	ADP
ijassa-386	130	16	,	,	PUNCT
ijassa-386	130	17	which	which	PRON
ijassa-386	130	18	provides	provide	VERB
ijassa-386	130	19	a	a	DET
ijassa-386	130	20	new	new	ADJ
ijassa-386	130	21	method	method	NOUN
ijassa-386	130	22	to	to	PART
ijassa-386	130	23	study	study	VERB
ijassa-386	130	24	system	system	NOUN
ijassa-386	130	25	complexity	complexity	NOUN
ijassa-386	130	26	through	through	ADP
ijassa-386	130	27	vector	vector	NOUN
ijassa-386	130	28	hyper	hyper	NOUN
ijassa-386	130	29	-	-	NOUN
ijassa-386	130	30	graphs	graph	NOUN
ijassa-386	130	31	.	.	PUNCT
ijassa-386	131	1	references	reference	NOUN
ijassa-386	131	2	[	[	X
ijassa-386	131	3	1	1	X
ijassa-386	131	4	]	]	X
ijassa-386	131	5	nicholas	nicholas	PROPN
ijassa-386	131	6	w.	w.	PROPN
ijassa-386	131	7	watkins	watkins	PROPN
ijassa-386	131	8	and	and	CCONJ
ijassa-386	131	9	mervyn	mervyn	PROPN
ijassa-386	131	10	p.	p.	PROPN
ijassa-386	131	11	freeman	freeman	PROPN
ijassa-386	131	12	.	.	PUNCT
ijassa-386	132	1	(	(	PUNCT
ijassa-386	132	2	2008	2008	NUM
ijassa-386	132	3	)	)	PUNCT
ijassa-386	132	4	,	,	PUNCT
ijassa-386	132	5	“	"	PUNCT
ijassa-386	132	6	natural	natural	ADJ
ijassa-386	132	7	complexity	complexity	NOUN
ijassa-386	132	8	”	"	PUNCT
ijassa-386	132	9	,	,	PUNCT
ijassa-386	132	10	science	science	NOUN
ijassa-386	132	11	,	,	PUNCT
ijassa-386	132	12	vol.320	vol.320	PROPN
ijassa-386	132	13	,	,	PUNCT
ijassa-386	132	14	no.5874	no.5874	PROPN
ijassa-386	132	15	,	,	PUNCT
ijassa-386	132	16	pp.323	pp.323	PROPN
ijassa-386	132	17	-	-	PUNCT
ijassa-386	132	18	324	324	NUM
ijassa-386	132	19	.	.	PUNCT
ijassa-386	133	1	[	[	X
ijassa-386	133	2	2	2	NUM
ijassa-386	133	3	]	]	X
ijassa-386	133	4	yi	yi	PROPN
ijassa-386	133	5	lin	lin	PROPN
ijassa-386	133	6	.	.	PUNCT
ijassa-386	134	1	(	(	PUNCT
ijassa-386	134	2	2008	2008	NUM
ijassa-386	134	3	)	)	PUNCT
ijassa-386	134	4	,	,	PUNCT
ijassa-386	134	5	systemic	systemic	ADJ
ijassa-386	134	6	yoyos	yoyos	NOUN
ijassa-386	134	7	:	:	PUNCT
ijassa-386	134	8	some	some	DET
ijassa-386	134	9	impacts	impact	NOUN
ijassa-386	134	10	of	of	ADP
ijassa-386	134	11	the	the	DET
ijassa-386	134	12	second	second	ADJ
ijassa-386	134	13	dimension	dimension	NOUN
ijassa-386	134	14	,	,	PUNCT
ijassa-386	134	15	crc	crc	NOUN
ijassa-386	134	16	press	press	NOUN
ijassa-386	134	17	.	.	PUNCT
ijassa-386	135	1	[	[	X
ijassa-386	135	2	3	3	NUM
ijassa-386	135	3	]	]	X
ijassa-386	135	4	pavel	pavel	PROPN
ijassa-386	135	5	kabat	kabat	PROPN
ijassa-386	135	6	.	.	PUNCT
ijassa-386	136	1	(	(	PUNCT
ijassa-386	136	2	2012	2012	NUM
ijassa-386	136	3	)	)	PUNCT
ijassa-386	136	4	,	,	PUNCT
ijassa-386	136	5	“	"	PUNCT
ijassa-386	136	6	systems	system	NOUN
ijassa-386	136	7	science	science	NOUN
ijassa-386	136	8	for	for	ADP
ijassa-386	136	9	policy	policy	NOUN
ijassa-386	136	10	evaluation	evaluation	NOUN
ijassa-386	136	11	”	"	PUNCT
ijassa-386	136	12	.	.	PUNCT
ijassa-386	137	1	science	science	NOUN
ijassa-386	137	2	,	,	PUNCT
ijassa-386	137	3	vol.336	vol.336	NOUN
ijassa-386	137	4	,	,	PUNCT
ijassa-386	137	5	no.6087	no.6087	PROPN
ijassa-386	137	6	,	,	PUNCT
ijassa-386	137	7	pp.1398	pp.1398	PROPN
ijassa-386	137	8	.	.	PUNCT
ijassa-386	138	1	[	[	X
ijassa-386	138	2	4	4	NUM
ijassa-386	138	3	]	]	X
ijassa-386	138	4	george	george	PROPN
ijassa-386	138	5	sugihara	sugihara	NOUN
ijassa-386	138	6	,	,	PUNCT
ijassa-386	138	7	robert	robert	PROPN
ijassa-386	138	8	may	may	PROPN
ijassa-386	138	9	,	,	PUNCT
ijassa-386	138	10	hao	hao	PROPN
ijassa-386	138	11	ye	ye	PROPN
ijassa-386	138	12	,	,	PUNCT
ijassa-386	138	13	chih	chih	PROPN
ijassa-386	138	14	-	-	PUNCT
ijassa-386	138	15	hao	hao	PROPN
ijassa-386	138	16	hsieh	hsieh	PROPN
ijassa-386	138	17	,	,	PUNCT
ijassa-386	138	18	ethan	ethan	PROPN
ijassa-386	138	19	deyle	deyle	PROPN
ijassa-386	138	20	,	,	PUNCT
ijassa-386	138	21	michael	michael	PROPN
ijassa-386	138	22	fogarty	fogarty	PROPN
ijassa-386	138	23	,	,	PUNCT
ijassa-386	138	24	and	and	CCONJ
ijassa-386	138	25	stephan	stephan	PROPN
ijassa-386	138	26	munch	munch	PROPN
ijassa-386	138	27	.	.	PUNCT
ijassa-386	139	1	(	(	PUNCT
ijassa-386	139	2	2012	2012	NUM
ijassa-386	139	3	)	)	PUNCT
ijassa-386	139	4	,	,	PUNCT
ijassa-386	139	5	“	"	PUNCT
ijassa-386	139	6	detecting	detect	VERB
ijassa-386	139	7	causality	causality	NOUN
ijassa-386	139	8	in	in	ADP
ijassa-386	139	9	complex	complex	ADJ
ijassa-386	139	10	ecosystems	ecosystem	NOUN
ijassa-386	139	11	”	"	PUNCT
ijassa-386	139	12	,	,	PUNCT
ijassa-386	139	13	science	science	NOUN
ijassa-386	139	14	,	,	PUNCT
ijassa-386	139	15	vol.338	vol.338	NOUN
ijassa-386	139	16	,	,	PUNCT
ijassa-386	139	17	no.6106	no.6106	NOUN
ijassa-386	139	18	,	,	PUNCT
ijassa-386	139	19	pp.496	pp.496	NOUN
ijassa-386	139	20	-	-	PUNCT
ijassa-386	139	21	500	500	NUM
ijassa-386	139	22	.	.	PUNCT
ijassa-386	140	1	[	[	X
ijassa-386	140	2	5	5	X
ijassa-386	140	3	]	]	PUNCT
ijassa-386	140	4	j.	j.	PROPN
ijassa-386	140	5	leskovec	leskovec	PROPN
ijassa-386	140	6	,	,	PUNCT
ijassa-386	140	7	j.	j.	PROPN
ijassa-386	140	8	kleinberg	kleinberg	PROPN
ijassa-386	140	9	and	and	CCONJ
ijassa-386	140	10	c	c	PROPN
ijassa-386	140	11	and	and	CCONJ
ijassa-386	140	12	faloutsos	faloutsos	PROPN
ijassa-386	140	13	.	.	PUNCT
ijassa-386	141	1	(	(	PUNCT
ijassa-386	141	2	2005	2005	NUM
ijassa-386	141	3	)	)	PUNCT
ijassa-386	141	4	,	,	PUNCT
ijassa-386	141	5	“	"	PUNCT
ijassa-386	141	6	graphs	graph	NOUN
ijassa-386	141	7	over	over	ADP
ijassa-386	141	8	time	time	NOUN
ijassa-386	141	9	:	:	PUNCT
ijassa-386	141	10	densification	densification	NOUN
ijassa-386	141	11	laws	law	NOUN
ijassa-386	141	12	,	,	PUNCT
ijassa-386	141	13	shrinking	shrink	VERB
ijassa-386	141	14	diameters	diameter	NOUN
ijassa-386	141	15	and	and	CCONJ
ijassa-386	141	16	possible	possible	ADJ
ijassa-386	141	17	explanations	explanation	NOUN
ijassa-386	141	18	”	"	PUNCT
ijassa-386	141	19	,	,	PUNCT
ijassa-386	141	20	acm	acm	PROPN
ijassa-386	141	21	sigkdd	sigkdd	NOUN
ijassa-386	141	22	international	international	ADJ
ijassa-386	141	23	conference	conference	NOUN
ijassa-386	141	24	on	on	ADP
ijassa-386	141	25	knowledge	knowledge	NOUN
ijassa-386	141	26	discovery	discovery	PROPN
ijassa-386	141	27	and	and	CCONJ
ijassa-386	141	28	data	datum	NOUN
ijassa-386	141	29	mining	mining	NOUN
ijassa-386	141	30	(	(	PUNCT
ijassa-386	141	31	kdd	kdd	PROPN
ijassa-386	141	32	)	)	PUNCT
ijassa-386	141	33	.	.	PUNCT
ijassa-386	142	1	[	[	X
ijassa-386	142	2	6	6	NUM
ijassa-386	142	3	]	]	SYM
ijassa-386	142	4	m.e.j	m.e.j	NOUN
ijassa-386	142	5	.	.	PUNCT
ijassa-386	142	6	newman	newman	PROPN
ijassa-386	142	7	.	.	PUNCT
ijassa-386	143	1	(	(	PUNCT
ijassa-386	143	2	2003	2003	NUM
ijassa-386	143	3	)	)	PUNCT
ijassa-386	143	4	,	,	PUNCT
ijassa-386	143	5	“	"	PUNCT
ijassa-386	143	6	the	the	DET
ijassa-386	143	7	structure	structure	NOUN
ijassa-386	143	8	and	and	CCONJ
ijassa-386	143	9	function	function	NOUN
ijassa-386	143	10	of	of	ADP
ijassa-386	143	11	complex	complex	ADJ
ijassa-386	143	12	networks	network	NOUN
ijassa-386	143	13	”	"	PUNCT
ijassa-386	143	14	,	,	PUNCT
ijassa-386	143	15	siam	siam	PROPN
ijassa-386	143	16	rev	rev	PROPN
ijassa-386	143	17	,	,	PUNCT
ijassa-386	143	18	vol.45	vol.45	X
ijassa-386	143	19	,	,	PUNCT
ijassa-386	143	20	no.2	no.2	PROPN
ijassa-386	143	21	,	,	PUNCT
ijassa-386	143	22	pp.167	pp.167	PROPN
ijassa-386	143	23	-	-	PUNCT
ijassa-386	143	24	256	256	NUM
ijassa-386	143	25	.	.	NOUN
ijassa-386	143	26	44	44	NUM
ijassa-386	143	27	dongyun	dongyun	NOUN
ijassa-386	143	28	yi	yi	NOUN
ijassa-386	143	29	:	:	PUNCT
ijassa-386	143	30	a	a	DET
ijassa-386	143	31	subspace	subspace	ADJ
ijassa-386	143	32	multi	multi	ADJ
ijassa-386	143	33	-	-	ADJ
ijassa-386	143	34	relation	relation	ADJ
ijassa-386	143	35	model	model	NOUN
ijassa-386	143	36	for	for	ADP
ijassa-386	143	37	the	the	DET
ijassa-386	143	38	expression	expression	NOUN
ijassa-386	143	39	of	of	ADP
ijassa-386	143	40	system	system	NOUN
ijassa-386	143	41	complexity	complexity	NOUN
ijassa-386	143	42	[	[	X
ijassa-386	143	43	7	7	X
ijassa-386	143	44	]	]	X
ijassa-386	143	45	s.	s.	PROPN
ijassa-386	143	46	boccaletti	boccaletti	PROPN
ijassa-386	143	47	,	,	PUNCT
ijassa-386	143	48	v.	v.	PROPN
ijassa-386	143	49	latora	latora	NOUN
ijassa-386	143	50	,	,	PUNCT
ijassa-386	143	51	y.	y.	PROPN
ijassa-386	143	52	moreno	moreno	PROPN
ijassa-386	143	53	,	,	PUNCT
ijassa-386	143	54	m.	m.	PROPN
ijassa-386	143	55	chavez	chavez	PROPN
ijassa-386	143	56	and	and	CCONJ
ijassa-386	143	57	d.-u	d.-u	PROPN
ijassa-386	143	58	.	.	PUNCT
ijassa-386	144	1	huang	huang	PROPN
ijassa-386	144	2	.	.	PUNCT
ijassa-386	144	3	(	(	PUNCT
ijassa-386	144	4	2006	2006	NUM
ijassa-386	144	5	)	)	PUNCT
ijassa-386	144	6	,	,	PUNCT
ijassa-386	144	7	“	"	PUNCT
ijassa-386	144	8	complex	complex	ADJ
ijassa-386	144	9	networks	network	NOUN
ijassa-386	144	10	:	:	PUNCT
ijassa-386	144	11	structure	structure	NOUN
ijassa-386	144	12	and	and	CCONJ
ijassa-386	144	13	dynamics	dynamic	NOUN
ijassa-386	144	14	”	"	PUNCT
ijassa-386	144	15	,	,	PUNCT
ijassa-386	144	16	phys	phy	NOUN
ijassa-386	144	17	.	.	PUNCT
ijassa-386	145	1	rep	rep	PROPN
ijassa-386	145	2	,	,	PUNCT
ijassa-386	145	3	vol.424	vol.424	PROPN
ijassa-386	145	4	,	,	PUNCT
ijassa-386	145	5	no.4	no.4	PROPN
ijassa-386	145	6	,	,	PUNCT
ijassa-386	145	7	pp.175	pp.175	PROPN
ijassa-386	145	8	-	-	PUNCT
ijassa-386	145	9	308	308	NUM
ijassa-386	145	10	.	.	PUNCT
ijassa-386	146	1	[	[	X
ijassa-386	146	2	8	8	NUM
ijassa-386	146	3	]	]	X
ijassa-386	146	4	l.	l.	PROPN
ijassa-386	146	5	da	da	PROPN
ijassa-386	146	6	,	,	PUNCT
ijassa-386	146	7	f.	f.	PROPN
ijassa-386	146	8	costa	costa	PROPN
ijassa-386	146	9	,	,	PUNCT
ijassa-386	146	10	f.a	f.a	PROPN
ijassa-386	146	11	.	.	PROPN
ijassa-386	146	12	rodrigues	rodrigues	PROPN
ijassa-386	146	13	,	,	PUNCT
ijassa-386	146	14	g.	g.	PROPN
ijassa-386	146	15	travieso	travieso	NOUN
ijassa-386	146	16	and	and	CCONJ
ijassa-386	146	17	p.r.u	p.r.u	NOUN
ijassa-386	146	18	.	.	PUNCT
ijassa-386	146	19	boas	boas	PROPN
ijassa-386	146	20	.	.	PUNCT
ijassa-386	147	1	(	(	PUNCT
ijassa-386	147	2	2006	2006	NUM
ijassa-386	147	3	)	)	PUNCT
ijassa-386	147	4	,	,	PUNCT
ijassa-386	147	5	“	"	PUNCT
ijassa-386	147	6	characterization	characterization	NOUN
ijassa-386	147	7	of	of	ADP
ijassa-386	147	8	complex	complex	ADJ
ijassa-386	147	9	networks	network	NOUN
ijassa-386	147	10	:	:	PUNCT
ijassa-386	147	11	a	a	DET
ijassa-386	147	12	survey	survey	NOUN
ijassa-386	147	13	of	of	ADP
ijassa-386	147	14	measurements	measurement	NOUN
ijassa-386	147	15	”	"	PUNCT
ijassa-386	147	16	,	,	PUNCT
ijassa-386	147	17	adv	adv	PROPN
ijassa-386	147	18	.	.	PUNCT
ijassa-386	148	1	phys	phy	NOUN
ijassa-386	148	2	,	,	PUNCT
ijassa-386	148	3	vol.56	vol.56	ADV
ijassa-386	148	4	,	,	PUNCT
ijassa-386	148	5	no.1	no.1	NUM
ijassa-386	148	6	,	,	PUNCT
ijassa-386	148	7	pp.167	pp.167	NOUN
ijassa-386	148	8	-	-	PUNCT
ijassa-386	148	9	242	242	NUM
ijassa-386	148	10	.	.	PUNCT
ijassa-386	149	1	[	[	X
ijassa-386	149	2	9	9	NUM
ijassa-386	149	3	]	]	PUNCT
ijassa-386	149	4	claude	claude	PROPN
ijassa-386	149	5	berge	berge	PROPN
ijassa-386	149	6	.	.	PUNCT
ijassa-386	150	1	(	(	PUNCT
ijassa-386	150	2	1989	1989	NUM
ijassa-386	150	3	)	)	PUNCT
ijassa-386	151	1	,	,	PUNCT
ijassa-386	151	2	hypergraphs	hypergraph	NOUN
ijassa-386	151	3	:	:	PUNCT
ijassa-386	151	4	combinatorics	combinatoric	NOUN
ijassa-386	151	5	of	of	ADP
ijassa-386	151	6	finite	finite	PROPN
ijassa-386	151	7	sets	set	NOUN
ijassa-386	151	8	,	,	PUNCT
ijassa-386	151	9	northholland	northholland	NOUN
ijassa-386	151	10	.	.	PUNCT
ijassa-386	152	1	[	[	X
ijassa-386	152	2	10	10	NUM
ijassa-386	152	3	]	]	X
ijassa-386	152	4	d.s.johnson	d.s.johnson	NOUN
ijassa-386	152	5	and	and	CCONJ
ijassa-386	152	6	h.o.pollak	h.o.pollak	PROPN
ijassa-386	152	7	.	.	PUNCT
ijassa-386	153	1	(	(	PUNCT
ijassa-386	153	2	2006	2006	NUM
ijassa-386	153	3	)	)	PUNCT
ijassa-386	153	4	,	,	PUNCT
ijassa-386	153	5	“	"	PUNCT
ijassa-386	153	6	hypergraph	hypergraph	VERB
ijassa-386	153	7	planarity	planarity	NOUN
ijassa-386	153	8	and	and	CCONJ
ijassa-386	153	9	the	the	DET
ijassa-386	153	10	complexity	complexity	NOUN
ijassa-386	153	11	of	of	ADP
ijassa-386	153	12	drawing	draw	VERB
ijassa-386	153	13	venn	venn	PROPN
ijassa-386	153	14	diagrams	diagram	NOUN
ijassa-386	153	15	”	"	PUNCT
ijassa-386	153	16	,	,	PUNCT
ijassa-386	153	17	journal	journal	NOUN
ijassa-386	153	18	of	of	ADP
ijassa-386	153	19	graph	graph	NOUN
ijassa-386	153	20	theory	theory	NOUN
ijassa-386	153	21	,	,	PUNCT
ijassa-386	153	22	vol.11	vol.11	PROPN
ijassa-386	153	23	,	,	PUNCT
ijassa-386	153	24	no.3	no.3	PROPN
ijassa-386	153	25	,	,	PUNCT
ijassa-386	153	26	pp.309	pp.309	PROPN
ijassa-386	153	27	-	-	PUNCT
ijassa-386	153	28	325	325	NUM
ijassa-386	153	29	.	.	PUNCT
ijassa-386	154	1	[	[	X
ijassa-386	154	2	11	11	NUM
ijassa-386	154	3	]	]	X
ijassa-386	154	4	vitaly	vitaly	PROPN
ijassa-386	154	5	i.voloshin	i.voloshin	PROPN
ijassa-386	154	6	.	.	PUNCT
ijassa-386	155	1	(	(	PUNCT
ijassa-386	155	2	2009	2009	NUM
ijassa-386	155	3	)	)	PUNCT
ijassa-386	155	4	,	,	PUNCT
ijassa-386	155	5	introduction	introduction	NOUN
ijassa-386	155	6	to	to	PART
ijassa-386	155	7	graph	graph	VERB
ijassa-386	155	8	and	and	CCONJ
ijassa-386	155	9	hypergraph	hypergraph	VERB
ijassa-386	155	10	theory	theory	NOUN
ijassa-386	155	11	,	,	PUNCT
ijassa-386	155	12	nova	nova	PROPN
ijassa-386	155	13	science	science	NOUN
ijassa-386	155	14	publishers	publisher	NOUN
ijassa-386	155	15	,	,	PUNCT
ijassa-386	155	16	inc	inc	PROPN
ijassa-386	155	17	.	.	PUNCT
ijassa-386	156	1	[	[	X
ijassa-386	156	2	12	12	NUM
ijassa-386	156	3	]	]	PUNCT
ijassa-386	156	4	xie	xie	PROPN
ijassa-386	156	5	zheng	zheng	PROPN
ijassa-386	156	6	,	,	PUNCT
ijassa-386	156	7	yi	yi	PROPN
ijassa-386	156	8	dong	dong	PROPN
ijassa-386	156	9	-	-	PUNCT
ijassa-386	156	10	yun	yun	PROPN
ijassa-386	156	11	,	,	PUNCT
ijassa-386	156	12	ouyang	ouyang	PROPN
ijassa-386	156	13	zhen	zhen	PROPN
ijassa-386	156	14	-	-	PUNCT
ijassa-386	156	15	zheng	zheng	PROPN
ijassa-386	156	16	and	and	CCONJ
ijassa-386	156	17	li	li	PROPN
ijassa-386	156	18	dong	dong	PROPN
ijassa-386	156	19	.	.	PUNCT
ijassa-386	156	20	(	(	PUNCT
ijassa-386	156	21	2012	2012	NUM
ijassa-386	156	22	)	)	PUNCT
ijassa-386	156	23	,	,	PUNCT
ijassa-386	156	24	“	"	PUNCT
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ijassa-386	156	28	modularity	modularity	NOUN
ijassa-386	156	29	reveal	reveal	VERB
ijassa-386	156	30	structure	structure	NOUN
ijassa-386	156	31	for	for	ADP
ijassa-386	156	32	documents	document	NOUN
ijassa-386	156	33	”	"	PUNCT
ijassa-386	156	34	,	,	PUNCT
ijassa-386	156	35	china	china	PROPN
ijassa-386	156	36	.	.	PUNCT
ijassa-386	157	1	phys	phy	NOUN
ijassa-386	157	2	.	.	PUNCT
ijassa-386	158	1	lett	lett	PROPN
ijassa-386	158	2	.	.	PROPN
ijassa-386	158	3	,	,	PUNCT
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ijassa-386	158	5	,	,	PUNCT
ijassa-386	158	6	no.3	no.3	NOUN
ijassa-386	158	7	.	.	PUNCT
ijassa-386	159	1	[	[	X
ijassa-386	159	2	13	13	NUM
ijassa-386	159	3	]	]	X
ijassa-386	159	4	dominique	dominique	PROPN
ijassa-386	159	5	lasalle	lasalle	PROPN
ijassa-386	159	6	and	and	CCONJ
ijassa-386	159	7	george	george	PROPN
ijassa-386	159	8	karypis	karypis	PROPN
ijassa-386	159	9	.	.	PUNCT
ijassa-386	160	1	(	(	PUNCT
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ijassa-386	160	3	)	)	PUNCT
ijassa-386	160	4	,	,	PUNCT
ijassa-386	160	5	“	"	PUNCT
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ijassa-386	160	7	-	-	ADJ
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ijassa-386	160	10	partitioning	partitioning	NOUN
ijassa-386	160	11	”	"	PUNCT
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ijassa-386	160	21	.	.	PUNCT
ijassa-386	161	1	[	[	X
ijassa-386	161	2	14	14	NUM
ijassa-386	161	3	]	]	X
ijassa-386	161	4	charu	charu	PROPN
ijassa-386	161	5	c.aggarwal	c.aggarwal	PROPN
ijassa-386	161	6	,	,	PUNCT
ijassa-386	161	7	joel	joel	PROPN
ijassa-386	161	8	l.wolf	l.wolf	PROPN
ijassa-386	161	9	,	,	PUNCT
ijassa-386	161	10	philip	philip	PROPN
ijassa-386	161	11	s.yu	s.yu	PROPN
ijassa-386	161	12	,	,	PUNCT
ijassa-386	161	13	cecilia	cecilia	PROPN
ijassa-386	161	14	m.	m.	NOUN
ijassa-386	161	15	procopiuc	procopiuc	PROPN
ijassa-386	161	16	and	and	CCONJ
ijassa-386	161	17	jong	jong	PROPN
ijassa-386	161	18	soo	soo	PROPN
ijassa-386	161	19	park	park	PROPN
ijassa-386	161	20	.	.	PUNCT
ijassa-386	162	1	(	(	PUNCT
ijassa-386	162	2	1999	1999	NUM
ijassa-386	162	3	)	)	PUNCT
ijassa-386	162	4	,	,	PUNCT
ijassa-386	162	5	“	"	PUNCT
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ijassa-386	162	7	algorithms	algorithm	NOUN
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ijassa-386	162	10	clustering	clustering	NOUN
ijassa-386	162	11	”	"	PUNCT
ijassa-386	162	12	,	,	PUNCT
ijassa-386	162	13	acm	acm	PROPN
ijassa-386	162	14	sigmod	sigmod	PROPN
ijassa-386	162	15	record	record	PROPN
ijassa-386	162	16	,	,	PUNCT
ijassa-386	162	17	new	new	PROPN
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ijassa-386	162	19	,	,	PUNCT
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ijassa-386	162	21	,	,	PUNCT
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ijassa-386	162	23	,	,	PUNCT
ijassa-386	162	24	pp.61	pp.61	NOUN
ijassa-386	162	25	-	-	PUNCT
ijassa-386	162	26	72	72	NUM
ijassa-386	162	27	.	.	PUNCT
ijassa-386	163	1	[	[	X
ijassa-386	163	2	15	15	NUM
ijassa-386	163	3	]	]	X
ijassa-386	163	4	rakesh	rakesh	PROPN
ijassa-386	163	5	agrawal	agrawal	PROPN
ijassa-386	163	6	,	,	PUNCT
ijassa-386	163	7	johannes	johannes	PROPN
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ijassa-386	163	9	,	,	PUNCT
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ijassa-386	163	12	and	and	CCONJ
ijassa-386	163	13	prabhakar	prabhakar	PROPN
ijassa-386	163	14	raghavan	raghavan	PROPN
ijassa-386	163	15	.	.	PUNCT
ijassa-386	164	1	(	(	PUNCT
ijassa-386	164	2	2005	2005	NUM
ijassa-386	164	3	)	)	PUNCT
ijassa-386	164	4	,	,	PUNCT
ijassa-386	164	5	“	"	PUNCT
ijassa-386	164	6	automatic	automatic	ADJ
ijassa-386	164	7	subspace	subspace	NOUN
ijassa-386	164	8	clustering	clustering	NOUN
ijassa-386	164	9	of	of	ADP
ijassa-386	164	10	high	high	ADJ
ijassa-386	164	11	dimensional	dimensional	ADJ
ijassa-386	164	12	data	datum	NOUN
ijassa-386	164	13	”	"	PUNCT
ijassa-386	164	14	,	,	PUNCT
ijassa-386	164	15	data	datum	NOUN
ijassa-386	164	16	mining	mining	NOUN
ijassa-386	164	17	and	and	CCONJ
ijassa-386	164	18	knowledge	knowledge	NOUN
ijassa-386	164	19	discovery	discovery	PROPN
ijassa-386	164	20	,	,	PUNCT
ijassa-386	164	21	vol.11	vol.11	PROPN
ijassa-386	164	22	,	,	PUNCT
ijassa-386	164	23	no.1	no.1	NUM
ijassa-386	164	24	,	,	PUNCT
ijassa-386	164	25	pp.5	pp.5	NOUN
ijassa-386	164	26	-	-	PUNCT
ijassa-386	164	27	33	33	NUM
ijassa-386	164	28	.	.	PUNCT
ijassa-386	165	1	[	[	X
ijassa-386	165	2	16	16	NUM
ijassa-386	165	3	]	]	PUNCT
ijassa-386	165	4	kriegel	kriegel	PROPN
ijassa-386	165	5	hans	hans	PROPN
ijassa-386	165	6	-	-	PUNCT
ijassa-386	165	7	peter	peter	PROPN
ijassa-386	165	8	,	,	PUNCT
ijassa-386	165	9	kroger	kroger	PROPN
ijassa-386	165	10	peer	peer	NOUN
ijassa-386	165	11	and	and	CCONJ
ijassa-386	165	12	zimek	zimek	PROPN
ijassa-386	165	13	arthur	arthur	PROPN
ijassa-386	165	14	.	.	PUNCT
ijassa-386	166	1	(	(	PUNCT
ijassa-386	166	2	2009	2009	NUM
ijassa-386	166	3	)	)	PUNCT
ijassa-386	166	4	,	,	PUNCT
ijassa-386	166	5	“	"	PUNCT
ijassa-386	166	6	clustering	cluster	VERB
ijassa-386	166	7	high	high	ADJ
ijassa-386	166	8	-	-	PUNCT
ijassa-386	166	9	dimensional	dimensional	ADJ
ijassa-386	166	10	data	datum	NOUN
ijassa-386	166	11	:	:	PUNCT
ijassa-386	166	12	a	a	DET
ijassa-386	166	13	survey	survey	NOUN
ijassa-386	166	14	on	on	ADP
ijassa-386	166	15	subspace	subspace	NOUN
ijassa-386	166	16	clustering	clustering	NOUN
ijassa-386	166	17	,	,	PUNCT
ijassa-386	166	18	pattern	pattern	NOUN
ijassa-386	166	19	-	-	PUNCT
ijassa-386	166	20	based	base	VERB
ijassa-386	166	21	clustering	clustering	NOUN
ijassa-386	166	22	,	,	PUNCT
ijassa-386	166	23	and	and	CCONJ
ijassa-386	166	24	correlation	correlation	NOUN
ijassa-386	166	25	clustering	clustering	NOUN
ijassa-386	166	26	”	"	PUNCT
ijassa-386	166	27	,	,	PUNCT
ijassa-386	166	28	acm	acm	NOUN
ijassa-386	166	29	transactions	transaction	NOUN
ijassa-386	166	30	on	on	ADP
ijassa-386	166	31	knowledge	knowledge	NOUN
ijassa-386	166	32	discovery	discovery	NOUN
ijassa-386	166	33	from	from	ADP
ijassa-386	166	34	data	data	PROPN
ijassa-386	166	35	,	,	PUNCT
ijassa-386	166	36	nwe	nwe	PROPN
ijassa-386	166	37	york	york	PROPN
ijassa-386	166	38	,	,	PUNCT
ijassa-386	166	39	vol.3	vol.3	PROPN
ijassa-386	166	40	,	,	PUNCT
ijassa-386	166	41	no.1	no.1	NUM
ijassa-386	166	42	,	,	PUNCT
ijassa-386	166	43	pp.1	pp.1	PROPN
ijassa-386	166	44	-	-	PUNCT
ijassa-386	166	45	58	58	NUM
ijassa-386	166	46	.	.	PUNCT
ijassa-386	167	1	[	[	X
ijassa-386	167	2	17	17	NUM
ijassa-386	167	3	]	]	PUNCT
ijassa-386	167	4	enron	enron	PROPN
ijassa-386	167	5	email	email	NOUN
ijassa-386	167	6	dataset	dataset	PROPN
ijassa-386	167	7	,	,	PUNCT
ijassa-386	167	8	http://www.cs.cmu.edu/	http://www.cs.cmu.edu/	PROPN
ijassa-386	167	9	enron/	enron/	NUM
ijassa-386	167	10	corresponding	correspond	VERB
ijassa-386	167	11	author	author	NOUN
ijassa-386	167	12	dongyun	dongyun	PROPN
ijassa-386	167	13	yi	yi	PROPN
ijassa-386	167	14	:	:	PUNCT
ijassa-386	167	15	dongyunyi@sina.com	dongyunyi@sina.com	X