id	sid	tid	token	lemma	pos
arestyrurj-165	1	1	microsoft	microsoft	PROPN
arestyrurj-165	1	2	word	word	NOUN
arestyrurj-165	1	3	[	[	X
arestyrurj-165	1	4	formatted	format	VERB
arestyrurj-165	1	5	]	]	PUNCT
arestyrurj-165	1	6	3	3	NUM
arestyrurj-165	1	7	learning	learn	VERB
arestyrurj-165	1	8	predictors	predictor	NOUN
arestyrurj-165	1	9	from	from	ADP
arestyrurj-165	1	10	multidimensional	multidimensional	ADJ
arestyrurj-165	1	11	data	datum	NOUN
arestyrurj-165	1	12	with	with	ADP
arestyrurj-165	1	13	tensor	tensor	NOUN
arestyrurj-165	1	14	factorizations	factorization	NOUN
arestyrurj-165	1	15	aresty	aresty	ADJ
arestyrurj-165	1	16	rutgers	rutgers	PROPN
arestyrurj-165	1	17	undergraduate	undergraduate	PROPN
arestyrurj-165	1	18	research	research	PROPN
arestyrurj-165	1	19	journal	journal	PROPN
arestyrurj-165	1	20	,	,	PUNCT
arestyrurj-165	1	21	volume	volume	NOUN
arestyrurj-165	1	22	i	i	PRON
arestyrurj-165	1	23	,	,	PUNCT
arestyrurj-165	1	24	issue	issue	VERB
arestyrurj-165	1	25	iii	iii	NOUN
arestyrurj-165	1	26	this	this	DET
arestyrurj-165	1	27	work	work	NOUN
arestyrurj-165	1	28	is	be	AUX
arestyrurj-165	1	29	licensed	license	VERB
arestyrurj-165	1	30	under	under	ADP
arestyrurj-165	1	31	a	a	DET
arestyrurj-165	1	32	creative	creative	ADJ
arestyrurj-165	1	33	commons	common	NOUN
arestyrurj-165	1	34	attribution	attribution	NOUN
arestyrurj-165	1	35	-	-	PUNCT
arestyrurj-165	1	36	noncommercial	noncommercial	ADJ
arestyrurj-165	1	37	-	-	PUNCT
arestyrurj-165	1	38	sharealike	sharealike	ADJ
arestyrurj-165	1	39	4.0	4.0	NUM
arestyrurj-165	1	40	international	international	ADJ
arestyrurj-165	1	41	license	license	NOUN
arestyrurj-165	1	42	.	.	PUNCT
arestyrurj-165	2	1	learning	learn	VERB
arestyrurj-165	2	2	predictors	predictor	NOUN
arestyrurj-165	2	3	from	from	ADP
arestyrurj-165	2	4	multi	multi	ADJ
arestyrurj-165	2	5	dimensional	dimensional	ADJ
arestyrurj-165	2	6	data	datum	NOUN
arestyrurj-165	2	7	with	with	ADP
arestyrurj-165	2	8	tensor	tensor	NOUN
arestyrurj-165	2	9	factorizations	factorization	NOUN
arestyrurj-165	2	10	soo	soo	PROPN
arestyrurj-165	2	11	min	min	PROPN
arestyrurj-165	2	12	kwon	kwon	PROPN
arestyrurj-165	2	13	,	,	PUNCT
arestyrurj-165	2	14	anand	anand	PROPN
arestyrurj-165	2	15	d.	d.	PROPN
arestyrurj-165	2	16	sarwate	sarwate	PROPN
arestyrurj-165	2	17	(	(	PUNCT
arestyrurj-165	2	18	faculty	faculty	NOUN
arestyrurj-165	2	19	advisor	advisor	NOUN
arestyrurj-165	2	20	)	)	PUNCT
arestyrurj-165	2	21	✵	✵	PROPN
arestyrurj-165	2	22	abstract	abstract	ADJ
arestyrurj-165	2	23	statistical	statistical	ADJ
arestyrurj-165	2	24	machine	machine	NOUN
arestyrurj-165	2	25	learning	learn	VERB
arestyrurj-165	2	26	algorithms	algorithm	NOUN
arestyrurj-165	2	27	often	often	ADV
arestyrurj-165	2	28	involve	involve	VERB
arestyrurj-165	2	29	learning	learn	VERB
arestyrurj-165	2	30	a	a	DET
arestyrurj-165	2	31	linear	linear	ADJ
arestyrurj-165	2	32	relationship	relationship	NOUN
arestyrurj-165	2	33	between	between	ADP
arestyrurj-165	2	34	dependent	dependent	ADJ
arestyrurj-165	2	35	and	and	CCONJ
arestyrurj-165	2	36	independent	independent	ADJ
arestyrurj-165	2	37	variables	variable	NOUN
arestyrurj-165	2	38	.	.	PUNCT
arestyrurj-165	3	1	this	this	DET
arestyrurj-165	3	2	relationship	relationship	NOUN
arestyrurj-165	3	3	is	be	AUX
arestyrurj-165	3	4	modeled	model	VERB
arestyrurj-165	3	5	as	as	ADP
arestyrurj-165	3	6	a	a	DET
arestyrurj-165	3	7	vector	vector	NOUN
arestyrurj-165	3	8	of	of	ADP
arestyrurj-165	3	9	numerical	numerical	ADJ
arestyrurj-165	3	10	values	value	NOUN
arestyrurj-165	3	11	,	,	PUNCT
arestyrurj-165	3	12	commonly	commonly	ADV
arestyrurj-165	3	13	referred	refer	VERB
arestyrurj-165	3	14	to	to	ADP
arestyrurj-165	3	15	as	as	ADP
arestyrurj-165	3	16	weights	weight	NOUN
arestyrurj-165	3	17	or	or	CCONJ
arestyrurj-165	3	18	predictors	predictor	NOUN
arestyrurj-165	3	19	.	.	PUNCT
arestyrurj-165	4	1	these	these	DET
arestyrurj-165	4	2	weights	weight	NOUN
arestyrurj-165	4	3	allow	allow	VERB
arestyrurj-165	4	4	us	we	PRON
arestyrurj-165	4	5	to	to	PART
arestyrurj-165	4	6	make	make	VERB
arestyrurj-165	4	7	predictions	prediction	NOUN
arestyrurj-165	4	8	,	,	PUNCT
arestyrurj-165	4	9	and	and	CCONJ
arestyrurj-165	4	10	the	the	DET
arestyrurj-165	4	11	quality	quality	NOUN
arestyrurj-165	4	12	of	of	ADP
arestyrurj-165	4	13	these	these	DET
arestyrurj-165	4	14	weights	weight	NOUN
arestyrurj-165	4	15	influence	influence	VERB
arestyrurj-165	4	16	the	the	DET
arestyrurj-165	4	17	accuracy	accuracy	NOUN
arestyrurj-165	4	18	of	of	ADP
arestyrurj-165	4	19	our	our	PRON
arestyrurj-165	4	20	predictions	prediction	NOUN
arestyrurj-165	4	21	.	.	PUNCT
arestyrurj-165	5	1	however	however	ADV
arestyrurj-165	5	2	,	,	PUNCT
arestyrurj-165	5	3	when	when	SCONJ
arestyrurj-165	5	4	the	the	DET
arestyrurj-165	5	5	dependent	dependent	ADJ
arestyrurj-165	5	6	variable	variable	NOUN
arestyrurj-165	5	7	inherently	inherently	ADV
arestyrurj-165	5	8	possesses	possess	VERB
arestyrurj-165	5	9	a	a	DET
arestyrurj-165	5	10	more	more	ADV
arestyrurj-165	5	11	complex	complex	ADJ
arestyrurj-165	5	12	,	,	PUNCT
arestyrurj-165	5	13	multidimensional	multidimensional	ADJ
arestyrurj-165	5	14	structure	structure	NOUN
arestyrurj-165	5	15	,	,	PUNCT
arestyrurj-165	5	16	it	it	PRON
arestyrurj-165	5	17	becomes	become	VERB
arestyrurj-165	5	18	increasingly	increasingly	ADV
arestyrurj-165	5	19	difficult	difficult	ADJ
arestyrurj-165	5	20	to	to	PART
arestyrurj-165	5	21	model	model	VERB
arestyrurj-165	5	22	the	the	DET
arestyrurj-165	5	23	relationship	relationship	NOUN
arestyrurj-165	5	24	with	with	ADP
arestyrurj-165	5	25	a	a	DET
arestyrurj-165	5	26	vector	vector	NOUN
arestyrurj-165	5	27	.	.	PUNCT
arestyrurj-165	6	1	in	in	ADP
arestyrurj-165	6	2	this	this	DET
arestyrurj-165	6	3	paper	paper	NOUN
arestyrurj-165	6	4	,	,	PUNCT
arestyrurj-165	6	5	we	we	PRON
arestyrurj-165	6	6	address	address	VERB
arestyrurj-165	6	7	this	this	DET
arestyrurj-165	6	8	issue	issue	NOUN
arestyrurj-165	6	9	by	by	ADP
arestyrurj-165	6	10	investigating	investigate	VERB
arestyrurj-165	6	11	machine	machine	NOUN
arestyrurj-165	6	12	learning	learn	VERB
arestyrurj-165	6	13	classification	classification	NOUN
arestyrurj-165	6	14	algorithms	algorithm	NOUN
arestyrurj-165	6	15	with	with	ADP
arestyrurj-165	6	16	multidimensional	multidimensional	ADJ
arestyrurj-165	6	17	(	(	PUNCT
arestyrurj-165	6	18	tensor	tensor	NOUN
arestyrurj-165	6	19	)	)	PUNCT
arestyrurj-165	6	20	structure	structure	NOUN
arestyrurj-165	6	21	.	.	PUNCT
arestyrurj-165	7	1	by	by	ADP
arestyrurj-165	7	2	imposing	impose	VERB
arestyrurj-165	7	3	tensor	tensor	NOUN
arestyrurj-165	7	4	factorizations	factorization	NOUN
arestyrurj-165	7	5	on	on	ADP
arestyrurj-165	7	6	the	the	DET
arestyrurj-165	7	7	predictors	predictor	NOUN
arestyrurj-165	7	8	,	,	PUNCT
arestyrurj-165	7	9	we	we	PRON
arestyrurj-165	7	10	can	can	AUX
arestyrurj-165	7	11	better	well	ADV
arestyrurj-165	7	12	model	model	VERB
arestyrurj-165	7	13	the	the	DET
arestyrurj-165	7	14	relationship	relationship	NOUN
arestyrurj-165	7	15	,	,	PUNCT
arestyrurj-165	7	16	as	as	SCONJ
arestyrurj-165	7	17	the	the	DET
arestyrurj-165	7	18	predictors	predictor	NOUN
arestyrurj-165	7	19	would	would	AUX
arestyrurj-165	7	20	take	take	VERB
arestyrurj-165	7	21	the	the	DET
arestyrurj-165	7	22	form	form	NOUN
arestyrurj-165	7	23	of	of	ADP
arestyrurj-165	7	24	the	the	DET
arestyrurj-165	7	25	data	datum	NOUN
arestyrurj-165	7	26	in	in	ADP
arestyrurj-165	7	27	question	question	NOUN
arestyrurj-165	7	28	.	.	PUNCT
arestyrurj-165	8	1	we	we	PRON
arestyrurj-165	8	2	empirically	empirically	ADV
arestyrurj-165	8	3	show	show	VERB
arestyrurj-165	8	4	that	that	SCONJ
arestyrurj-165	8	5	our	our	PRON
arestyrurj-165	8	6	approach	approach	NOUN
arestyrurj-165	8	7	works	work	VERB
arestyrurj-165	8	8	more	more	ADV
arestyrurj-165	8	9	efficiently	efficiently	ADV
arestyrurj-165	8	10	than	than	ADP
arestyrurj-165	8	11	the	the	DET
arestyrurj-165	8	12	traditional	traditional	ADJ
arestyrurj-165	8	13	machine	machine	NOUN
arestyrurj-165	8	14	learning	learning	NOUN
arestyrurj-165	8	15	method	method	NOUN
arestyrurj-165	8	16	when	when	SCONJ
arestyrurj-165	8	17	the	the	DET
arestyrurj-165	8	18	data	datum	NOUN
arestyrurj-165	8	19	possesses	possess	VERB
arestyrurj-165	8	20	both	both	CCONJ
arestyrurj-165	8	21	an	an	DET
arestyrurj-165	8	22	exact	exact	NOUN
arestyrurj-165	8	23	and	and	CCONJ
arestyrurj-165	8	24	an	an	DET
arestyrurj-165	8	25	approximate	approximate	ADJ
arestyrurj-165	8	26	tensor	tensor	NOUN
arestyrurj-165	8	27	structure	structure	NOUN
arestyrurj-165	8	28	.	.	PUNCT
arestyrurj-165	9	1	additionally	additionally	ADV
arestyrurj-165	9	2	,	,	PUNCT
arestyrurj-165	9	3	we	we	PRON
arestyrurj-165	9	4	show	show	VERB
arestyrurj-165	9	5	that	that	SCONJ
arestyrurj-165	9	6	estimating	estimate	VERB
arestyrurj-165	9	7	predictors	predictor	NOUN
arestyrurj-165	9	8	with	with	ADP
arestyrurj-165	9	9	these	these	DET
arestyrurj-165	9	10	factorizations	factorization	NOUN
arestyrurj-165	9	11	also	also	ADV
arestyrurj-165	9	12	allow	allow	VERB
arestyrurj-165	9	13	us	we	PRON
arestyrurj-165	9	14	to	to	PART
arestyrurj-165	9	15	solve	solve	VERB
arestyrurj-165	9	16	for	for	ADP
arestyrurj-165	9	17	fewer	few	ADJ
arestyrurj-165	9	18	parameters	parameter	NOUN
arestyrurj-165	9	19	,	,	PUNCT
arestyrurj-165	9	20	making	make	VERB
arestyrurj-165	9	21	computation	computation	NOUN
arestyrurj-165	9	22	more	more	ADV
arestyrurj-165	9	23	feasible	feasible	ADJ
arestyrurj-165	9	24	for	for	ADP
arestyrurj-165	9	25	multidimensional	multidimensional	ADJ
arestyrurj-165	9	26	data	datum	NOUN
arestyrurj-165	9	27	.	.	PUNCT
arestyrurj-165	10	1	1	1	NUM
arestyrurj-165	10	2	introduction	introduction	NOUN
arestyrurj-165	10	3	machine	machine	NOUN
arestyrurj-165	10	4	learning	learn	VERB
arestyrurj-165	10	5	classification	classification	NOUN
arestyrurj-165	10	6	algorithms	algorithm	NOUN
arestyrurj-165	10	7	are	be	AUX
arestyrurj-165	10	8	widely	widely	ADV
arestyrurj-165	10	9	used	use	VERB
arestyrurj-165	10	10	in	in	ADP
arestyrurj-165	10	11	many	many	ADJ
arestyrurj-165	10	12	applications	application	NOUN
arestyrurj-165	10	13	such	such	ADJ
arestyrurj-165	10	14	as	as	ADP
arestyrurj-165	10	15	fraud	fraud	NOUN
arestyrurj-165	10	16	and	and	CCONJ
arestyrurj-165	10	17	spam	spam	NOUN
arestyrurj-165	10	18	detection	detection	NOUN
arestyrurj-165	10	19	.	.	PUNCT
arestyrurj-165	11	1	the	the	DET
arestyrurj-165	11	2	objective	objective	NOUN
arestyrurj-165	11	3	of	of	ADP
arestyrurj-165	11	4	these	these	DET
arestyrurj-165	11	5	algorithms	algorithm	NOUN
arestyrurj-165	11	6	is	be	AUX
arestyrurj-165	11	7	to	to	PART
arestyrurj-165	11	8	model	model	VERB
arestyrurj-165	11	9	a	a	DET
arestyrurj-165	11	10	linear	linear	ADJ
arestyrurj-165	11	11	relationship	relationship	NOUN
arestyrurj-165	11	12	between	between	ADP
arestyrurj-165	11	13	the	the	DET
arestyrurj-165	11	14	independent	independent	ADJ
arestyrurj-165	11	15	(	(	PUNCT
arestyrurj-165	11	16	e.g.	e.g.	ADV
arestyrurj-165	11	17	card	card	NOUN
arestyrurj-165	11	18	transactions	transaction	NOUN
arestyrurj-165	11	19	,	,	PUNCT
arestyrurj-165	11	20	amount	amount	NOUN
arestyrurj-165	11	21	spent	spend	VERB
arestyrurj-165	11	22	)	)	PUNCT
arestyrurj-165	11	23	and	and	CCONJ
arestyrurj-165	11	24	dependent	dependent	ADJ
arestyrurj-165	11	25	(	(	PUNCT
arestyrurj-165	11	26	e.g.	e.g.	ADV
arestyrurj-165	11	27	fraud	fraud	NOUN
arestyrurj-165	11	28	or	or	CCONJ
arestyrurj-165	11	29	not	not	PART
arestyrurj-165	11	30	fraud	fraud	NOUN
arestyrurj-165	11	31	)	)	PUNCT
arestyrurj-165	11	32	variables	variable	NOUN
arestyrurj-165	11	33	.	.	PUNCT
arestyrurj-165	12	1	this	this	DET
arestyrurj-165	12	2	relationship	relationship	NOUN
arestyrurj-165	12	3	is	be	AUX
arestyrurj-165	12	4	generally	generally	ADV
arestyrurj-165	12	5	modeled	model	VERB
arestyrurj-165	12	6	by	by	ADP
arestyrurj-165	12	7	learning	learn	VERB
arestyrurj-165	12	8	a	a	DET
arestyrurj-165	12	9	hyperplane	hyperplane	NOUN
arestyrurj-165	12	10	that	that	PRON
arestyrurj-165	12	11	best	well	ADV
arestyrurj-165	12	12	separates	separate	VERB
arestyrurj-165	12	13	the	the	DET
arestyrurj-165	12	14	two	two	NUM
arestyrurj-165	12	15	classes	class	NOUN
arestyrurj-165	12	16	of	of	ADP
arestyrurj-165	12	17	data	datum	NOUN
arestyrurj-165	12	18	as	as	SCONJ
arestyrurj-165	12	19	shown	show	VERB
arestyrurj-165	12	20	in	in	ADP
arestyrurj-165	12	21	figure	figure	NOUN
arestyrurj-165	12	22	1	1	NUM
arestyrurj-165	12	23	.	.	PUNCT
arestyrurj-165	13	1	the	the	DET
arestyrurj-165	13	2	hyperplane	hyperplane	NOUN
arestyrurj-165	13	3	is	be	AUX
arestyrurj-165	13	4	constructed	construct	VERB
arestyrurj-165	13	5	of	of	ADP
arestyrurj-165	13	6	weights	weight	NOUN
arestyrurj-165	13	7	and	and	CCONJ
arestyrurj-165	13	8	biases	bias	NOUN
arestyrurj-165	13	9	,	,	PUNCT
arestyrurj-165	13	10	which	which	PRON
arestyrurj-165	13	11	can	can	AUX
arestyrurj-165	13	12	simply	simply	ADV
arestyrurj-165	13	13	be	be	AUX
arestyrurj-165	13	14	interpreted	interpret	VERB
arestyrurj-165	13	15	as	as	ADP
arestyrurj-165	13	16	the	the	DET
arestyrurj-165	13	17	slope	slope	NOUN
arestyrurj-165	13	18	and	and	CCONJ
arestyrurj-165	13	19	intercept	intercept	NOUN
arestyrurj-165	13	20	,	,	PUNCT
arestyrurj-165	13	21	respectively	respectively	ADV
arestyrurj-165	13	22	.	.	PUNCT
arestyrurj-165	14	1	one	one	PRON
arestyrurj-165	14	2	can	can	AUX
arestyrurj-165	14	3	solve	solve	VERB
arestyrurj-165	14	4	or	or	CCONJ
arestyrurj-165	14	5	estimate	estimate	VERB
arestyrurj-165	14	6	these	these	DET
arestyrurj-165	14	7	values	value	NOUN
arestyrurj-165	14	8	by	by	ADP
arestyrurj-165	14	9	learning	learn	VERB
arestyrurj-165	14	10	the	the	DET
arestyrurj-165	14	11	parameters	parameter	NOUN
arestyrurj-165	14	12	that	that	PRON
arestyrurj-165	14	13	most	most	ADV
arestyrurj-165	14	14	accurately	accurately	ADV
arestyrurj-165	14	15	describe	describe	VERB
arestyrurj-165	14	16	the	the	DET
arestyrurj-165	14	17	observed	observe	VERB
arestyrurj-165	14	18	data	data	NOUN
arestyrurj-165	14	19	points	point	NOUN
arestyrurj-165	14	20	.	.	PUNCT
arestyrurj-165	15	1	in	in	ADP
arestyrurj-165	15	2	machine	machine	NOUN
arestyrurj-165	15	3	learning	learning	NOUN
arestyrurj-165	15	4	,	,	PUNCT
arestyrurj-165	15	5	we	we	PRON
arestyrurj-165	15	6	solve	solve	VERB
arestyrurj-165	15	7	for	for	ADP
arestyrurj-165	15	8	these	these	DET
arestyrurj-165	15	9	parameters	parameter	NOUN
arestyrurj-165	15	10	(	(	PUNCT
arestyrurj-165	15	11	or	or	CCONJ
arestyrurj-165	15	12	predictors	predictor	NOUN
arestyrurj-165	15	13	)	)	PUNCT
arestyrurj-165	15	14	through	through	ADP
arestyrurj-165	15	15	empirical	empirical	ADJ
arestyrurj-165	15	16	risk	risk	NOUN
arestyrurj-165	15	17	minimization	minimization	NOUN
arestyrurj-165	15	18	(	(	PUNCT
arestyrurj-165	15	19	erm	erm	PROPN
arestyrurj-165	15	20	)	)	PUNCT
arestyrurj-165	15	21	.	.	PUNCT
arestyrurj-165	16	1	the	the	DET
arestyrurj-165	16	2	erm	erm	PROPN
arestyrurj-165	16	3	framework	framework	NOUN
arestyrurj-165	16	4	tries	try	VERB
arestyrurj-165	16	5	to	to	PART
arestyrurj-165	16	6	estimate	estimate	VERB
arestyrurj-165	16	7	the	the	DET
arestyrurj-165	16	8	parameters	parameter	NOUN
arestyrurj-165	16	9	that	that	PRON
arestyrurj-165	16	10	minimize	minimize	VERB
arestyrurj-165	16	11	the	the	DET
arestyrurj-165	16	12	`	`	PUNCT
arestyrurj-165	16	13	`	`	PUNCT
arestyrurj-165	16	14	risk	risk	NOUN
arestyrurj-165	16	15	’’	’'	PUNCT
arestyrurj-165	16	16	or	or	CCONJ
arestyrurj-165	16	17	error	error	NOUN
arestyrurj-165	16	18	of	of	ADP
arestyrurj-165	16	19	a	a	DET
arestyrurj-165	16	20	loss	loss	NOUN
arestyrurj-165	16	21	function	function	NOUN
arestyrurj-165	16	22	between	between	ADP
arestyrurj-165	16	23	the	the	DET
arestyrurj-165	16	24	true	true	ADJ
arestyrurj-165	16	25	and	and	CCONJ
arestyrurj-165	16	26	computed	computed	ADJ
arestyrurj-165	16	27	predictors	predictor	NOUN
arestyrurj-165	16	28	given	give	VERB
arestyrurj-165	16	29	data	datum	NOUN
arestyrurj-165	16	30	.	.	PUNCT
arestyrurj-165	17	1	the	the	DET
arestyrurj-165	17	2	minimization	minimization	NOUN
arestyrurj-165	17	3	of	of	ADP
arestyrurj-165	17	4	this	this	DET
arestyrurj-165	17	5	loss	loss	NOUN
arestyrurj-165	17	6	function	function	NOUN
arestyrurj-165	17	7	measures	measure	VERB
arestyrurj-165	17	8	the	the	DET
arestyrurj-165	17	9	`	`	PUNCT
arestyrurj-165	17	10	`	`	PUNCT
arestyrurj-165	17	11	closeness	closeness	NOUN
arestyrurj-165	17	12	’’	’'	PUNCT
arestyrurj-165	17	13	of	of	ADP
arestyrurj-165	17	14	the	the	DET
arestyrurj-165	17	15	predictors	predictor	NOUN
arestyrurj-165	17	16	,	,	PUNCT
arestyrurj-165	17	17	where	where	SCONJ
arestyrurj-165	17	18	a	a	DET
arestyrurj-165	17	19	smaller	small	ADJ
arestyrurj-165	17	20	objective	objective	ADJ
arestyrurj-165	17	21	function	function	NOUN
arestyrurj-165	17	22	value	value	NOUN
arestyrurj-165	17	23	would	would	AUX
arestyrurj-165	17	24	account	account	VERB
arestyrurj-165	17	25	for	for	ADP
arestyrurj-165	17	26	a	a	DET
arestyrurj-165	17	27	more	more	ADV
arestyrurj-165	17	28	accurate	accurate	ADJ
arestyrurj-165	17	29	model	model	NOUN
arestyrurj-165	17	30	.	.	PUNCT
arestyrurj-165	18	1	there	there	PRON
arestyrurj-165	18	2	are	be	VERB
arestyrurj-165	18	3	many	many	ADJ
arestyrurj-165	18	4	different	different	ADJ
arestyrurj-165	18	5	machine	machine	NOUN
arestyrurj-165	18	6	learning	learn	VERB
arestyrurj-165	18	7	classification	classification	NOUN
arestyrurj-165	18	8	algorithms	algorithm	NOUN
arestyrurj-165	18	9	,	,	PUNCT
arestyrurj-165	18	10	and	and	CCONJ
arestyrurj-165	18	11	each	each	DET
arestyrurj-165	18	12	algorithm	algorithm	NOUN
arestyrurj-165	18	13	has	have	VERB
arestyrurj-165	18	14	a	a	DET
arestyrurj-165	18	15	different	different	ADJ
arestyrurj-165	18	16	loss	loss	NOUN
arestyrurj-165	18	17	function	function	NOUN
arestyrurj-165	18	18	.	.	PUNCT
arestyrurj-165	19	1	however	however	ADV
arestyrurj-165	19	2	,	,	PUNCT
arestyrurj-165	19	3	since	since	SCONJ
arestyrurj-165	19	4	many	many	ADJ
arestyrurj-165	19	5	loss	loss	NOUN
arestyrurj-165	19	6	functions	function	NOUN
arestyrurj-165	19	7	try	try	VERB
arestyrurj-165	19	8	to	to	PART
arestyrurj-165	19	9	model	model	VERB
arestyrurj-165	19	10	a	a	DET
arestyrurj-165	19	11	linear	linear	ADJ
arestyrurj-165	19	12	relationship	relationship	NOUN
arestyrurj-165	19	13	,	,	PUNCT
arestyrurj-165	19	14	there	there	PRON
arestyrurj-165	19	15	is	be	VERB
arestyrurj-165	19	16	an	an	DET
arestyrurj-165	19	17	implicit	implicit	ADJ
arestyrurj-165	19	18	need	need	NOUN
arestyrurj-165	19	19	for	for	ADP
arestyrurj-165	19	20	our	our	PRON
arestyrurj-165	19	21	figure	figure	NOUN
arestyrurj-165	19	22	1	1	NUM
arestyrurj-165	19	23	:	:	PUNCT
arestyrurj-165	19	24	visualization	visualization	NOUN
arestyrurj-165	19	25	of	of	ADP
arestyrurj-165	19	26	learning	learn	VERB
arestyrurj-165	19	27	a	a	DET
arestyrurj-165	19	28	line	line	NOUN
arestyrurj-165	19	29	(	(	PUNCT
arestyrurj-165	19	30	or	or	CCONJ
arestyrurj-165	19	31	hyperplane	hyperplane	NOUN
arestyrurj-165	19	32	in	in	ADP
arestyrurj-165	19	33	higher	high	ADJ
arestyrurj-165	19	34	dimensional	dimensional	ADJ
arestyrurj-165	19	35	space	space	NOUN
arestyrurj-165	19	36	)	)	PUNCT
arestyrurj-165	19	37	that	that	PRON
arestyrurj-165	19	38	best	good	ADJ
arestyrurj-165	19	39	separates	separate	VERB
arestyrurj-165	19	40	two	two	NUM
arestyrurj-165	19	41	classes	class	NOUN
arestyrurj-165	19	42	of	of	ADP
arestyrurj-165	19	43	data	data	PROPN
arestyrurj-165	19	44	.	.	PUNCT
arestyrurj-165	20	1	machine	machine	NOUN
arestyrurj-165	20	2	learning	learn	VERB
arestyrurj-165	20	3	algorithms	algorithm	NOUN
arestyrurj-165	20	4	estimate	estimate	VERB
arestyrurj-165	20	5	these	these	DET
arestyrurj-165	20	6	weights	weight	NOUN
arestyrurj-165	20	7	,	,	PUNCT
arestyrurj-165	20	8	𝑊	𝑊	PROPN
arestyrurj-165	20	9	,	,	PUNCT
arestyrurj-165	20	10	and	and	CCONJ
arestyrurj-165	20	11	bias	bias	NOUN
arestyrurj-165	20	12	,	,	PUNCT
arestyrurj-165	20	13	𝑏	𝑏	NOUN
arestyrurj-165	20	14	,	,	PUNCT
arestyrurj-165	20	15	through	through	ADP
arestyrurj-165	20	16	empirical	empirical	ADJ
arestyrurj-165	20	17	risk	risk	NOUN
arestyrurj-165	20	18	minimization	minimization	NOUN
arestyrurj-165	20	19	.	.	PUNCT
arestyrurj-165	21	1	aresty	aresty	ADJ
arestyrurj-165	21	2	rutgers	rutgers	PROPN
arestyrurj-165	21	3	undergraduate	undergraduate	PROPN
arestyrurj-165	21	4	research	research	PROPN
arestyrurj-165	21	5	journal	journal	PROPN
arestyrurj-165	21	6	,	,	PUNCT
arestyrurj-165	21	7	volume	volume	NOUN
arestyrurj-165	21	8	i	i	PRON
arestyrurj-165	21	9	,	,	PUNCT
arestyrurj-165	21	10	issue	issue	VERB
arestyrurj-165	21	11	iii	iii	NUM
arestyrurj-165	21	12	data	datum	NOUN
arestyrurj-165	21	13	to	to	PART
arestyrurj-165	21	14	be	be	AUX
arestyrurj-165	21	15	vectorized	vectorize	VERB
arestyrurj-165	21	16	.	.	PUNCT
arestyrurj-165	22	1	if	if	SCONJ
arestyrurj-165	22	2	our	our	PRON
arestyrurj-165	22	3	data	data	NOUN
arestyrurj-165	22	4	samples	sample	NOUN
arestyrurj-165	22	5	were	be	AUX
arestyrurj-165	22	6	to	to	PART
arestyrurj-165	22	7	be	be	AUX
arestyrurj-165	22	8	multidimensional	multidimensional	ADJ
arestyrurj-165	22	9	,	,	PUNCT
arestyrurj-165	22	10	vectorization	vectorization	NOUN
arestyrurj-165	22	11	would	would	AUX
arestyrurj-165	22	12	make	make	VERB
arestyrurj-165	22	13	estimation	estimation	NOUN
arestyrurj-165	22	14	of	of	ADP
arestyrurj-165	22	15	accurate	accurate	ADJ
arestyrurj-165	22	16	predictors	predictor	NOUN
arestyrurj-165	22	17	much	much	ADV
arestyrurj-165	22	18	more	more	ADV
arestyrurj-165	22	19	challenging	challenging	ADJ
arestyrurj-165	22	20	.	.	PUNCT
arestyrurj-165	23	1	for	for	ADP
arestyrurj-165	23	2	example	example	NOUN
arestyrurj-165	23	3	,	,	PUNCT
arestyrurj-165	23	4	consider	consider	VERB
arestyrurj-165	23	5	a	a	DET
arestyrurj-165	23	6	different	different	ADJ
arestyrurj-165	23	7	scenario	scenario	NOUN
arestyrurj-165	23	8	in	in	ADP
arestyrurj-165	23	9	which	which	PRON
arestyrurj-165	23	10	one	one	PRON
arestyrurj-165	23	11	would	would	AUX
arestyrurj-165	23	12	like	like	VERB
arestyrurj-165	23	13	to	to	PART
arestyrurj-165	23	14	make	make	VERB
arestyrurj-165	23	15	movie	movie	NOUN
arestyrurj-165	23	16	recommendations	recommendation	NOUN
arestyrurj-165	23	17	for	for	ADP
arestyrurj-165	23	18	a	a	DET
arestyrurj-165	23	19	user	user	NOUN
arestyrurj-165	23	20	given	give	VERB
arestyrurj-165	23	21	the	the	DET
arestyrurj-165	23	22	number	number	NOUN
arestyrurj-165	23	23	of	of	ADP
arestyrurj-165	23	24	movies	movie	NOUN
arestyrurj-165	23	25	watched	watch	VERB
arestyrurj-165	23	26	in	in	ADP
arestyrurj-165	23	27	a	a	DET
arestyrurj-165	23	28	certain	certain	ADJ
arestyrurj-165	23	29	genre	genre	NOUN
arestyrurj-165	23	30	.	.	PUNCT
arestyrurj-165	24	1	this	this	DET
arestyrurj-165	24	2	data	datum	NOUN
arestyrurj-165	24	3	can	can	AUX
arestyrurj-165	24	4	easily	easily	ADV
arestyrurj-165	24	5	be	be	AUX
arestyrurj-165	24	6	stored	store	VERB
arestyrurj-165	24	7	in	in	ADP
arestyrurj-165	24	8	the	the	DET
arestyrurj-165	24	9	form	form	NOUN
arestyrurj-165	24	10	of	of	ADP
arestyrurj-165	24	11	a	a	DET
arestyrurj-165	24	12	matrix	matrix	NOUN
arestyrurj-165	24	13	,	,	PUNCT
arestyrurj-165	24	14	where	where	SCONJ
arestyrurj-165	24	15	the	the	DET
arestyrurj-165	24	16	rows	row	NOUN
arestyrurj-165	24	17	represent	represent	VERB
arestyrurj-165	24	18	each	each	DET
arestyrurj-165	24	19	user	user	NOUN
arestyrurj-165	24	20	,	,	PUNCT
arestyrurj-165	24	21	and	and	CCONJ
arestyrurj-165	24	22	the	the	DET
arestyrurj-165	24	23	columns	column	NOUN
arestyrurj-165	24	24	represent	represent	VERB
arestyrurj-165	24	25	the	the	DET
arestyrurj-165	24	26	movie	movie	NOUN
arestyrurj-165	24	27	genre	genre	NOUN
arestyrurj-165	24	28	.	.	PUNCT
arestyrurj-165	25	1	however	however	ADV
arestyrurj-165	25	2	,	,	PUNCT
arestyrurj-165	25	3	what	what	PRON
arestyrurj-165	25	4	happens	happen	VERB
arestyrurj-165	25	5	when	when	SCONJ
arestyrurj-165	25	6	a	a	DET
arestyrurj-165	25	7	user	user	NOUN
arestyrurj-165	25	8	’s	’s	PART
arestyrurj-165	25	9	movie	movie	NOUN
arestyrurj-165	25	10	preferences	preference	NOUN
arestyrurj-165	25	11	change	change	VERB
arestyrurj-165	25	12	over	over	ADP
arestyrurj-165	25	13	time	time	NOUN
arestyrurj-165	25	14	?	?	PUNCT
arestyrurj-165	26	1	as	as	SCONJ
arestyrurj-165	26	2	shown	show	VERB
arestyrurj-165	26	3	in	in	ADP
arestyrurj-165	26	4	figure	figure	NOUN
arestyrurj-165	26	5	2	2	NUM
arestyrurj-165	26	6	,	,	PUNCT
arestyrurj-165	26	7	we	we	PRON
arestyrurj-165	26	8	can	can	AUX
arestyrurj-165	26	9	capture	capture	VERB
arestyrurj-165	26	10	this	this	DET
arestyrurj-165	26	11	third	third	ADJ
arestyrurj-165	26	12	variable	variable	NOUN
arestyrurj-165	26	13	(	(	PUNCT
arestyrurj-165	26	14	and	and	CCONJ
arestyrurj-165	26	15	many	many	ADJ
arestyrurj-165	26	16	others	other	NOUN
arestyrurj-165	26	17	)	)	PUNCT
arestyrurj-165	26	18	by	by	ADP
arestyrurj-165	26	19	modelling	model	VERB
arestyrurj-165	26	20	the	the	DET
arestyrurj-165	26	21	observations	observation	NOUN
arestyrurj-165	26	22	in	in	ADP
arestyrurj-165	26	23	the	the	DET
arestyrurj-165	26	24	form	form	NOUN
arestyrurj-165	26	25	of	of	ADP
arestyrurj-165	26	26	a	a	DET
arestyrurj-165	26	27	tensor	tensor	NOUN
arestyrurj-165	26	28	,	,	PUNCT
arestyrurj-165	26	29	as	as	SCONJ
arestyrurj-165	26	30	it	it	PRON
arestyrurj-165	26	31	matches	match	VERB
arestyrurj-165	26	32	the	the	DET
arestyrurj-165	26	33	structure	structure	NOUN
arestyrurj-165	26	34	of	of	ADP
arestyrurj-165	26	35	the	the	DET
arestyrurj-165	26	36	data	datum	NOUN
arestyrurj-165	26	37	.	.	PUNCT
arestyrurj-165	27	1	clearly	clearly	ADV
arestyrurj-165	27	2	,	,	PUNCT
arestyrurj-165	27	3	the	the	DET
arestyrurj-165	27	4	structure	structure	NOUN
arestyrurj-165	27	5	of	of	ADP
arestyrurj-165	27	6	this	this	DET
arestyrurj-165	27	7	tensor	tensor	NOUN
arestyrurj-165	27	8	is	be	AUX
arestyrurj-165	27	9	significant	significant	ADJ
arestyrurj-165	27	10	for	for	ADP
arestyrurj-165	27	11	accurate	accurate	ADJ
arestyrurj-165	27	12	data	datum	NOUN
arestyrurj-165	27	13	analysis	analysis	NOUN
arestyrurj-165	27	14	.	.	PUNCT
arestyrurj-165	28	1	if	if	SCONJ
arestyrurj-165	28	2	the	the	DET
arestyrurj-165	28	3	orderings	ordering	NOUN
arestyrurj-165	28	4	of	of	ADP
arestyrurj-165	28	5	the	the	DET
arestyrurj-165	28	6	movies	movie	NOUN
arestyrurj-165	28	7	watched	watch	VERB
arestyrurj-165	28	8	were	be	AUX
arestyrurj-165	28	9	swapped	swap	VERB
arestyrurj-165	28	10	for	for	ADP
arestyrurj-165	28	11	two	two	NUM
arestyrurj-165	28	12	given	give	VERB
arestyrurj-165	28	13	users	user	NOUN
arestyrurj-165	28	14	,	,	PUNCT
arestyrurj-165	28	15	incorrect	incorrect	ADJ
arestyrurj-165	28	16	recommendations	recommendation	NOUN
arestyrurj-165	28	17	could	could	AUX
arestyrurj-165	28	18	be	be	AUX
arestyrurj-165	28	19	made	make	VERB
arestyrurj-165	28	20	.	.	PUNCT
arestyrurj-165	29	1	vectorizing	vectorize	VERB
arestyrurj-165	29	2	this	this	DET
arestyrurj-165	29	3	data	data	NOUN
arestyrurj-165	29	4	does	do	AUX
arestyrurj-165	29	5	not	not	PART
arestyrurj-165	29	6	account	account	VERB
arestyrurj-165	29	7	for	for	ADP
arestyrurj-165	29	8	these	these	DET
arestyrurj-165	29	9	types	type	NOUN
arestyrurj-165	29	10	of	of	ADP
arestyrurj-165	29	11	structures	structure	NOUN
arestyrurj-165	29	12	,	,	PUNCT
arestyrurj-165	29	13	making	make	VERB
arestyrurj-165	29	14	inference	inference	NOUN
arestyrurj-165	29	15	much	much	ADV
arestyrurj-165	29	16	more	more	ADV
arestyrurj-165	29	17	challenging	challenging	ADJ
arestyrurj-165	29	18	.	.	PUNCT
arestyrurj-165	30	1	there	there	PRON
arestyrurj-165	30	2	are	be	VERB
arestyrurj-165	30	3	many	many	ADJ
arestyrurj-165	30	4	modern	modern	ADJ
arestyrurj-165	30	5	applications	application	NOUN
arestyrurj-165	30	6	that	that	PRON
arestyrurj-165	30	7	involve	involve	VERB
arestyrurj-165	30	8	analyzing	analyze	VERB
arestyrurj-165	30	9	data	datum	NOUN
arestyrurj-165	30	10	with	with	ADP
arestyrurj-165	30	11	intrinsically	intrinsically	ADV
arestyrurj-165	30	12	many	many	ADJ
arestyrurj-165	30	13	more	more	ADJ
arestyrurj-165	30	14	dimensions	dimension	NOUN
arestyrurj-165	30	15	,	,	PUNCT
arestyrurj-165	30	16	including	include	VERB
arestyrurj-165	30	17	medical	medical	ADJ
arestyrurj-165	30	18	imaging,[3,13	imaging,[3,13	NOUN
arestyrurj-165	30	19	]	]	PUNCT
arestyrurj-165	30	20	image	image	NOUN
arestyrurj-165	30	21	processing,[5,18	processing,[5,18	NOUN
arestyrurj-165	30	22	]	]	X
arestyrurj-165	30	23	and	and	CCONJ
arestyrurj-165	30	24	seismic	seismic	ADJ
arestyrurj-165	30	25	data	datum	NOUN
arestyrurj-165	30	26	analysis.[8	analysis.[8	PUNCT
arestyrurj-165	30	27	]	]	PUNCT
arestyrurj-165	30	28	in	in	ADP
arestyrurj-165	30	29	most	most	ADJ
arestyrurj-165	30	30	of	of	ADP
arestyrurj-165	30	31	these	these	DET
arestyrurj-165	30	32	settings	setting	NOUN
arestyrurj-165	30	33	,	,	PUNCT
arestyrurj-165	30	34	the	the	DET
arestyrurj-165	30	35	objective	objective	NOUN
arestyrurj-165	30	36	is	be	AUX
arestyrurj-165	30	37	similar	similar	ADJ
arestyrurj-165	30	38	to	to	ADP
arestyrurj-165	30	39	that	that	PRON
arestyrurj-165	30	40	of	of	ADP
arestyrurj-165	30	41	the	the	DET
arestyrurj-165	30	42	traditional	traditional	ADJ
arestyrurj-165	30	43	machine	machine	NOUN
arestyrurj-165	30	44	learning	learn	VERB
arestyrurj-165	30	45	goal	goal	NOUN
arestyrurj-165	30	46	:	:	PUNCT
arestyrurj-165	30	47	to	to	PART
arestyrurj-165	30	48	formulate	formulate	VERB
arestyrurj-165	30	49	a	a	DET
arestyrurj-165	30	50	problem	problem	NOUN
arestyrurj-165	30	51	of	of	ADP
arestyrurj-165	30	52	prediction	prediction	NOUN
arestyrurj-165	30	53	to	to	PART
arestyrurj-165	30	54	establish	establish	VERB
arestyrurj-165	30	55	an	an	DET
arestyrurj-165	30	56	association	association	NOUN
arestyrurj-165	30	57	between	between	ADP
arestyrurj-165	30	58	the	the	DET
arestyrurj-165	30	59	tensor	tensor	NOUN
arestyrurj-165	30	60	covariates	covariate	NOUN
arestyrurj-165	30	61	(	(	PUNCT
arestyrurj-165	30	62	independent	independent	ADJ
arestyrurj-165	30	63	variable	variable	NOUN
arestyrurj-165	30	64	)	)	PUNCT
arestyrurj-165	30	65	and	and	CCONJ
arestyrurj-165	30	66	outcomes	outcome	NOUN
arestyrurj-165	30	67	(	(	PUNCT
arestyrurj-165	30	68	dependent	dependent	ADJ
arestyrurj-165	30	69	variable	variable	NOUN
arestyrurj-165	30	70	)	)	PUNCT
arestyrurj-165	30	71	.	.	PUNCT
arestyrurj-165	31	1	however	however	ADV
arestyrurj-165	31	2	,	,	PUNCT
arestyrurj-165	31	3	as	as	SCONJ
arestyrurj-165	31	4	previously	previously	ADV
arestyrurj-165	31	5	mentioned	mention	VERB
arestyrurj-165	31	6	,	,	PUNCT
arestyrurj-165	31	7	most	most	ADJ
arestyrurj-165	31	8	machine	machine	NOUN
arestyrurj-165	31	9	learning	learn	VERB
arestyrurj-165	31	10	frameworks	framework	NOUN
arestyrurj-165	31	11	are	be	AUX
arestyrurj-165	31	12	formulated	formulate	VERB
arestyrurj-165	31	13	for	for	ADP
arestyrurj-165	31	14	vector	vector	NOUN
arestyrurj-165	31	15	spaces	space	NOUN
arestyrurj-165	31	16	,	,	PUNCT
arestyrurj-165	31	17	making	make	VERB
arestyrurj-165	31	18	statistical	statistical	ADJ
arestyrurj-165	31	19	inference	inference	NOUN
arestyrurj-165	31	20	challenging	challenge	VERB
arestyrurj-165	31	21	for	for	ADP
arestyrurj-165	31	22	tensor	tensor	NOUN
arestyrurj-165	31	23	data	datum	NOUN
arestyrurj-165	31	24	.	.	PUNCT
arestyrurj-165	32	1	in	in	ADP
arestyrurj-165	32	2	addition	addition	NOUN
arestyrurj-165	32	3	,	,	PUNCT
arestyrurj-165	32	4	in	in	ADP
arestyrurj-165	32	5	most	most	ADJ
arestyrurj-165	32	6	of	of	ADP
arestyrurj-165	32	7	these	these	DET
arestyrurj-165	32	8	domains	domain	NOUN
arestyrurj-165	32	9	,	,	PUNCT
arestyrurj-165	32	10	the	the	DET
arestyrurj-165	32	11	tensor	tensor	NOUN
arestyrurj-165	32	12	data	datum	NOUN
arestyrurj-165	32	13	also	also	ADV
arestyrurj-165	32	14	exhibits	exhibit	VERB
arestyrurj-165	32	15	high	high	ADJ
arestyrurj-165	32	16	dimensions	dimension	NOUN
arestyrurj-165	32	17	.	.	PUNCT
arestyrurj-165	33	1	for	for	ADP
arestyrurj-165	33	2	example	example	NOUN
arestyrurj-165	33	3	,	,	PUNCT
arestyrurj-165	33	4	in	in	ADP
arestyrurj-165	33	5	medicine	medicine	NOUN
arestyrurj-165	33	6	,	,	PUNCT
arestyrurj-165	33	7	tensor	tensor	NOUN
arestyrurj-165	33	8	data	data	NOUN
arestyrurj-165	33	9	samples	sample	NOUN
arestyrurj-165	33	10	may	may	AUX
arestyrurj-165	33	11	be	be	AUX
arestyrurj-165	33	12	of	of	ADP
arestyrurj-165	33	13	dimensions	dimension	NOUN
arestyrurj-165	33	14	128	128	NUM
arestyrurj-165	33	15	×	×	NOUN
arestyrurj-165	33	16	128	128	NUM
arestyrurj-165	33	17	×	×	NOUN
arestyrurj-165	33	18	128	128	NUM
arestyrurj-165	33	19	or	or	CCONJ
arestyrurj-165	33	20	greater	great	ADJ
arestyrurj-165	33	21	.	.	PUNCT
arestyrurj-165	34	1	naively	naively	ADV
arestyrurj-165	34	2	turning	turn	VERB
arestyrurj-165	34	3	this	this	DET
arestyrurj-165	34	4	array	array	NOUN
arestyrurj-165	34	5	into	into	ADP
arestyrurj-165	34	6	a	a	DET
arestyrurj-165	34	7	vector	vector	NOUN
arestyrurj-165	34	8	for	for	ADP
arestyrurj-165	34	9	traditional	traditional	ADJ
arestyrurj-165	34	10	machine	machine	NOUN
arestyrurj-165	34	11	learning	learning	NOUN
arestyrurj-165	34	12	would	would	AUX
arestyrurj-165	34	13	result	result	VERB
arestyrurj-165	34	14	in	in	ADP
arestyrurj-165	34	15	solving	solve	VERB
arestyrurj-165	34	16	for	for	ADP
arestyrurj-165	34	17	128	128	NUM
arestyrurj-165	34	18	=	=	SYM
arestyrurj-165	34	19	2,097,152	2,097,152	NUM
arestyrurj-165	34	20	coefficients	coefficient	NOUN
arestyrurj-165	34	21	.	.	PUNCT
arestyrurj-165	35	1	in	in	ADP
arestyrurj-165	35	2	this	this	DET
arestyrurj-165	35	3	scenario	scenario	NOUN
arestyrurj-165	35	4	,	,	PUNCT
arestyrurj-165	35	5	vectorization	vectorization	NOUN
arestyrurj-165	35	6	not	not	PART
arestyrurj-165	35	7	only	only	ADV
arestyrurj-165	35	8	destroys	destroy	VERB
arestyrurj-165	35	9	the	the	DET
arestyrurj-165	35	10	structure	structure	NOUN
arestyrurj-165	35	11	of	of	ADP
arestyrurj-165	35	12	the	the	DET
arestyrurj-165	35	13	data	datum	NOUN
arestyrurj-165	35	14	,	,	PUNCT
arestyrurj-165	35	15	but	but	CCONJ
arestyrurj-165	35	16	also	also	ADV
arestyrurj-165	35	17	makes	make	VERB
arestyrurj-165	35	18	computation	computation	NOUN
arestyrurj-165	35	19	infeasible	infeasible	ADJ
arestyrurj-165	35	20	.	.	PUNCT
arestyrurj-165	36	1	related	relate	VERB
arestyrurj-165	36	2	works	work	NOUN
arestyrurj-165	36	3	recently	recently	ADV
arestyrurj-165	36	4	,	,	PUNCT
arestyrurj-165	36	5	work	work	VERB
arestyrurj-165	36	6	on	on	ADP
arestyrurj-165	36	7	tensor	tensor	NOUN
arestyrurj-165	36	8	-	-	PUNCT
arestyrurj-165	36	9	based	base	VERB
arestyrurj-165	36	10	machine	machine	NOUN
arestyrurj-165	36	11	learning	learning	NOUN
arestyrurj-165	36	12	approaches	approach	NOUN
arestyrurj-165	36	13	uses	use	VERB
arestyrurj-165	36	14	tensor	tensor	NOUN
arestyrurj-165	36	15	factorizations	factorization	NOUN
arestyrurj-165	36	16	to	to	PART
arestyrurj-165	36	17	reduce	reduce	VERB
arestyrurj-165	36	18	the	the	DET
arestyrurj-165	36	19	number	number	NOUN
arestyrurj-165	36	20	of	of	ADP
arestyrurj-165	36	21	coefficients	coefficient	NOUN
arestyrurj-165	36	22	to	to	PART
arestyrurj-165	36	23	be	be	AUX
arestyrurj-165	36	24	estimated.[10,15,21	estimated.[10,15,21	PROPN
arestyrurj-165	36	25	]	]	PUNCT
arestyrurj-165	36	26	specifically	specifically	ADV
arestyrurj-165	36	27	,	,	PUNCT
arestyrurj-165	36	28	tensor	tensor	NOUN
arestyrurj-165	36	29	decompositions	decomposition	NOUN
arestyrurj-165	36	30	are	be	AUX
arestyrurj-165	36	31	imposed	impose	VERB
arestyrurj-165	36	32	on	on	ADP
arestyrurj-165	36	33	the	the	DET
arestyrurj-165	36	34	coefficients	coefficient	NOUN
arestyrurj-165	36	35	as	as	ADP
arestyrurj-165	36	36	a	a	DET
arestyrurj-165	36	37	scheme	scheme	NOUN
arestyrurj-165	36	38	of	of	ADP
arestyrurj-165	36	39	feature	feature	NOUN
arestyrurj-165	36	40	selection	selection	NOUN
arestyrurj-165	36	41	or	or	CCONJ
arestyrurj-165	36	42	dimensionality	dimensionality	NOUN
arestyrurj-165	36	43	reduction	reduction	NOUN
arestyrurj-165	36	44	.	.	PUNCT
arestyrurj-165	37	1	integrating	integrate	VERB
arestyrurj-165	37	2	such	such	ADJ
arestyrurj-165	37	3	decomposition	decomposition	NOUN
arestyrurj-165	37	4	structures	structure	NOUN
arestyrurj-165	37	5	solves	solve	NOUN
arestyrurj-165	37	6	for	for	ADP
arestyrurj-165	37	7	low	low	ADJ
arestyrurj-165	37	8	rank	rank	NOUN
arestyrurj-165	37	9	approximations	approximation	NOUN
arestyrurj-165	37	10	of	of	ADP
arestyrurj-165	37	11	the	the	DET
arestyrurj-165	37	12	true	true	ADJ
arestyrurj-165	37	13	predictor	predictor	NOUN
arestyrurj-165	37	14	,	,	PUNCT
arestyrurj-165	37	15	rather	rather	ADV
arestyrurj-165	37	16	than	than	ADP
arestyrurj-165	37	17	the	the	DET
arestyrurj-165	37	18	vector	vector	NOUN
arestyrurj-165	37	19	counterpart	counterpart	NOUN
arestyrurj-165	37	20	.	.	PUNCT
arestyrurj-165	38	1	zhou	zhou	PROPN
arestyrurj-165	38	2	et	et	PROPN
arestyrurj-165	38	3	al	al	PROPN
arestyrurj-165	38	4	.	.	PROPN
arestyrurj-165	38	5	proposes	propose	VERB
arestyrurj-165	38	6	a	a	DET
arestyrurj-165	38	7	tensor	tensor	NOUN
arestyrurj-165	38	8	regression	regression	NOUN
arestyrurj-165	38	9	model	model	NOUN
arestyrurj-165	38	10	with	with	ADP
arestyrurj-165	38	11	additional	additional	ADJ
arestyrurj-165	38	12	independent	independent	ADJ
arestyrurj-165	38	13	variables	variable	NOUN
arestyrurj-165	38	14	for	for	ADP
arestyrurj-165	38	15	predicting	predict	VERB
arestyrurj-165	38	16	continuous	continuous	ADJ
arestyrurj-165	38	17	values	value	NOUN
arestyrurj-165	38	18	given	give	VERB
arestyrurj-165	38	19	fmri	fmri	PROPN
arestyrurj-165	38	20	data.[21	data.[21	PROPN
arestyrurj-165	38	21	]	]	PUNCT
arestyrurj-165	38	22	for	for	ADP
arestyrurj-165	38	23	parameter	parameter	NOUN
arestyrurj-165	38	24	estimation	estimation	NOUN
arestyrurj-165	38	25	,	,	PUNCT
arestyrurj-165	38	26	they	they	PRON
arestyrurj-165	38	27	propose	propose	VERB
arestyrurj-165	38	28	a	a	DET
arestyrurj-165	38	29	maximum	maximum	ADJ
arestyrurj-165	38	30	likelihood	likelihood	NOUN
arestyrurj-165	38	31	(	(	PUNCT
arestyrurj-165	38	32	ml	ml	NOUN
arestyrurj-165	38	33	)	)	PUNCT
arestyrurj-165	38	34	approach	approach	NOUN
arestyrurj-165	38	35	using	use	VERB
arestyrurj-165	38	36	a	a	DET
arestyrurj-165	38	37	block	block	NOUN
arestyrurj-165	38	38	relaxation	relaxation	NOUN
arestyrurj-165	38	39	algorithm	algorithm	NOUN
arestyrurj-165	38	40	,	,	PUNCT
arestyrurj-165	38	41	which	which	PRON
arestyrurj-165	38	42	we	we	PRON
arestyrurj-165	38	43	adopt	adopt	VERB
arestyrurj-165	38	44	to	to	PART
arestyrurj-165	38	45	formulate	formulate	VERB
arestyrurj-165	38	46	tensor	tensor	NOUN
arestyrurj-165	38	47	classification	classification	NOUN
arestyrurj-165	38	48	models	model	NOUN
arestyrurj-165	38	49	.	.	PUNCT
arestyrurj-165	39	1	tan	tan	PROPN
arestyrurj-165	39	2	et	et	PROPN
arestyrurj-165	39	3	al	al	PROPN
arestyrurj-165	39	4	.	.	PROPN
arestyrurj-165	39	5	proposes	propose	VERB
arestyrurj-165	39	6	a	a	DET
arestyrurj-165	39	7	logistic	logistic	ADJ
arestyrurj-165	39	8	tensor	tensor	NOUN
arestyrurj-165	39	9	regression	regression	NOUN
arestyrurj-165	39	10	model	model	NOUN
arestyrurj-165	39	11	with	with	ADP
arestyrurj-165	39	12	a	a	DET
arestyrurj-165	39	13	ℓ	ℓ	NOUN
arestyrurj-165	39	14	norm	norm	NOUN
arestyrurj-165	39	15	regularization	regularization	NOUN
arestyrurj-165	39	16	to	to	PART
arestyrurj-165	39	17	induce	induce	VERB
arestyrurj-165	39	18	sparsity.[15	sparsity.[15	NOUN
arestyrurj-165	39	19	]	]	PUNCT
arestyrurj-165	39	20	we	we	PRON
arestyrurj-165	39	21	observe	observe	VERB
arestyrurj-165	39	22	that	that	SCONJ
arestyrurj-165	39	23	this	this	DET
arestyrurj-165	39	24	technique	technique	NOUN
arestyrurj-165	39	25	efficiently	efficiently	ADV
arestyrurj-165	39	26	exploits	exploit	VERB
arestyrurj-165	39	27	structure	structure	NOUN
arestyrurj-165	39	28	,	,	PUNCT
arestyrurj-165	39	29	which	which	PRON
arestyrurj-165	39	30	motivates	motivate	VERB
arestyrurj-165	39	31	us	we	PRON
arestyrurj-165	39	32	to	to	PART
arestyrurj-165	39	33	generalize	generalize	VERB
arestyrurj-165	39	34	and	and	CCONJ
arestyrurj-165	39	35	formulate	formulate	VERB
arestyrurj-165	39	36	more	more	ADJ
arestyrurj-165	39	37	classification	classification	NOUN
arestyrurj-165	39	38	problems	problem	NOUN
arestyrurj-165	39	39	with	with	ADP
arestyrurj-165	39	40	different	different	ADJ
arestyrurj-165	39	41	regularization	regularization	NOUN
arestyrurj-165	39	42	(	(	PUNCT
arestyrurj-165	39	43	e.g.	e.g.	ADV
arestyrurj-165	39	44	ℓ	ℓ	NOUN
arestyrurj-165	39	45	norm	norm	NOUN
arestyrurj-165	39	46	)	)	PUNCT
arestyrurj-165	39	47	,	,	PUNCT
arestyrurj-165	39	48	and	and	CCONJ
arestyrurj-165	39	49	on	on	ADP
arestyrurj-165	39	50	different	different	ADJ
arestyrurj-165	39	51	datasets	dataset	NOUN
arestyrurj-165	39	52	.	.	PUNCT
arestyrurj-165	40	1	our	our	PRON
arestyrurj-165	40	2	contribution	contribution	NOUN
arestyrurj-165	40	3	in	in	ADP
arestyrurj-165	40	4	this	this	DET
arestyrurj-165	40	5	paper	paper	NOUN
arestyrurj-165	40	6	,	,	PUNCT
arestyrurj-165	40	7	we	we	PRON
arestyrurj-165	40	8	investigate	investigate	VERB
arestyrurj-165	40	9	the	the	DET
arestyrurj-165	40	10	performance	performance	NOUN
arestyrurj-165	40	11	of	of	ADP
arestyrurj-165	40	12	machine	machine	NOUN
arestyrurj-165	40	13	learning	learn	VERB
arestyrurj-165	40	14	classifiers	classifier	NOUN
arestyrurj-165	40	15	with	with	ADP
arestyrurj-165	40	16	a	a	DET
arestyrurj-165	40	17	candecomp/	candecomp/	NUM
arestyrurj-165	40	18	parafac	parafac	NOUN
arestyrurj-165	40	19	(	(	PUNCT
arestyrurj-165	40	20	cp	cp	NOUN
arestyrurj-165	40	21	)	)	PUNCT
arestyrurj-165	40	22	decomposition	decomposition	NOUN
arestyrurj-165	40	23	structure	structure	NOUN
arestyrurj-165	40	24	on	on	ADP
arestyrurj-165	40	25	the	the	DET
arestyrurj-165	40	26	coefficients	coefficient	NOUN
arestyrurj-165	40	27	/	/	SYM
arestyrurj-165	40	28	predictors	predictor	NOUN
arestyrurj-165	40	29	.	.	PUNCT
arestyrurj-165	41	1	we	we	PRON
arestyrurj-165	41	2	have	have	AUX
arestyrurj-165	41	3	seen	see	VERB
arestyrurj-165	41	4	in	in	ADP
arestyrurj-165	41	5	previous	previous	ADJ
arestyrurj-165	41	6	literature	literature	NOUN
arestyrurj-165	41	7	that	that	PRON
arestyrurj-165	41	8	these	these	DET
arestyrurj-165	41	9	methods	method	NOUN
arestyrurj-165	41	10	work	work	VERB
arestyrurj-165	41	11	efficiently	efficiently	ADV
arestyrurj-165	41	12	for	for	ADP
arestyrurj-165	41	13	solving	solve	VERB
arestyrurj-165	41	14	linear	linear	ADJ
arestyrurj-165	41	15	regression	regression	NOUN
arestyrurj-165	41	16	and	and	CCONJ
arestyrurj-165	41	17	logistic	logistic	ADJ
arestyrurj-165	41	18	regression	regression	NOUN
arestyrurj-165	41	19	coefficients.[15,21	coefficients.[15,21	VERB
arestyrurj-165	41	20	]	]	PUNCT
arestyrurj-165	41	21	we	we	PRON
arestyrurj-165	41	22	solve	solve	VERB
arestyrurj-165	41	23	classification	classification	NOUN
arestyrurj-165	41	24	problems	problem	NOUN
arestyrurj-165	41	25	,	,	PUNCT
arestyrurj-165	41	26	namely	namely	ADV
arestyrurj-165	41	27	support	support	VERB
arestyrurj-165	41	28	vector	vector	NOUN
arestyrurj-165	41	29	machines	machine	NOUN
arestyrurj-165	41	30	and	and	CCONJ
arestyrurj-165	41	31	logistic	logistic	ADJ
arestyrurj-165	41	32	regression	regression	NOUN
arestyrurj-165	41	33	figure	figure	NOUN
arestyrurj-165	41	34	2	2	NUM
arestyrurj-165	41	35	:	:	PUNCT
arestyrurj-165	41	36	example	example	NOUN
arestyrurj-165	41	37	of	of	ADP
arestyrurj-165	41	38	modeling	model	VERB
arestyrurj-165	41	39	observations	observation	NOUN
arestyrurj-165	41	40	:	:	PUNCT
arestyrurj-165	41	41	left	left	ADJ
arestyrurj-165	41	42	–	–	PUNCT
arestyrurj-165	41	43	matrix	matrix	NOUN
arestyrurj-165	41	44	,	,	PUNCT
arestyrurj-165	41	45	right	right	ADJ
arestyrurj-165	41	46	–	–	PUNCT
arestyrurj-165	41	47	tensor	tensor	NOUN
arestyrurj-165	41	48	aresty	aresty	ADJ
arestyrurj-165	41	49	rutgers	rutgers	PROPN
arestyrurj-165	41	50	undergraduate	undergraduate	PROPN
arestyrurj-165	41	51	research	research	PROPN
arestyrurj-165	41	52	journal	journal	PROPN
arestyrurj-165	41	53	,	,	PUNCT
arestyrurj-165	41	54	volume	volume	NOUN
arestyrurj-165	41	55	i	i	PRON
arestyrurj-165	41	56	,	,	PUNCT
arestyrurj-165	41	57	issue	issue	VERB
arestyrurj-165	41	58	iii	iii	NOUN
arestyrurj-165	41	59	on	on	ADP
arestyrurj-165	41	60	both	both	CCONJ
arestyrurj-165	41	61	synthetic	synthetic	ADJ
arestyrurj-165	41	62	and	and	CCONJ
arestyrurj-165	41	63	real	real	ADJ
arestyrurj-165	41	64	data	datum	NOUN
arestyrurj-165	41	65	.	.	PUNCT
arestyrurj-165	42	1	the	the	DET
arestyrurj-165	42	2	rest	rest	NOUN
arestyrurj-165	42	3	of	of	ADP
arestyrurj-165	42	4	this	this	DET
arestyrurj-165	42	5	paper	paper	NOUN
arestyrurj-165	42	6	is	be	AUX
arestyrurj-165	42	7	organized	organize	VERB
arestyrurj-165	42	8	as	as	SCONJ
arestyrurj-165	42	9	follows	follow	VERB
arestyrurj-165	42	10	.	.	PUNCT
arestyrurj-165	43	1	we	we	PRON
arestyrurj-165	43	2	first	first	ADV
arestyrurj-165	43	3	discuss	discuss	VERB
arestyrurj-165	43	4	some	some	DET
arestyrurj-165	43	5	tensor	tensor	NOUN
arestyrurj-165	43	6	algebra	algebra	NOUN
arestyrurj-165	43	7	and	and	CCONJ
arestyrurj-165	43	8	notation	notation	NOUN
arestyrurj-165	43	9	that	that	PRON
arestyrurj-165	43	10	will	will	AUX
arestyrurj-165	43	11	be	be	AUX
arestyrurj-165	43	12	used	use	VERB
arestyrurj-165	43	13	throughout	throughout	ADP
arestyrurj-165	43	14	this	this	DET
arestyrurj-165	43	15	paper	paper	NOUN
arestyrurj-165	43	16	.	.	PUNCT
arestyrurj-165	44	1	then	then	ADV
arestyrurj-165	44	2	,	,	PUNCT
arestyrurj-165	44	3	we	we	PRON
arestyrurj-165	44	4	propose	propose	VERB
arestyrurj-165	44	5	the	the	DET
arestyrurj-165	44	6	objective	objective	ADJ
arestyrurj-165	44	7	functions	function	NOUN
arestyrurj-165	44	8	as	as	ADV
arestyrurj-165	44	9	well	well	ADV
arestyrurj-165	44	10	as	as	ADP
arestyrurj-165	44	11	a	a	DET
arestyrurj-165	44	12	short	short	ADJ
arestyrurj-165	44	13	analysis	analysis	NOUN
arestyrurj-165	44	14	of	of	ADP
arestyrurj-165	44	15	the	the	DET
arestyrurj-165	44	16	cp	cp	PROPN
arestyrurj-165	44	17	structured	structure	VERB
arestyrurj-165	44	18	machine	machine	NOUN
arestyrurj-165	44	19	learning	learning	NOUN
arestyrurj-165	44	20	problems	problem	NOUN
arestyrurj-165	44	21	.	.	PUNCT
arestyrurj-165	45	1	we	we	PRON
arestyrurj-165	45	2	motivate	motivate	VERB
arestyrurj-165	45	3	and	and	CCONJ
arestyrurj-165	45	4	show	show	VERB
arestyrurj-165	45	5	results	result	NOUN
arestyrurj-165	45	6	of	of	ADP
arestyrurj-165	45	7	our	our	PRON
arestyrurj-165	45	8	approach	approach	NOUN
arestyrurj-165	45	9	by	by	ADP
arestyrurj-165	45	10	fixing	fix	VERB
arestyrurj-165	45	11	and	and	CCONJ
arestyrurj-165	45	12	solving	solve	VERB
arestyrurj-165	45	13	for	for	ADP
arestyrurj-165	45	14	the	the	DET
arestyrurj-165	45	15	true	true	ADJ
arestyrurj-165	45	16	predictor	predictor	NOUN
arestyrurj-165	45	17	.	.	PUNCT
arestyrurj-165	46	1	we	we	PRON
arestyrurj-165	46	2	compare	compare	VERB
arestyrurj-165	46	3	the	the	DET
arestyrurj-165	46	4	results	result	NOUN
arestyrurj-165	46	5	from	from	ADP
arestyrurj-165	46	6	the	the	DET
arestyrurj-165	46	7	tensor	tensor	NOUN
arestyrurj-165	46	8	structured	structure	VERB
arestyrurj-165	46	9	algorithm	algorithm	NOUN
arestyrurj-165	46	10	as	as	SCONJ
arestyrurj-165	46	11	opposed	oppose	VERB
arestyrurj-165	46	12	to	to	ADP
arestyrurj-165	46	13	the	the	DET
arestyrurj-165	46	14	unstructured	unstructured	ADJ
arestyrurj-165	46	15	vector	vector	NOUN
arestyrurj-165	46	16	algorithm	algorithm	NOUN
arestyrurj-165	46	17	.	.	PUNCT
arestyrurj-165	47	1	our	our	PRON
arestyrurj-165	47	2	contributions	contribution	NOUN
arestyrurj-165	47	3	can	can	AUX
arestyrurj-165	47	4	be	be	AUX
arestyrurj-165	47	5	summarized	summarize	VERB
arestyrurj-165	47	6	as	as	SCONJ
arestyrurj-165	47	7	follows	follow	VERB
arestyrurj-165	47	8	:	:	PUNCT
arestyrurj-165	47	9			PRON
arestyrurj-165	47	10	we	we	PRON
arestyrurj-165	47	11	perform	perform	VERB
arestyrurj-165	47	12	experiments	experiment	NOUN
arestyrurj-165	47	13	to	to	PART
arestyrurj-165	47	14	show	show	VERB
arestyrurj-165	47	15	that	that	SCONJ
arestyrurj-165	47	16	our	our	PRON
arestyrurj-165	47	17	structured	structured	ADJ
arestyrurj-165	47	18	method	method	NOUN
arestyrurj-165	47	19	works	work	VERB
arestyrurj-165	47	20	more	more	ADV
arestyrurj-165	47	21	efficiently	efficiently	ADV
arestyrurj-165	47	22	than	than	ADP
arestyrurj-165	47	23	the	the	DET
arestyrurj-165	47	24	traditional	traditional	ADJ
arestyrurj-165	47	25	method	method	NOUN
arestyrurj-165	47	26	when	when	SCONJ
arestyrurj-165	47	27	the	the	DET
arestyrurj-165	47	28	true	true	ADJ
arestyrurj-165	47	29	predictor	predictor	NOUN
arestyrurj-165	47	30	exhibits	exhibit	VERB
arestyrurj-165	47	31	both	both	DET
arestyrurj-165	47	32	an	an	DET
arestyrurj-165	47	33	approximate	approximate	ADJ
arestyrurj-165	47	34	and	and	CCONJ
arestyrurj-165	47	35	exact	exact	ADJ
arestyrurj-165	47	36	low	low	ADJ
arestyrurj-165	47	37	rank	rank	NOUN
arestyrurj-165	47	38	structure	structure	NOUN
arestyrurj-165	47	39	.	.	PUNCT
arestyrurj-165	48	1			X
arestyrurj-165	48	2	we	we	PRON
arestyrurj-165	48	3	show	show	VERB
arestyrurj-165	48	4	that	that	SCONJ
arestyrurj-165	48	5	our	our	PRON
arestyrurj-165	48	6	structured	structured	ADJ
arestyrurj-165	48	7	approach	approach	NOUN
arestyrurj-165	48	8	solves	solve	NOUN
arestyrurj-165	48	9	for	for	ADP
arestyrurj-165	48	10	fewer	few	ADJ
arestyrurj-165	48	11	coefficients	coefficient	NOUN
arestyrurj-165	48	12	more	more	ADV
arestyrurj-165	48	13	efficiently	efficiently	ADV
arestyrurj-165	48	14	than	than	ADP
arestyrurj-165	48	15	the	the	DET
arestyrurj-165	48	16	traditional	traditional	ADJ
arestyrurj-165	48	17	approach	approach	NOUN
arestyrurj-165	48	18	with	with	ADP
arestyrurj-165	48	19	a	a	DET
arestyrurj-165	48	20	dimensionality	dimensionality	NOUN
arestyrurj-165	48	21	reduction	reduction	NOUN
arestyrurj-165	48	22	step	step	NOUN
arestyrurj-165	48	23	(	(	PUNCT
arestyrurj-165	48	24	e.g.	e.g.	ADV
arestyrurj-165	48	25	principal	principal	ADJ
arestyrurj-165	48	26	component	component	NOUN
arestyrurj-165	48	27	analysis	analysis	NOUN
arestyrurj-165	48	28	)	)	PUNCT
arestyrurj-165	48	29	.	.	PUNCT
arestyrurj-165	49	1			X
arestyrurj-165	49	2	we	we	PRON
arestyrurj-165	49	3	develop	develop	VERB
arestyrurj-165	49	4	algorithms	algorithm	NOUN
arestyrurj-165	49	5	to	to	PART
arestyrurj-165	49	6	solve	solve	VERB
arestyrurj-165	49	7	machine	machine	NOUN
arestyrurj-165	49	8	learning	learning	NOUN
arestyrurj-165	49	9	problems	problem	NOUN
arestyrurj-165	49	10	with	with	ADP
arestyrurj-165	49	11	decomposition	decomposition	NOUN
arestyrurj-165	49	12	of	of	ADP
arestyrurj-165	49	13	𝑛	𝑛	DET
arestyrurj-165	49	14	-dimensional	-dimensional	ADJ
arestyrurj-165	49	15	tensors	tensor	NOUN
arestyrurj-165	49	16	with	with	ADP
arestyrurj-165	49	17	an	an	DET
arestyrurj-165	49	18	alternating	alternate	VERB
arestyrurj-165	49	19	minimization	minimization	NOUN
arestyrurj-165	49	20	scheme	scheme	NOUN
arestyrurj-165	49	21	.	.	PUNCT
arestyrurj-165	50	1	2	2	NUM
arestyrurj-165	50	2	preliminaries	preliminary	NOUN
arestyrurj-165	50	3	we	we	PRON
arestyrurj-165	50	4	dedicate	dedicate	VERB
arestyrurj-165	50	5	this	this	DET
arestyrurj-165	50	6	section	section	NOUN
arestyrurj-165	50	7	to	to	PART
arestyrurj-165	50	8	discuss	discuss	VERB
arestyrurj-165	50	9	some	some	PRON
arestyrurj-165	50	10	of	of	ADP
arestyrurj-165	50	11	the	the	DET
arestyrurj-165	50	12	concepts	concept	NOUN
arestyrurj-165	50	13	used	use	VERB
arestyrurj-165	50	14	throughout	throughout	ADP
arestyrurj-165	50	15	this	this	DET
arestyrurj-165	50	16	paper	paper	NOUN
arestyrurj-165	50	17	.	.	PUNCT
arestyrurj-165	51	1	due	due	ADP
arestyrurj-165	51	2	to	to	ADP
arestyrurj-165	51	3	the	the	DET
arestyrurj-165	51	4	theoretical	theoretical	ADJ
arestyrurj-165	51	5	nature	nature	NOUN
arestyrurj-165	51	6	of	of	ADP
arestyrurj-165	51	7	this	this	DET
arestyrurj-165	51	8	work	work	NOUN
arestyrurj-165	51	9	,	,	PUNCT
arestyrurj-165	51	10	the	the	DET
arestyrurj-165	51	11	technical	technical	ADJ
arestyrurj-165	51	12	description	description	NOUN
arestyrurj-165	51	13	may	may	AUX
arestyrurj-165	51	14	require	require	VERB
arestyrurj-165	51	15	some	some	DET
arestyrurj-165	51	16	mathematical	mathematical	ADJ
arestyrurj-165	51	17	maturity	maturity	NOUN
arestyrurj-165	51	18	.	.	PUNCT
arestyrurj-165	52	1	the	the	DET
arestyrurj-165	52	2	reader	reader	NOUN
arestyrurj-165	52	3	interested	interested	ADJ
arestyrurj-165	52	4	in	in	ADP
arestyrurj-165	52	5	the	the	DET
arestyrurj-165	52	6	empirical	empirical	ADJ
arestyrurj-165	52	7	findings	finding	NOUN
arestyrurj-165	52	8	can	can	AUX
arestyrurj-165	52	9	skip	skip	VERB
arestyrurj-165	52	10	to	to	ADP
arestyrurj-165	52	11	section	section	NOUN
arestyrurj-165	52	12	4	4	NUM
arestyrurj-165	52	13	.	.	PUNCT
arestyrurj-165	52	14	for	for	ADP
arestyrurj-165	52	15	a	a	DET
arestyrurj-165	52	16	complete	complete	ADJ
arestyrurj-165	52	17	introduction	introduction	NOUN
arestyrurj-165	52	18	to	to	ADP
arestyrurj-165	52	19	tensors	tensor	NOUN
arestyrurj-165	52	20	,	,	PUNCT
arestyrurj-165	52	21	see	see	VERB
arestyrurj-165	52	22	the	the	DET
arestyrurj-165	52	23	comprehensive	comprehensive	ADJ
arestyrurj-165	52	24	survey	survey	NOUN
arestyrurj-165	52	25	of	of	ADP
arestyrurj-165	52	26	kolda	kolda	NOUN
arestyrurj-165	52	27	and	and	CCONJ
arestyrurj-165	52	28	bader	bader	PROPN
arestyrurj-165	52	29	and	and	CCONJ
arestyrurj-165	52	30	rabanser	rabanser	NOUN
arestyrurj-165	52	31	et	et	PROPN
arestyrurj-165	52	32	al.[6,14	al.[6,14	ADV
arestyrurj-165	52	33	]	]	PUNCT
arestyrurj-165	52	34	tensors	tensor	NOUN
arestyrurj-165	52	35	are	be	AUX
arestyrurj-165	52	36	simply	simply	ADV
arestyrurj-165	52	37	defined	define	VERB
arestyrurj-165	52	38	as	as	ADP
arestyrurj-165	52	39	multidimensional	multidimensional	ADJ
arestyrurj-165	52	40	arrays	array	NOUN
arestyrurj-165	52	41	,	,	PUNCT
arestyrurj-165	52	42	and	and	CCONJ
arestyrurj-165	52	43	these	these	DET
arestyrurj-165	52	44	two	two	NUM
arestyrurj-165	52	45	terms	term	NOUN
arestyrurj-165	52	46	will	will	AUX
arestyrurj-165	52	47	be	be	AUX
arestyrurj-165	52	48	used	use	VERB
arestyrurj-165	52	49	interchangeably	interchangeably	ADV
arestyrurj-165	52	50	.	.	PUNCT
arestyrurj-165	53	1	we	we	PRON
arestyrurj-165	53	2	will	will	AUX
arestyrurj-165	53	3	denote	denote	VERB
arestyrurj-165	53	4	vectors	vector	NOUN
arestyrurj-165	53	5	with	with	ADP
arestyrurj-165	53	6	lower	low	ADJ
arestyrurj-165	53	7	case	case	NOUN
arestyrurj-165	53	8	letters	letter	NOUN
arestyrurj-165	53	9	(	(	PUNCT
arestyrurj-165	53	10	𝑥	𝑥	NOUN
arestyrurj-165	53	11	)	)	PUNCT
arestyrurj-165	53	12	,	,	PUNCT
arestyrurj-165	53	13	matrices	matrix	NOUN
arestyrurj-165	53	14	with	with	ADP
arestyrurj-165	53	15	capital	capital	NOUN
arestyrurj-165	53	16	letters	letter	NOUN
arestyrurj-165	53	17	(	(	PUNCT
arestyrurj-165	53	18	𝑋	𝑋	NOUN
arestyrurj-165	53	19	)	)	PUNCT
arestyrurj-165	53	20	,	,	PUNCT
arestyrurj-165	53	21	and	and	CCONJ
arestyrurj-165	53	22	tensors	tensor	NOUN
arestyrurj-165	53	23	as	as	ADP
arestyrurj-165	53	24	bold	bold	ADJ
arestyrurj-165	53	25	capital	capital	NOUN
arestyrurj-165	53	26	letters	letter	NOUN
arestyrurj-165	53	27	(	(	PUNCT
arestyrurj-165	53	28	𝐗	𝐗	PROPN
arestyrurj-165	53	29	)	)	PUNCT
arestyrurj-165	53	30	.	.	PUNCT
arestyrurj-165	54	1	i.	i.	PROPN
arestyrurj-165	54	2	tensor	tensor	NOUN
arestyrurj-165	54	3	reorderings	reordering	NOUN
arestyrurj-165	54	4	let	let	VERB
arestyrurj-165	54	5	𝐗	𝐗	PRON
arestyrurj-165	54	6	be	be	AUX
arestyrurj-165	54	7	a	a	DET
arestyrurj-165	54	8	third	third	ADJ
arestyrurj-165	54	9	-	-	PUNCT
arestyrurj-165	54	10	order	order	NOUN
arestyrurj-165	54	11	tensor	tensor	NOUN
arestyrurj-165	54	12	of	of	ADP
arestyrurj-165	54	13	dimensions	dimension	NOUN
arestyrurj-165	54	14	𝐗	𝐗	NOUN
arestyrurj-165	54	15	∈	∈	NOUN
arestyrurj-165	54	16	ℝ	ℝ	PROPN
arestyrurj-165	54	17	×	×	ADJ
arestyrurj-165	54	18	×	×	NOUN
arestyrurj-165	54	19	with	with	ADP
arestyrurj-165	54	20	the	the	DET
arestyrurj-165	54	21	two	two	NUM
arestyrurj-165	54	22	frontal	frontal	ADJ
arestyrurj-165	54	23	slices	slice	NOUN
arestyrurj-165	54	24	defined	define	VERB
arestyrurj-165	54	25	by	by	ADP
arestyrurj-165	54	26	𝑋	𝑋	PROPN
arestyrurj-165	54	27	,	,	PUNCT
arestyrurj-165	54	28	𝑋	𝑋	PROPN
arestyrurj-165	54	29	∈	∈	PROPN
arestyrurj-165	54	30	ℝ	ℝ	PROPN
arestyrurj-165	54	31	×	×	NOUN
arestyrurj-165	54	32	:	:	PUNCT
arestyrurj-165	54	33	vectorization	vectorization	NOUN
arestyrurj-165	54	34	we	we	PRON
arestyrurj-165	54	35	can	can	AUX
arestyrurj-165	54	36	create	create	VERB
arestyrurj-165	54	37	a	a	DET
arestyrurj-165	54	38	vector	vector	NOUN
arestyrurj-165	54	39	from	from	ADP
arestyrurj-165	54	40	any	any	DET
arestyrurj-165	54	41	matrix	matrix	NOUN
arestyrurj-165	54	42	or	or	CCONJ
arestyrurj-165	54	43	tensor	tensor	NOUN
arestyrurj-165	54	44	by	by	ADP
arestyrurj-165	54	45	stacking	stack	VERB
arestyrurj-165	54	46	the	the	DET
arestyrurj-165	54	47	row	row	NOUN
arestyrurj-165	54	48	or	or	CCONJ
arestyrurj-165	54	49	column	column	NOUN
arestyrurj-165	54	50	elements	element	NOUN
arestyrurj-165	54	51	into	into	ADP
arestyrurj-165	54	52	a	a	DET
arestyrurj-165	54	53	row	row	NOUN
arestyrurj-165	54	54	or	or	CCONJ
arestyrurj-165	54	55	column	column	NOUN
arestyrurj-165	54	56	vector	vector	NOUN
arestyrurj-165	54	57	,	,	PUNCT
arestyrurj-165	54	58	respectively	respectively	ADV
arestyrurj-165	54	59	.	.	PUNCT
arestyrurj-165	55	1	for	for	ADP
arestyrurj-165	55	2	example	example	NOUN
arestyrurj-165	55	3	,	,	PUNCT
arestyrurj-165	55	4	vectorizing	vectorize	VERB
arestyrurj-165	55	5	the	the	DET
arestyrurj-165	55	6	tensor	tensor	NOUN
arestyrurj-165	55	7	𝐗	𝐗	NOUN
arestyrurj-165	55	8	by	by	ADP
arestyrurj-165	55	9	its	its	PRON
arestyrurj-165	55	10	columns	column	NOUN
arestyrurj-165	55	11	would	would	AUX
arestyrurj-165	55	12	yield	yield	VERB
arestyrurj-165	55	13	the	the	DET
arestyrurj-165	55	14	following	follow	VERB
arestyrurj-165	55	15	column	column	NOUN
arestyrurj-165	55	16	vector	vector	NOUN
arestyrurj-165	55	17	:	:	PUNCT
arestyrurj-165	55	18	where	where	SCONJ
arestyrurj-165	55	19	we	we	PRON
arestyrurj-165	55	20	stack	stack	VERB
arestyrurj-165	55	21	the	the	DET
arestyrurj-165	55	22	columns	column	NOUN
arestyrurj-165	55	23	from	from	ADP
arestyrurj-165	55	24	the	the	DET
arestyrurj-165	55	25	first	first	ADJ
arestyrurj-165	55	26	frontal	frontal	ADJ
arestyrurj-165	55	27	slice	slice	NOUN
arestyrurj-165	55	28	,	,	PUNCT
arestyrurj-165	55	29	𝑋	𝑋	NOUN
arestyrurj-165	55	30	and	and	CCONJ
arestyrurj-165	55	31	the	the	DET
arestyrurj-165	55	32	second	second	ADJ
arestyrurj-165	55	33	frontal	frontal	ADJ
arestyrurj-165	55	34	slice	slice	NOUN
arestyrurj-165	55	35	,	,	PUNCT
arestyrurj-165	55	36	𝑋	𝑋	NOUN
arestyrurj-165	55	37	.	.	PUNCT
arestyrurj-165	56	1	the	the	DET
arestyrurj-165	56	2	dimensions	dimension	NOUN
arestyrurj-165	56	3	of	of	ADP
arestyrurj-165	56	4	the	the	DET
arestyrurj-165	56	5	resulting	result	VERB
arestyrurj-165	56	6	vector	vector	NOUN
arestyrurj-165	56	7	would	would	AUX
arestyrurj-165	56	8	be	be	AUX
arestyrurj-165	56	9	𝑥	𝑥	DET
arestyrurj-165	56	10	∈	∈	PROPN
arestyrurj-165	56	11	ℝ	ℝ	PROPN
arestyrurj-165	56	12	.	.	PUNCT
arestyrurj-165	57	1	matricization	matricization	PROPN
arestyrurj-165	57	2	the	the	DET
arestyrurj-165	57	3	𝑛-mode	𝑛-mode	PROPN
arestyrurj-165	57	4	matricization	matricization	NOUN
arestyrurj-165	57	5	(	(	PUNCT
arestyrurj-165	57	6	or	or	CCONJ
arestyrurj-165	57	7	unfolding	unfold	VERB
arestyrurj-165	57	8	)	)	PUNCT
arestyrurj-165	57	9	of	of	ADP
arestyrurj-165	57	10	a	a	DET
arestyrurj-165	57	11	tensor	tensor	NOUN
arestyrurj-165	57	12	𝐘	𝐘	NOUN
arestyrurj-165	57	13	∈	∈	NOUN
arestyrurj-165	57	14	ℝ	ℝ	PROPN
arestyrurj-165	57	15	×	×	NOUN
arestyrurj-165	57	16	×	×	NOUN
arestyrurj-165	57	17	…	…	SYM
arestyrurj-165	57	18	×	×	NOUN
arestyrurj-165	57	19	is	be	AUX
arestyrurj-165	57	20	denoted	denote	VERB
arestyrurj-165	57	21	as	as	ADP
arestyrurj-165	57	22	𝑌	𝑌	PROPN
arestyrurj-165	57	23	(	(	PUNCT
arestyrurj-165	57	24	)	)	PUNCT
arestyrurj-165	57	25	,	,	PUNCT
arestyrurj-165	57	26	where	where	SCONJ
arestyrurj-165	57	27	𝑌	𝑌	PROPN
arestyrurj-165	57	28	(	(	PUNCT
arestyrurj-165	57	29	)	)	PUNCT
arestyrurj-165	57	30	has	have	VERB
arestyrurj-165	57	31	the	the	DET
arestyrurj-165	57	32	columns	column	NOUN
arestyrurj-165	57	33	of	of	ADP
arestyrurj-165	57	34	the	the	DET
arestyrurj-165	57	35	𝑛	𝑛	DET
arestyrurj-165	57	36	-mode	-mode	NOUN
arestyrurj-165	57	37	fibers	fiber	NOUN
arestyrurj-165	57	38	.	.	PUNCT
arestyrurj-165	58	1	consider	consider	VERB
arestyrurj-165	58	2	the	the	DET
arestyrurj-165	58	3	same	same	ADJ
arestyrurj-165	58	4	tensor	tensor	NOUN
arestyrurj-165	58	5	𝐗	𝐗	NOUN
arestyrurj-165	58	6	from	from	ADP
arestyrurj-165	58	7	the	the	DET
arestyrurj-165	58	8	previous	previous	ADJ
arestyrurj-165	58	9	example	example	NOUN
arestyrurj-165	58	10	.	.	PUNCT
arestyrurj-165	59	1	then	then	ADV
arestyrurj-165	59	2	the	the	DET
arestyrurj-165	59	3	three	three	NUM
arestyrurj-165	59	4	𝑛-mode	𝑛-mode	NOUN
arestyrurj-165	59	5	matricizations	matricization	NOUN
arestyrurj-165	59	6	are	be	AUX
arestyrurj-165	59	7	the	the	DET
arestyrurj-165	59	8	following	follow	VERB
arestyrurj-165	59	9	:	:	PUNCT
arestyrurj-165	59	10	one	one	PRON
arestyrurj-165	59	11	can	can	AUX
arestyrurj-165	59	12	think	think	VERB
arestyrurj-165	59	13	of	of	ADP
arestyrurj-165	59	14	matricization	matricization	NOUN
arestyrurj-165	59	15	as	as	ADP
arestyrurj-165	59	16	a	a	DET
arestyrurj-165	59	17	generalization	generalization	NOUN
arestyrurj-165	59	18	of	of	ADP
arestyrurj-165	59	19	vectorization	vectorization	NOUN
arestyrurj-165	59	20	but	but	CCONJ
arestyrurj-165	59	21	to	to	ADP
arestyrurj-165	59	22	matrices	matrix	NOUN
arestyrurj-165	59	23	.	.	PUNCT
arestyrurj-165	60	1	since	since	SCONJ
arestyrurj-165	60	2	our	our	PRON
arestyrurj-165	60	3	example	example	NOUN
arestyrurj-165	60	4	𝐗	𝐗	NOUN
arestyrurj-165	60	5	is	be	AUX
arestyrurj-165	60	6	a	a	DET
arestyrurj-165	60	7	third	third	ADJ
arestyrurj-165	60	8	-	-	PUNCT
arestyrurj-165	60	9	order	order	NOUN
arestyrurj-165	60	10	tensor	tensor	NOUN
arestyrurj-165	60	11	,	,	PUNCT
arestyrurj-165	60	12	we	we	PRON
arestyrurj-165	60	13	have	have	VERB
arestyrurj-165	60	14	three	three	NUM
arestyrurj-165	60	15	matrices	matrix	NOUN
arestyrurj-165	60	16	from	from	ADP
arestyrurj-165	60	17	matricization	matricization	NOUN
arestyrurj-165	60	18	,	,	PUNCT
arestyrurj-165	60	19	one	one	NUM
arestyrurj-165	60	20	for	for	ADP
arestyrurj-165	60	21	each	each	DET
arestyrurj-165	60	22	mode	mode	NOUN
arestyrurj-165	60	23	.	.	PUNCT
arestyrurj-165	61	1	ii	ii	PROPN
arestyrurj-165	61	2	.	.	PUNCT
arestyrurj-165	62	1	vector	vector	PROPN
arestyrurj-165	62	2	&	&	CCONJ
arestyrurj-165	62	3	matrix	matrix	NOUN
arestyrurj-165	62	4	products	product	NOUN
arestyrurj-165	62	5	outer	outer	ADJ
arestyrurj-165	62	6	product	product	NOUN
arestyrurj-165	62	7	let	let	VERB
arestyrurj-165	62	8	𝑎	𝑎	NOUN
arestyrurj-165	62	9	and	and	CCONJ
arestyrurj-165	62	10	𝑏	𝑏	NOUN
arestyrurj-165	62	11	be	be	AUX
arestyrurj-165	62	12	two	two	NUM
arestyrurj-165	62	13	vectors	vector	NOUN
arestyrurj-165	62	14	of	of	ADP
arestyrurj-165	62	15	dimensions	dimension	NOUN
arestyrurj-165	62	16	𝑎	𝑎	PROPN
arestyrurj-165	62	17	∈	∈	NOUN
arestyrurj-165	62	18	ℝ	ℝ	NOUN
arestyrurj-165	62	19	and	and	CCONJ
arestyrurj-165	62	20	𝑏	𝑏	PRON
arestyrurj-165	62	21	∈	∈	PROPN
arestyrurj-165	62	22	ℝ	ℝ	PROPN
arestyrurj-165	62	23	,	,	PUNCT
arestyrurj-165	62	24	aresty	aresty	ADJ
arestyrurj-165	62	25	rutgers	rutgers	PROPN
arestyrurj-165	62	26	undergraduate	undergraduate	PROPN
arestyrurj-165	62	27	research	research	PROPN
arestyrurj-165	62	28	journal	journal	PROPN
arestyrurj-165	62	29	,	,	PUNCT
arestyrurj-165	62	30	volume	volume	NOUN
arestyrurj-165	62	31	i	i	PRON
arestyrurj-165	62	32	,	,	PUNCT
arestyrurj-165	62	33	issue	issue	VERB
arestyrurj-165	62	34	iii	iii	NUM
arestyrurj-165	62	35	the	the	DET
arestyrurj-165	62	36	outer	outer	ADJ
arestyrurj-165	62	37	product	product	NOUN
arestyrurj-165	62	38	of	of	ADP
arestyrurj-165	62	39	𝑎	𝑎	NOUN
arestyrurj-165	62	40	and	and	CCONJ
arestyrurj-165	62	41	𝑏	𝑏	NOUN
arestyrurj-165	62	42	,	,	PUNCT
arestyrurj-165	62	43	denoted	denote	VERB
arestyrurj-165	62	44	as	as	ADP
arestyrurj-165	62	45	𝑎	𝑎	PROPN
arestyrurj-165	62	46	○	○	PROPN
arestyrurj-165	62	47	𝑏	𝑏	PROPN
arestyrurj-165	62	48	,	,	PUNCT
arestyrurj-165	62	49	is	be	AUX
arestyrurj-165	62	50	a	a	DET
arestyrurj-165	62	51	matrix	matrix	NOUN
arestyrurj-165	62	52	of	of	ADP
arestyrurj-165	62	53	dimensions	dimension	NOUN
arestyrurj-165	62	54	(	(	PUNCT
arestyrurj-165	62	55	𝑎	𝑎	X
arestyrurj-165	62	56	○	○	PROPN
arestyrurj-165	62	57	𝑏	𝑏	NOUN
arestyrurj-165	62	58	)	)	PUNCT
arestyrurj-165	62	59	∈	∈	PROPN
arestyrurj-165	62	60	ℝ	ℝ	PROPN
arestyrurj-165	62	61	×	×	NOUN
arestyrurj-165	62	62	,	,	PUNCT
arestyrurj-165	62	63	note	note	VERB
arestyrurj-165	62	64	that	that	SCONJ
arestyrurj-165	62	65	this	this	DET
arestyrurj-165	62	66	outer	outer	ADJ
arestyrurj-165	62	67	product	product	NOUN
arestyrurj-165	62	68	is	be	AUX
arestyrurj-165	62	69	not	not	PART
arestyrurj-165	62	70	only	only	ADV
arestyrurj-165	62	71	limited	limit	VERB
arestyrurj-165	62	72	to	to	ADP
arestyrurj-165	62	73	vectors	vector	NOUN
arestyrurj-165	62	74	,	,	PUNCT
arestyrurj-165	62	75	and	and	CCONJ
arestyrurj-165	62	76	can	can	AUX
arestyrurj-165	62	77	be	be	AUX
arestyrurj-165	62	78	generalized	generalize	VERB
arestyrurj-165	62	79	to	to	ADP
arestyrurj-165	62	80	matrices	matrix	NOUN
arestyrurj-165	62	81	and	and	CCONJ
arestyrurj-165	62	82	tensors	tensor	NOUN
arestyrurj-165	62	83	as	as	ADV
arestyrurj-165	62	84	well	well	ADV
arestyrurj-165	62	85	.	.	PUNCT
arestyrurj-165	63	1	kronecker	kronecker	NOUN
arestyrurj-165	63	2	product	product	NOUN
arestyrurj-165	63	3	let	let	VERB
arestyrurj-165	63	4	𝐴	𝐴	PROPN
arestyrurj-165	63	5	and	and	CCONJ
arestyrurj-165	63	6	𝐵	𝐵	NOUN
arestyrurj-165	63	7	be	be	VERB
arestyrurj-165	63	8	two	two	NUM
arestyrurj-165	63	9	matrices	matrix	NOUN
arestyrurj-165	63	10	of	of	ADP
arestyrurj-165	63	11	dimensions	dimension	NOUN
arestyrurj-165	64	1	𝐴	𝐴	PROPN
arestyrurj-165	64	2	∈	∈	PROPN
arestyrurj-165	64	3	ℝ	ℝ	PROPN
arestyrurj-165	64	4	×	×	NOUN
arestyrurj-165	64	5	and	and	CCONJ
arestyrurj-165	64	6	𝐵	𝐵	NOUN
arestyrurj-165	64	7	∈	∈	NOUN
arestyrurj-165	64	8	ℝ	ℝ	PROPN
arestyrurj-165	64	9	×	×	NOUN
arestyrurj-165	64	10	,	,	PUNCT
arestyrurj-165	64	11	the	the	DET
arestyrurj-165	64	12	kronecker	kronecker	NOUN
arestyrurj-165	64	13	product	product	NOUN
arestyrurj-165	64	14	of	of	ADP
arestyrurj-165	64	15	𝐴	𝐴	PROPN
arestyrurj-165	64	16	and	and	CCONJ
arestyrurj-165	64	17	𝐵	𝐵	PROPN
arestyrurj-165	64	18	,	,	PUNCT
arestyrurj-165	64	19	denoted	denote	VERB
arestyrurj-165	64	20	as	as	ADP
arestyrurj-165	64	21	𝐴	𝐴	PROPN
arestyrurj-165	64	22	⊗	⊗	PROPN
arestyrurj-165	64	23	𝐵	𝐵	PROPN
arestyrurj-165	64	24	,	,	PUNCT
arestyrurj-165	64	25	is	be	AUX
arestyrurj-165	64	26	a	a	DET
arestyrurj-165	64	27	matrix	matrix	NOUN
arestyrurj-165	64	28	of	of	ADP
arestyrurj-165	64	29	dimensions	dimension	NOUN
arestyrurj-165	64	30	(	(	PUNCT
arestyrurj-165	64	31	𝐴	𝐴	PROPN
arestyrurj-165	64	32	⊗	⊗	PROPN
arestyrurj-165	64	33	𝐵	𝐵	PROPN
arestyrurj-165	64	34	)	)	PUNCT
arestyrurj-165	64	35	∈	∈	PROPN
arestyrurj-165	64	36	ℝ	ℝ	PROPN
arestyrurj-165	64	37	×	×	NOUN
arestyrurj-165	64	38	,	,	PUNCT
arestyrurj-165	64	39	in	in	ADP
arestyrurj-165	64	40	essence	essence	NOUN
arestyrurj-165	64	41	,	,	PUNCT
arestyrurj-165	64	42	the	the	DET
arestyrurj-165	64	43	kronecker	kronecker	NOUN
arestyrurj-165	64	44	product	product	NOUN
arestyrurj-165	64	45	is	be	AUX
arestyrurj-165	64	46	computed	compute	VERB
arestyrurj-165	64	47	by	by	ADP
arestyrurj-165	64	48	multiplying	multiply	VERB
arestyrurj-165	64	49	every	every	DET
arestyrurj-165	64	50	element	element	NOUN
arestyrurj-165	64	51	in	in	ADP
arestyrurj-165	64	52	the	the	DET
arestyrurj-165	64	53	first	first	ADJ
arestyrurj-165	64	54	matrix	matrix	NOUN
arestyrurj-165	64	55	,	,	PUNCT
arestyrurj-165	64	56	𝐴	𝐴	PROPN
arestyrurj-165	64	57	,	,	PUNCT
arestyrurj-165	64	58	by	by	ADP
arestyrurj-165	64	59	the	the	DET
arestyrurj-165	64	60	entire	entire	ADJ
arestyrurj-165	64	61	second	second	ADJ
arestyrurj-165	64	62	matrix	matrix	NOUN
arestyrurj-165	64	63	,	,	PUNCT
arestyrurj-165	64	64	𝐵.	𝐵.	PROPN
arestyrurj-165	64	65	khatri	khatri	PROPN
arestyrurj-165	64	66	-	-	PUNCT
arestyrurj-165	64	67	rao	rao	PROPN
arestyrurj-165	64	68	product	product	NOUN
arestyrurj-165	64	69	the	the	DET
arestyrurj-165	64	70	khatri	khatri	PROPN
arestyrurj-165	64	71	–	–	PUNCT
arestyrurj-165	64	72	rao	rao	NOUN
arestyrurj-165	64	73	product	product	NOUN
arestyrurj-165	64	74	is	be	AUX
arestyrurj-165	64	75	the	the	DET
arestyrurj-165	64	76	columnwise	columnwise	NOUN
arestyrurj-165	64	77	kronecker	kronecker	NOUN
arestyrurj-165	64	78	product	product	NOUN
arestyrurj-165	64	79	.	.	PUNCT
arestyrurj-165	65	1	consider	consider	VERB
arestyrurj-165	65	2	two	two	NUM
arestyrurj-165	65	3	(	(	PUNCT
arestyrurj-165	65	4	different	different	ADJ
arestyrurj-165	65	5	)	)	PUNCT
arestyrurj-165	65	6	matrices	matrix	NOUN
arestyrurj-165	65	7	𝐴	𝐴	NOUN
arestyrurj-165	65	8	∈	∈	NOUN
arestyrurj-165	65	9	ℝ	ℝ	PROPN
arestyrurj-165	65	10	×	×	NOUN
arestyrurj-165	65	11	and	and	CCONJ
arestyrurj-165	65	12	𝐵	𝐵	NOUN
arestyrurj-165	65	13	∈	∈	NOUN
arestyrurj-165	65	14	ℝ	ℝ	PROPN
arestyrurj-165	65	15	×	×	NOUN
arestyrurj-165	65	16	.	.	PUNCT
arestyrurj-165	66	1	the	the	DET
arestyrurj-165	66	2	khatri	khatri	PROPN
arestyrurj-165	66	3	–	–	PUNCT
arestyrurj-165	66	4	rao	rao	NOUN
arestyrurj-165	66	5	product	product	NOUN
arestyrurj-165	66	6	of	of	ADP
arestyrurj-165	66	7	𝐴	𝐴	PROPN
arestyrurj-165	66	8	and	and	CCONJ
arestyrurj-165	66	9	𝐵	𝐵	PROPN
arestyrurj-165	66	10	,	,	PUNCT
arestyrurj-165	66	11	denoted	denote	VERB
arestyrurj-165	66	12	as	as	ADP
arestyrurj-165	66	13	𝐴	𝐴	PROPN
arestyrurj-165	66	14	⊙	⊙	PROPN
arestyrurj-165	66	15	𝐵	𝐵	PROPN
arestyrurj-165	66	16	,	,	PUNCT
arestyrurj-165	66	17	is	be	AUX
arestyrurj-165	66	18	a	a	DET
arestyrurj-165	66	19	matrix	matrix	NOUN
arestyrurj-165	66	20	of	of	ADP
arestyrurj-165	66	21	dimensions	dimension	NOUN
arestyrurj-165	66	22	(	(	PUNCT
arestyrurj-165	66	23	𝐴	𝐴	PROPN
arestyrurj-165	66	24	⊙	⊙	PROPN
arestyrurj-165	66	25	𝐵	𝐵	PROPN
arestyrurj-165	66	26	)	)	PUNCT
arestyrurj-165	66	27	∈	∈	PROPN
arestyrurj-165	66	28	ℝ	ℝ	PROPN
arestyrurj-165	66	29	×	×	NOUN
arestyrurj-165	66	30	,	,	PUNCT
arestyrurj-165	66	31	here	here	ADV
arestyrurj-165	66	32	,	,	PUNCT
arestyrurj-165	66	33	we	we	PRON
arestyrurj-165	66	34	are	be	AUX
arestyrurj-165	66	35	taking	take	VERB
arestyrurj-165	66	36	the	the	DET
arestyrurj-165	66	37	kronecker	kronecker	NOUN
arestyrurj-165	66	38	product	product	NOUN
arestyrurj-165	66	39	between	between	ADP
arestyrurj-165	66	40	every	every	DET
arestyrurj-165	66	41	column	column	NOUN
arestyrurj-165	66	42	vector	vector	NOUN
arestyrurj-165	66	43	from	from	ADP
arestyrurj-165	66	44	𝐴	𝐴	PROPN
arestyrurj-165	66	45	and	and	CCONJ
arestyrurj-165	66	46	𝐵.	𝐵.	PROPN
arestyrurj-165	66	47	note	note	VERB
arestyrurj-165	66	48	that	that	SCONJ
arestyrurj-165	66	49	if	if	SCONJ
arestyrurj-165	66	50	𝐴	𝐴	PROPN
arestyrurj-165	66	51	and	and	CCONJ
arestyrurj-165	66	52	𝐵	𝐵	PROPN
arestyrurj-165	66	53	itself	itself	PRON
arestyrurj-165	66	54	were	be	AUX
arestyrurj-165	66	55	column	column	NOUN
arestyrurj-165	66	56	vectors	vector	NOUN
arestyrurj-165	66	57	,	,	PUNCT
arestyrurj-165	66	58	i.e.	i.e.	X
arestyrurj-165	66	59	𝑛	𝑛	X
arestyrurj-165	66	60	=	=	SYM
arestyrurj-165	66	61	1	1	NUM
arestyrurj-165	66	62	,	,	PUNCT
arestyrurj-165	66	63	then	then	ADV
arestyrurj-165	66	64	the	the	DET
arestyrurj-165	66	65	khatri	khatri	PROPN
arestyrurj-165	66	66	–	–	PUNCT
arestyrurj-165	66	67	rao	rao	NOUN
arestyrurj-165	66	68	product	product	NOUN
arestyrurj-165	66	69	is	be	AUX
arestyrurj-165	66	70	equivalent	equivalent	ADJ
arestyrurj-165	66	71	to	to	ADP
arestyrurj-165	66	72	the	the	DET
arestyrurj-165	66	73	kronecker	kronecker	NOUN
arestyrurj-165	66	74	product	product	NOUN
arestyrurj-165	66	75	,	,	PUNCT
arestyrurj-165	66	76	𝐴	𝐴	PROPN
arestyrurj-165	66	77	⊙	⊙	NOUN
arestyrurj-165	66	78	𝐵	𝐵	PROPN
arestyrurj-165	66	79	=	=	PROPN
arestyrurj-165	66	80	𝐴	𝐴	PROPN
arestyrurj-165	66	81	⊗	⊗	PROPN
arestyrurj-165	66	82	𝐵.	𝐵.	PROPN
arestyrurj-165	66	83	iii	iii	PROPN
arestyrurj-165	66	84	.	.	PROPN
arestyrurj-165	66	85	tensor	tensor	NOUN
arestyrurj-165	66	86	decomposition	decomposition	NOUN
arestyrurj-165	66	87	tensor	tensor	NOUN
arestyrurj-165	66	88	decompositions	decomposition	NOUN
arestyrurj-165	66	89	are	be	AUX
arestyrurj-165	66	90	generalizations	generalization	NOUN
arestyrurj-165	66	91	of	of	ADP
arestyrurj-165	66	92	matrix	matrix	NOUN
arestyrurj-165	66	93	factorizations	factorization	NOUN
arestyrurj-165	66	94	to	to	ADP
arestyrurj-165	66	95	multidimensional	multidimensional	ADJ
arestyrurj-165	66	96	arrays.[20	arrays.[20	NOUN
arestyrurj-165	66	97	]	]	PUNCT
arestyrurj-165	66	98	we	we	PRON
arestyrurj-165	66	99	introduce	introduce	VERB
arestyrurj-165	66	100	one	one	NUM
arestyrurj-165	66	101	tensor	tensor	NOUN
arestyrurj-165	66	102	factorization	factorization	NOUN
arestyrurj-165	66	103	scheme	scheme	NOUN
arestyrurj-165	66	104	that	that	PRON
arestyrurj-165	66	105	is	be	AUX
arestyrurj-165	66	106	important	important	ADJ
arestyrurj-165	66	107	in	in	ADP
arestyrurj-165	66	108	understanding	understand	VERB
arestyrurj-165	66	109	the	the	DET
arestyrurj-165	66	110	setting	setting	NOUN
arestyrurj-165	66	111	of	of	ADP
arestyrurj-165	66	112	our	our	PRON
arestyrurj-165	66	113	algorithm	algorithm	NOUN
arestyrurj-165	66	114	.	.	PUNCT
arestyrurj-165	67	1	in	in	ADP
arestyrurj-165	67	2	the	the	DET
arestyrurj-165	67	3	matricized	matricized	ADJ
arestyrurj-165	67	4	form	form	NOUN
arestyrurj-165	67	5	,	,	PUNCT
arestyrurj-165	67	6	we	we	PRON
arestyrurj-165	67	7	show	show	VERB
arestyrurj-165	67	8	that	that	SCONJ
arestyrurj-165	67	9	this	this	DET
arestyrurj-165	67	10	factorization	factorization	NOUN
arestyrurj-165	67	11	has	have	VERB
arestyrurj-165	67	12	useful	useful	ADJ
arestyrurj-165	67	13	properties	property	NOUN
arestyrurj-165	67	14	to	to	PART
arestyrurj-165	67	15	be	be	AUX
arestyrurj-165	67	16	solved	solve	VERB
arestyrurj-165	67	17	with	with	ADP
arestyrurj-165	67	18	an	an	DET
arestyrurj-165	67	19	alternating	alternate	VERB
arestyrurj-165	67	20	minimization	minimization	NOUN
arestyrurj-165	67	21	scheme	scheme	NOUN
arestyrurj-165	67	22	.	.	PUNCT
arestyrurj-165	68	1	candecomp	candecomp	PROPN
arestyrurj-165	68	2	/	/	SYM
arestyrurj-165	68	3	parafac	parafac	NOUN
arestyrurj-165	68	4	(	(	PUNCT
arestyrurj-165	68	5	cp	cp	NOUN
arestyrurj-165	68	6	)	)	PUNCT
arestyrurj-165	68	7	decomposition	decomposition	NOUN
arestyrurj-165	68	8	the	the	DET
arestyrurj-165	68	9	objective	objective	NOUN
arestyrurj-165	68	10	of	of	ADP
arestyrurj-165	68	11	the	the	DET
arestyrurj-165	68	12	cp	cp	PROPN
arestyrurj-165	68	13	decomposition	decomposition	NOUN
arestyrurj-165	68	14	is	be	AUX
arestyrurj-165	68	15	to	to	PART
arestyrurj-165	68	16	express	express	VERB
arestyrurj-165	68	17	a	a	DET
arestyrurj-165	68	18	tensor	tensor	NOUN
arestyrurj-165	68	19	as	as	ADP
arestyrurj-165	68	20	the	the	DET
arestyrurj-165	68	21	sum	sum	NOUN
arestyrurj-165	68	22	of	of	ADP
arestyrurj-165	68	23	component	component	NOUN
arestyrurj-165	68	24	rank	rank	NOUN
arestyrurj-165	68	25	–	–	PUNCT
arestyrurj-165	68	26	one	one	NUM
arestyrurj-165	68	27	tensors	tensor	NOUN
arestyrurj-165	68	28	,	,	PUNCT
arestyrurj-165	68	29	i.e.	i.e.	X
arestyrurj-165	68	30	vectors	vector	NOUN
arestyrurj-165	68	31	,	,	PUNCT
arestyrurj-165	68	32	as	as	SCONJ
arestyrurj-165	68	33	depicted	depict	VERB
arestyrurj-165	68	34	in	in	ADP
arestyrurj-165	68	35	figure	figure	NOUN
arestyrurj-165	68	36	3	3	NUM
arestyrurj-165	68	37	.	.	PUNCT
arestyrurj-165	69	1	for	for	ADP
arestyrurj-165	69	2	example	example	NOUN
arestyrurj-165	69	3	,	,	PUNCT
arestyrurj-165	69	4	consider	consider	VERB
arestyrurj-165	69	5	a	a	DET
arestyrurj-165	69	6	third	third	ADJ
arestyrurj-165	69	7	-	-	PUNCT
arestyrurj-165	69	8	order	order	NOUN
arestyrurj-165	69	9	tensor	tensor	NOUN
arestyrurj-165	69	10	𝐗	𝐗	NOUN
arestyrurj-165	69	11	∈	∈	NOUN
arestyrurj-165	69	12	ℝ	ℝ	PROPN
arestyrurj-165	69	13	×	×	NOUN
arestyrurj-165	69	14	×	×	NOUN
arestyrurj-165	69	15	.	.	PUNCT
arestyrurj-165	70	1	we	we	PRON
arestyrurj-165	70	2	can	can	AUX
arestyrurj-165	70	3	approximate	approximate	VERB
arestyrurj-165	70	4	this	this	DET
arestyrurj-165	70	5	tensor	tensor	NOUN
arestyrurj-165	70	6	as	as	ADP
arestyrurj-165	70	7	the	the	DET
arestyrurj-165	70	8	following	following	NOUN
arestyrurj-165	70	9	where	where	SCONJ
arestyrurj-165	70	10	”	"	PUNCT
arestyrurj-165	70	11	○	○	ADJ
arestyrurj-165	70	12	”	"	PUNCT
arestyrurj-165	70	13	denotes	denote	VERB
arestyrurj-165	70	14	the	the	DET
arestyrurj-165	70	15	outer	outer	ADJ
arestyrurj-165	70	16	product	product	NOUN
arestyrurj-165	70	17	,	,	PUNCT
arestyrurj-165	70	18	r	r	NOUN
arestyrurj-165	70	19	represents	represent	VERB
arestyrurj-165	70	20	the	the	DET
arestyrurj-165	70	21	rank	rank	NOUN
arestyrurj-165	70	22	(	(	PUNCT
arestyrurj-165	70	23	positive	positive	ADJ
arestyrurj-165	70	24	integer	integer	NOUN
arestyrurj-165	70	25	)	)	PUNCT
arestyrurj-165	70	26	,	,	PUNCT
arestyrurj-165	70	27	and	and	CCONJ
arestyrurj-165	70	28	𝑎	𝑎	PRON
arestyrurj-165	70	29	∈	∈	NOUN
arestyrurj-165	70	30	ℝ	ℝ	NOUN
arestyrurj-165	70	31	,	,	PUNCT
arestyrurj-165	70	32	𝑏	𝑏	PROPN
arestyrurj-165	70	33	∈	∈	PROPN
arestyrurj-165	70	34	ℝ	ℝ	PROPN
arestyrurj-165	70	35	,	,	PUNCT
arestyrurj-165	70	36	and	and	CCONJ
arestyrurj-165	70	37	𝑐	𝑐	PROPN
arestyrurj-165	70	38	∈	∈	NOUN
arestyrurj-165	70	39	ℝ	ℝ	PROPN
arestyrurj-165	70	40	for	for	ADP
arestyrurj-165	70	41	𝑟	𝑟	NOUN
arestyrurj-165	70	42	=	=	SYM
arestyrurj-165	70	43	1	1	NUM
arestyrurj-165	70	44	,	,	PUNCT
arestyrurj-165	70	45	.	.	PUNCT
arestyrurj-165	70	46	.	.	PUNCT
arestyrurj-165	71	1	.	.	PUNCT
arestyrurj-165	72	1	,	,	PUNCT
arestyrurj-165	72	2	𝑅	𝑅	PROPN
arestyrurj-165	72	3	.	.	PUNCT
arestyrurj-165	73	1	we	we	PRON
arestyrurj-165	73	2	can	can	AUX
arestyrurj-165	73	3	formalize	formalize	VERB
arestyrurj-165	73	4	this	this	DET
arestyrurj-165	73	5	decomposition	decomposition	NOUN
arestyrurj-165	73	6	as	as	ADP
arestyrurj-165	73	7	the	the	DET
arestyrurj-165	73	8	following	follow	VERB
arestyrurj-165	73	9	optimization	optimization	NOUN
arestyrurj-165	73	10	problem	problem	NOUN
arestyrurj-165	73	11	:	:	PUNCT
arestyrurj-165	73	12	where	where	SCONJ
arestyrurj-165	73	13	𝐗	𝐗	PRON
arestyrurj-165	73	14	would	would	AUX
arestyrurj-165	73	15	represent	represent	VERB
arestyrurj-165	73	16	a	a	DET
arestyrurj-165	73	17	low	low	ADJ
arestyrurj-165	73	18	rank	rank	NOUN
arestyrurj-165	73	19	approximation	approximation	NOUN
arestyrurj-165	73	20	of	of	ADP
arestyrurj-165	73	21	𝐗.	𝐗.	PROPN
arestyrurj-165	73	22	the	the	DET
arestyrurj-165	73	23	factor	factor	NOUN
arestyrurj-165	73	24	matrices	matrix	NOUN
arestyrurj-165	73	25	or	or	CCONJ
arestyrurj-165	73	26	cp	cp	NUM
arestyrurj-165	73	27	factors	factor	NOUN
arestyrurj-165	73	28	are	be	AUX
arestyrurj-165	73	29	matrices	matrix	NOUN
arestyrurj-165	73	30	with	with	ADP
arestyrurj-165	73	31	the	the	DET
arestyrurj-165	73	32	rank	rank	NOUN
arestyrurj-165	73	33	–	–	PUNCT
arestyrurj-165	73	34	one	one	NUM
arestyrurj-165	73	35	tensors	tensor	NOUN
arestyrurj-165	73	36	as	as	ADP
arestyrurj-165	73	37	entries	entry	NOUN
arestyrurj-165	73	38	.	.	PUNCT
arestyrurj-165	74	1	from	from	ADP
arestyrurj-165	74	2	the	the	DET
arestyrurj-165	74	3	previous	previous	ADJ
arestyrurj-165	74	4	three	three	NUM
arestyrurj-165	74	5	-	-	PUNCT
arestyrurj-165	74	6	dimensional	dimensional	ADJ
arestyrurj-165	74	7	case	case	NOUN
arestyrurj-165	74	8	,	,	PUNCT
arestyrurj-165	74	9	𝐴	𝐴	PROPN
arestyrurj-165	74	10	∈	∈	PROPN
arestyrurj-165	74	11	ℝ	ℝ	PROPN
arestyrurj-165	74	12	×	×	NOUN
arestyrurj-165	74	13	would	would	AUX
arestyrurj-165	74	14	be	be	AUX
arestyrurj-165	74	15	an	an	DET
arestyrurj-165	74	16	estimated	estimate	VERB
arestyrurj-165	74	17	cp	cp	NUM
arestyrurj-165	74	18	factor	factor	NOUN
arestyrurj-165	74	19	with	with	ADP
arestyrurj-165	74	20	entries	entry	NOUN
arestyrurj-165	74	21	figure	figure	VERB
arestyrurj-165	74	22	3	3	NUM
arestyrurj-165	74	23	:	:	PUNCT
arestyrurj-165	74	24	graphical	graphical	ADJ
arestyrurj-165	74	25	representation	representation	NOUN
arestyrurj-165	74	26	of	of	ADP
arestyrurj-165	74	27	the	the	DET
arestyrurj-165	74	28	candecomp/	candecomp/	NUM
arestyrurj-165	74	29	parafac	parafac	NOUN
arestyrurj-165	74	30	decomposition	decomposition	NOUN
arestyrurj-165	74	31	–	–	PUNCT
arestyrurj-165	74	32	low	low	ADJ
arestyrurj-165	74	33	rank	rank	NOUN
arestyrurj-165	74	34	approximation	approximation	NOUN
arestyrurj-165	74	35	of	of	ADP
arestyrurj-165	74	36	a	a	DET
arestyrurj-165	74	37	third	third	ADJ
arestyrurj-165	74	38	–	–	PUNCT
arestyrurj-165	74	39	order	order	NOUN
arestyrurj-165	74	40	tensor	tensor	NOUN
arestyrurj-165	74	41	aresty	aresty	ADJ
arestyrurj-165	74	42	rutgers	rutgers	PROPN
arestyrurj-165	74	43	undergraduate	undergraduate	PROPN
arestyrurj-165	74	44	research	research	PROPN
arestyrurj-165	74	45	journal	journal	PROPN
arestyrurj-165	74	46	,	,	PUNCT
arestyrurj-165	74	47	volume	volume	NOUN
arestyrurj-165	74	48	i	i	PRON
arestyrurj-165	74	49	,	,	PUNCT
arestyrurj-165	74	50	issue	issue	VERB
arestyrurj-165	74	51	iii	iii	NOUN
arestyrurj-165	74	52	with	with	ADP
arestyrurj-165	74	53	these	these	DET
arestyrurj-165	74	54	definitions	definition	NOUN
arestyrurj-165	74	55	and	and	CCONJ
arestyrurj-165	74	56	the	the	DET
arestyrurj-165	74	57	products	product	NOUN
arestyrurj-165	74	58	defined	define	VERB
arestyrurj-165	74	59	previously	previously	ADV
arestyrurj-165	74	60	,	,	PUNCT
arestyrurj-165	74	61	we	we	PRON
arestyrurj-165	74	62	can	can	AUX
arestyrurj-165	74	63	formulate	formulate	VERB
arestyrurj-165	74	64	some	some	DET
arestyrurj-165	74	65	useful	useful	ADJ
arestyrurj-165	74	66	properties	property	NOUN
arestyrurj-165	74	67	for	for	ADP
arestyrurj-165	74	68	the	the	DET
arestyrurj-165	74	69	third	third	ADJ
arestyrurj-165	74	70	–	–	PUNCT
arestyrurj-165	74	71	order	order	NOUN
arestyrurj-165	74	72	case	case	NOUN
arestyrurj-165	74	73	:	:	PUNCT
arestyrurj-165	74	74	these	these	DET
arestyrurj-165	74	75	relationships	relationship	NOUN
arestyrurj-165	74	76	can	can	AUX
arestyrurj-165	74	77	easily	easily	ADV
arestyrurj-165	74	78	be	be	AUX
arestyrurj-165	74	79	generalized	generalize	VERB
arestyrurj-165	74	80	to	to	PART
arestyrurj-165	74	81	𝑛mode	𝑛mode	VERB
arestyrurj-165	74	82	tensors	tensor	NOUN
arestyrurj-165	74	83	,	,	PUNCT
arestyrurj-165	74	84	but	but	CCONJ
arestyrurj-165	74	85	for	for	ADP
arestyrurj-165	74	86	the	the	DET
arestyrurj-165	74	87	purposes	purpose	NOUN
arestyrurj-165	74	88	of	of	ADP
arestyrurj-165	74	89	this	this	DET
arestyrurj-165	74	90	paper	paper	NOUN
arestyrurj-165	74	91	,	,	PUNCT
arestyrurj-165	74	92	𝑛	𝑛	NOUN
arestyrurj-165	74	93	=	=	SYM
arestyrurj-165	74	94	3	3	NUM
arestyrurj-165	74	95	will	will	AUX
arestyrurj-165	74	96	suffice	suffice	VERB
arestyrurj-165	74	97	.	.	PUNCT
arestyrurj-165	75	1	we	we	PRON
arestyrurj-165	75	2	will	will	AUX
arestyrurj-165	75	3	show	show	VERB
arestyrurj-165	75	4	how	how	SCONJ
arestyrurj-165	75	5	we	we	PRON
arestyrurj-165	75	6	can	can	AUX
arestyrurj-165	75	7	use	use	VERB
arestyrurj-165	75	8	these	these	DET
arestyrurj-165	75	9	equations	equation	NOUN
arestyrurj-165	75	10	for	for	ADP
arestyrurj-165	75	11	our	our	PRON
arestyrurj-165	75	12	alternating	alternate	VERB
arestyrurj-165	75	13	minimization	minimization	NOUN
arestyrurj-165	75	14	algorithm	algorithm	NOUN
arestyrurj-165	75	15	in	in	ADP
arestyrurj-165	75	16	the	the	DET
arestyrurj-165	75	17	following	follow	VERB
arestyrurj-165	75	18	sections	section	NOUN
arestyrurj-165	75	19	.	.	PUNCT
arestyrurj-165	76	1	there	there	PRON
arestyrurj-165	76	2	also	also	ADV
arestyrurj-165	76	3	are	be	AUX
arestyrurj-165	76	4	other	other	ADJ
arestyrurj-165	76	5	useful	useful	ADJ
arestyrurj-165	76	6	tensor	tensor	NOUN
arestyrurj-165	76	7	factorizations	factorization	NOUN
arestyrurj-165	76	8	,	,	PUNCT
arestyrurj-165	76	9	such	such	ADJ
arestyrurj-165	76	10	as	as	ADP
arestyrurj-165	76	11	the	the	DET
arestyrurj-165	76	12	tucker	tucker	PROPN
arestyrurj-165	76	13	decomposition	decomposition	NOUN
arestyrurj-165	76	14	,	,	PUNCT
arestyrurj-165	76	15	which	which	PRON
arestyrurj-165	76	16	is	be	AUX
arestyrurj-165	76	17	explained	explain	VERB
arestyrurj-165	76	18	in	in	ADP
arestyrurj-165	76	19	detail	detail	NOUN
arestyrurj-165	76	20	in	in	ADP
arestyrurj-165	76	21	the	the	DET
arestyrurj-165	76	22	survey	survey	NOUN
arestyrurj-165	76	23	paper.[6	paper.[6	NOUN
arestyrurj-165	76	24	]	]	PUNCT
arestyrurj-165	76	25	iv	iv	X
arestyrurj-165	76	26	.	.	PUNCT
arestyrurj-165	76	27	machine	machine	NOUN
arestyrurj-165	76	28	learning	learn	VERB
arestyrurj-165	76	29	optimization	optimization	NOUN
arestyrurj-165	76	30	problems	problem	NOUN
arestyrurj-165	76	31	many	many	ADJ
arestyrurj-165	76	32	machine	machine	NOUN
arestyrurj-165	76	33	learning	learn	VERB
arestyrurj-165	76	34	algorithms	algorithm	NOUN
arestyrurj-165	76	35	can	can	AUX
arestyrurj-165	76	36	be	be	AUX
arestyrurj-165	76	37	framed	frame	VERB
arestyrurj-165	76	38	as	as	ADP
arestyrurj-165	76	39	empirical	empirical	ADJ
arestyrurj-165	76	40	risk	risk	NOUN
arestyrurj-165	76	41	minimization	minimization	NOUN
arestyrurj-165	76	42	(	(	PUNCT
arestyrurj-165	76	43	erm	erm	PROPN
arestyrurj-165	76	44	)	)	PUNCT
arestyrurj-165	76	45	problems	problem	NOUN
arestyrurj-165	76	46	.	.	PUNCT
arestyrurj-165	77	1	the	the	DET
arestyrurj-165	77	2	empirical	empirical	ADJ
arestyrurj-165	77	3	risk	risk	NOUN
arestyrurj-165	77	4	is	be	AUX
arestyrurj-165	77	5	defined	define	VERB
arestyrurj-165	77	6	in	in	ADP
arestyrurj-165	77	7	terms	term	NOUN
arestyrurj-165	77	8	of	of	ADP
arestyrurj-165	77	9	a	a	DET
arestyrurj-165	77	10	risk	risk	NOUN
arestyrurj-165	77	11	,	,	PUNCT
arestyrurj-165	77	12	or	or	CCONJ
arestyrurj-165	77	13	loss	loss	NOUN
arestyrurj-165	77	14	function	function	NOUN
arestyrurj-165	77	15	ℓ	ℓ	PROPN
arestyrurj-165	77	16	(	(	PUNCT
arestyrurj-165	77	17	·	·	PUNCT
arestyrurj-165	77	18	)	)	PUNCT
arestyrurj-165	77	19	.	.	PUNCT
arestyrurj-165	78	1	for	for	ADP
arestyrurj-165	78	2	linear	linear	PROPN
arestyrurj-165	78	3	classifiers	classifier	NOUN
arestyrurj-165	78	4	,	,	PUNCT
arestyrurj-165	78	5	the	the	DET
arestyrurj-165	78	6	loss	loss	NOUN
arestyrurj-165	78	7	of	of	ADP
arestyrurj-165	78	8	a	a	DET
arestyrurj-165	78	9	linear	linear	ADJ
arestyrurj-165	78	10	predictor	predictor	NOUN
arestyrurj-165	78	11	𝑤	𝑤	ADP
arestyrurj-165	78	12	on	on	ADP
arestyrurj-165	78	13	the	the	DET
arestyrurj-165	78	14	data	data	NOUN
arestyrurj-165	78	15	sample	sample	NOUN
arestyrurj-165	78	16	(	(	PUNCT
arestyrurj-165	78	17	𝑥	𝑥	INTJ
arestyrurj-165	78	18	,	,	PUNCT
arestyrurj-165	78	19	𝑦	𝑦	NOUN
arestyrurj-165	78	20	)	)	PUNCT
arestyrurj-165	78	21	can	can	AUX
arestyrurj-165	78	22	be	be	AUX
arestyrurj-165	78	23	written	write	VERB
arestyrurj-165	78	24	as	as	ADP
arestyrurj-165	78	25	ℓ(𝑤	ℓ(𝑤	NOUN
arestyrurj-165	78	26	𝑥	𝑥	PROPN
arestyrurj-165	78	27	,	,	PUNCT
arestyrurj-165	78	28	𝑦	𝑦	NOUN
arestyrurj-165	78	29	)	)	PUNCT
arestyrurj-165	78	30	and	and	CCONJ
arestyrurj-165	78	31	the	the	DET
arestyrurj-165	78	32	average	average	ADJ
arestyrurj-165	78	33	empirical	empirical	ADJ
arestyrurj-165	78	34	risk	risk	NOUN
arestyrurj-165	78	35	as	as	ADP
arestyrurj-165	78	36	∑	∑	PROPN
arestyrurj-165	78	37	ℓ(𝑤	ℓ(𝑤	NOUN
arestyrurj-165	78	38	𝑥	𝑥	PROPN
arestyrurj-165	78	39	,	,	PUNCT
arestyrurj-165	78	40	𝑦	𝑦	NOUN
arestyrurj-165	78	41	)	)	PUNCT
arestyrurj-165	78	42	.	.	PUNCT
arestyrurj-165	79	1	we	we	PRON
arestyrurj-165	79	2	discuss	discuss	VERB
arestyrurj-165	79	3	these	these	DET
arestyrurj-165	79	4	loss	loss	NOUN
arestyrurj-165	79	5	functions	function	NOUN
arestyrurj-165	79	6	for	for	ADP
arestyrurj-165	79	7	some	some	DET
arestyrurj-165	79	8	common	common	ADJ
arestyrurj-165	79	9	classifiers	classifier	NOUN
arestyrurj-165	79	10	and	and	CCONJ
arestyrurj-165	79	11	how	how	SCONJ
arestyrurj-165	79	12	we	we	PRON
arestyrurj-165	79	13	can	can	AUX
arestyrurj-165	79	14	use	use	VERB
arestyrurj-165	79	15	them	they	PRON
arestyrurj-165	79	16	to	to	PART
arestyrurj-165	79	17	solve	solve	VERB
arestyrurj-165	79	18	tensor	tensor	NOUN
arestyrurj-165	79	19	structured	structure	VERB
arestyrurj-165	79	20	erm	erm	PROPN
arestyrurj-165	79	21	problems	problem	NOUN
arestyrurj-165	79	22	.	.	PUNCT
arestyrurj-165	80	1	support	support	NOUN
arestyrurj-165	80	2	vector	vector	NOUN
arestyrurj-165	80	3	machines	machine	NOUN
arestyrurj-165	80	4	consider	consider	VERB
arestyrurj-165	80	5	a	a	DET
arestyrurj-165	80	6	dataset	dataset	NOUN
arestyrurj-165	80	7	with	with	ADP
arestyrurj-165	80	8	𝑛	𝑛	DET
arestyrurj-165	80	9	samples	sample	NOUN
arestyrurj-165	80	10	,	,	PUNCT
arestyrurj-165	80	11	i.e.	i.e.	X
arestyrurj-165	80	12	{	{	PUNCT
arestyrurj-165	80	13	(	(	PUNCT
arestyrurj-165	80	14	𝑥	𝑥	INTJ
arestyrurj-165	80	15	,	,	PUNCT
arestyrurj-165	80	16	𝑦	𝑦	NOUN
arestyrurj-165	80	17	)	)	PUNCT
arestyrurj-165	80	18	}	}	PUNCT
arestyrurj-165	80	19	,	,	PUNCT
arestyrurj-165	80	20	where	where	SCONJ
arestyrurj-165	80	21	𝑦	𝑦	X
arestyrurj-165	80	22	∈	∈	NOUN
arestyrurj-165	80	23	{	{	PUNCT
arestyrurj-165	80	24	−1,1	−1,1	NOUN
arestyrurj-165	80	25	}	}	PUNCT
arestyrurj-165	80	26	.	.	PUNCT
arestyrurj-165	81	1	support	support	NOUN
arestyrurj-165	81	2	vector	vector	NOUN
arestyrurj-165	81	3	machine	machine	NOUN
arestyrurj-165	81	4	(	(	PUNCT
arestyrurj-165	81	5	svm	svm	PROPN
arestyrurj-165	81	6	)	)	PUNCT
arestyrurj-165	81	7	or	or	CCONJ
arestyrurj-165	81	8	maximum	maximum	ADJ
arestyrurj-165	81	9	margin	margin	NOUN
arestyrurj-165	81	10	linear	linear	NOUN
arestyrurj-165	81	11	classifier	classifier	NOUN
arestyrurj-165	81	12	is	be	AUX
arestyrurj-165	81	13	a	a	DET
arestyrurj-165	81	14	binary	binary	ADJ
arestyrurj-165	81	15	classifier	classifier	NOUN
arestyrurj-165	81	16	that	that	PRON
arestyrurj-165	81	17	finds	find	VERB
arestyrurj-165	81	18	a	a	DET
arestyrurj-165	81	19	hyperplane	hyperplane	NOUN
arestyrurj-165	81	20	to	to	PART
arestyrurj-165	81	21	best	well	ADV
arestyrurj-165	81	22	separate	separate	VERB
arestyrurj-165	81	23	the	the	DET
arestyrurj-165	81	24	data	datum	NOUN
arestyrurj-165	81	25	,	,	PUNCT
arestyrurj-165	81	26	while	while	SCONJ
arestyrurj-165	81	27	making	make	VERB
arestyrurj-165	81	28	minimal	minimal	ADJ
arestyrurj-165	81	29	margin	margin	NOUN
arestyrurj-165	81	30	violations.[4	violations.[4	NOUN
arestyrurj-165	81	31	]	]	X
arestyrurj-165	81	32	svm	svm	PROPN
arestyrurj-165	81	33	uses	use	VERB
arestyrurj-165	81	34	a	a	DET
arestyrurj-165	81	35	loss	loss	NOUN
arestyrurj-165	81	36	function	function	NOUN
arestyrurj-165	81	37	called	call	VERB
arestyrurj-165	81	38	the	the	DET
arestyrurj-165	81	39	hinge	hinge	NOUN
arestyrurj-165	81	40	loss	loss	NOUN
arestyrurj-165	81	41	function	function	NOUN
arestyrurj-165	81	42	,	,	PUNCT
arestyrurj-165	81	43	defined	define	VERB
arestyrurj-165	81	44	by	by	ADP
arestyrurj-165	81	45	where	where	SCONJ
arestyrurj-165	81	46	𝑤	𝑤	ADV
arestyrurj-165	81	47	is	be	AUX
arestyrurj-165	81	48	the	the	DET
arestyrurj-165	81	49	coefficients	coefficient	NOUN
arestyrurj-165	81	50	of	of	ADP
arestyrurj-165	81	51	the	the	DET
arestyrurj-165	81	52	separating	separate	VERB
arestyrurj-165	81	53	hyperplane	hyperplane	NOUN
arestyrurj-165	81	54	.	.	PUNCT
arestyrurj-165	82	1	with	with	ADP
arestyrurj-165	82	2	a	a	DET
arestyrurj-165	82	3	penalty	penalty	NOUN
arestyrurj-165	82	4	(	(	PUNCT
arestyrurj-165	82	5	or	or	CCONJ
arestyrurj-165	82	6	regularizer	regularizer	NOUN
arestyrurj-165	82	7	)	)	PUNCT
arestyrurj-165	82	8	,	,	PUNCT
arestyrurj-165	82	9	we	we	PRON
arestyrurj-165	82	10	can	can	AUX
arestyrurj-165	82	11	mathematically	mathematically	ADV
arestyrurj-165	82	12	formulate	formulate	VERB
arestyrurj-165	82	13	svm	svm	NOUN
arestyrurj-165	82	14	as	as	ADP
arestyrurj-165	82	15	the	the	DET
arestyrurj-165	82	16	following	follow	VERB
arestyrurj-165	82	17	erm	erm	PROPN
arestyrurj-165	82	18	problem	problem	NOUN
arestyrurj-165	82	19	:	:	PUNCT
arestyrurj-165	82	20	the	the	DET
arestyrurj-165	82	21	regularization	regularization	NOUN
arestyrurj-165	82	22	term	term	NOUN
arestyrurj-165	82	23	,	,	PUNCT
arestyrurj-165	82	24	λ	λ	PROPN
arestyrurj-165	82	25	,	,	PUNCT
arestyrurj-165	82	26	is	be	AUX
arestyrurj-165	82	27	used	use	VERB
arestyrurj-165	82	28	to	to	PART
arestyrurj-165	82	29	penalize	penalize	VERB
arestyrurj-165	82	30	the	the	DET
arestyrurj-165	82	31	features	feature	NOUN
arestyrurj-165	82	32	,	,	PUNCT
arestyrurj-165	82	33	and	and	CCONJ
arestyrurj-165	82	34	hence	hence	ADV
arestyrurj-165	82	35	weights	weight	NOUN
arestyrurj-165	82	36	,	,	PUNCT
arestyrurj-165	82	37	that	that	PRON
arestyrurj-165	82	38	do	do	AUX
arestyrurj-165	82	39	not	not	PART
arestyrurj-165	82	40	necessarily	necessarily	ADV
arestyrurj-165	82	41	contribute	contribute	VERB
arestyrurj-165	82	42	to	to	ADP
arestyrurj-165	82	43	the	the	DET
arestyrurj-165	82	44	prediction	prediction	NOUN
arestyrurj-165	82	45	outcome	outcome	NOUN
arestyrurj-165	82	46	.	.	PUNCT
arestyrurj-165	83	1	here	here	ADV
arestyrurj-165	83	2	,	,	PUNCT
arestyrurj-165	83	3	we	we	PRON
arestyrurj-165	83	4	are	be	AUX
arestyrurj-165	83	5	considering	consider	VERB
arestyrurj-165	83	6	the	the	DET
arestyrurj-165	83	7	ℓ	ℓ	NOUN
arestyrurj-165	83	8	penalty	penalty	NOUN
arestyrurj-165	83	9	,	,	PUNCT
arestyrurj-165	83	10	but	but	CCONJ
arestyrurj-165	83	11	there	there	PRON
arestyrurj-165	83	12	are	be	VERB
arestyrurj-165	83	13	other	other	ADJ
arestyrurj-165	83	14	regularizers	regularizer	NOUN
arestyrurj-165	83	15	such	such	ADJ
arestyrurj-165	83	16	as	as	ADP
arestyrurj-165	83	17	the	the	DET
arestyrurj-165	83	18	ℓ	ℓ	PROPN
arestyrurj-165	83	19	penalty	penalty	NOUN
arestyrurj-165	83	20	.	.	PUNCT
arestyrurj-165	84	1	we	we	PRON
arestyrurj-165	84	2	use	use	VERB
arestyrurj-165	84	3	these	these	DET
arestyrurj-165	84	4	regularization	regularization	NOUN
arestyrurj-165	84	5	terms	term	NOUN
arestyrurj-165	84	6	in	in	ADP
arestyrurj-165	84	7	our	our	PRON
arestyrurj-165	84	8	loss	loss	NOUN
arestyrurj-165	84	9	function	function	NOUN
arestyrurj-165	84	10	to	to	PART
arestyrurj-165	84	11	estimate	estimate	VERB
arestyrurj-165	84	12	a	a	DET
arestyrurj-165	84	13	more	more	ADV
arestyrurj-165	84	14	accurate	accurate	ADJ
arestyrurj-165	84	15	model	model	NOUN
arestyrurj-165	84	16	.	.	PUNCT
arestyrurj-165	85	1	logistic	logistic	ADJ
arestyrurj-165	85	2	regression	regression	NOUN
arestyrurj-165	85	3	similarly	similarly	ADV
arestyrurj-165	85	4	,	,	PUNCT
arestyrurj-165	85	5	consider	consider	VERB
arestyrurj-165	85	6	a	a	DET
arestyrurj-165	85	7	dataset	dataset	NOUN
arestyrurj-165	85	8	with	with	ADP
arestyrurj-165	85	9	𝑛	𝑛	DET
arestyrurj-165	85	10	samples	sample	NOUN
arestyrurj-165	85	11	,	,	PUNCT
arestyrurj-165	85	12	i.e.	i.e.	X
arestyrurj-165	85	13	{	{	PUNCT
arestyrurj-165	85	14	(	(	PUNCT
arestyrurj-165	85	15	𝑥	𝑥	INTJ
arestyrurj-165	85	16	,	,	PUNCT
arestyrurj-165	85	17	𝑦	𝑦	NOUN
arestyrurj-165	85	18	)	)	PUNCT
arestyrurj-165	85	19	}	}	PUNCT
arestyrurj-165	85	20	,	,	PUNCT
arestyrurj-165	85	21	where	where	SCONJ
arestyrurj-165	85	22	𝑦	𝑦	X
arestyrurj-165	85	23	∈	∈	NOUN
arestyrurj-165	85	24	{	{	PUNCT
arestyrurj-165	85	25	−1,1	−1,1	NOUN
arestyrurj-165	85	26	}	}	PUNCT
arestyrurj-165	85	27	.	.	PUNCT
arestyrurj-165	86	1	the	the	DET
arestyrurj-165	86	2	objective	objective	NOUN
arestyrurj-165	86	3	of	of	ADP
arestyrurj-165	86	4	logistic	logistic	ADJ
arestyrurj-165	86	5	regression	regression	NOUN
arestyrurj-165	86	6	(	(	PUNCT
arestyrurj-165	86	7	logit	logit	PROPN
arestyrurj-165	86	8	)	)	PUNCT
arestyrurj-165	86	9	is	be	AUX
arestyrurj-165	86	10	the	the	DET
arestyrurj-165	86	11	same	same	ADJ
arestyrurj-165	86	12	as	as	ADP
arestyrurj-165	86	13	svm	svm	ADJ
arestyrurj-165	86	14	,	,	PUNCT
arestyrurj-165	86	15	with	with	ADP
arestyrurj-165	86	16	a	a	DET
arestyrurj-165	86	17	different	different	ADJ
arestyrurj-165	86	18	loss	loss	NOUN
arestyrurj-165	86	19	function	function	NOUN
arestyrurj-165	86	20	called	call	VERB
arestyrurj-165	86	21	the	the	DET
arestyrurj-165	86	22	logistic	logistic	ADJ
arestyrurj-165	86	23	loss	loss	NOUN
arestyrurj-165	86	24	function	function	NOUN
arestyrurj-165	86	25	,	,	PUNCT
arestyrurj-165	86	26	defined	define	VERB
arestyrurj-165	86	27	by	by	ADP
arestyrurj-165	86	28	the	the	DET
arestyrurj-165	86	29	logistic	logistic	ADJ
arestyrurj-165	86	30	loss	loss	NOUN
arestyrurj-165	86	31	function	function	NOUN
arestyrurj-165	86	32	takes	take	VERB
arestyrurj-165	86	33	the	the	DET
arestyrurj-165	86	34	form	form	NOUN
arestyrurj-165	86	35	of	of	ADP
arestyrurj-165	86	36	the	the	DET
arestyrurj-165	86	37	sigmoid	sigmoid	NOUN
arestyrurj-165	86	38	function	function	NOUN
arestyrurj-165	86	39	.	.	PUNCT
arestyrurj-165	87	1	with	with	ADP
arestyrurj-165	87	2	a	a	DET
arestyrurj-165	87	3	regularization	regularization	NOUN
arestyrurj-165	87	4	term	term	NOUN
arestyrurj-165	87	5	,	,	PUNCT
arestyrurj-165	87	6	we	we	PRON
arestyrurj-165	87	7	can	can	AUX
arestyrurj-165	87	8	define	define	VERB
arestyrurj-165	87	9	logistic	logistic	ADJ
arestyrurj-165	87	10	regression	regression	NOUN
arestyrurj-165	87	11	as	as	ADP
arestyrurj-165	87	12	the	the	DET
arestyrurj-165	87	13	following	follow	VERB
arestyrurj-165	87	14	erm	erm	PROPN
arestyrurj-165	87	15	problem	problem	NOUN
arestyrurj-165	87	16	:	:	PUNCT
arestyrurj-165	87	17	we	we	PRON
arestyrurj-165	87	18	only	only	ADV
arestyrurj-165	87	19	introduce	introduce	VERB
arestyrurj-165	87	20	the	the	DET
arestyrurj-165	87	21	objective	objective	ADJ
arestyrurj-165	87	22	function	function	NOUN
arestyrurj-165	87	23	of	of	ADP
arestyrurj-165	87	24	these	these	DET
arestyrurj-165	87	25	two	two	NUM
arestyrurj-165	87	26	classifiers	classifier	NOUN
arestyrurj-165	87	27	,	,	PUNCT
arestyrurj-165	87	28	as	as	SCONJ
arestyrurj-165	87	29	we	we	PRON
arestyrurj-165	87	30	will	will	AUX
arestyrurj-165	87	31	construct	construct	VERB
arestyrurj-165	87	32	the	the	DET
arestyrurj-165	87	33	cp	cp	PROPN
arestyrurj-165	87	34	structured	structured	ADJ
arestyrurj-165	87	35	algorithm	algorithm	NOUN
arestyrurj-165	87	36	with	with	ADP
arestyrurj-165	87	37	these	these	DET
arestyrurj-165	87	38	functions	function	NOUN
arestyrurj-165	87	39	in	in	ADP
arestyrurj-165	87	40	the	the	DET
arestyrurj-165	87	41	following	follow	VERB
arestyrurj-165	87	42	section	section	NOUN
arestyrurj-165	87	43	.	.	PUNCT
arestyrurj-165	88	1	note	note	VERB
arestyrurj-165	88	2	that	that	SCONJ
arestyrurj-165	88	3	we	we	PRON
arestyrurj-165	88	4	do	do	AUX
arestyrurj-165	88	5	not	not	PART
arestyrurj-165	88	6	include	include	VERB
arestyrurj-165	88	7	the	the	DET
arestyrurj-165	88	8	bias	bias	NOUN
arestyrurj-165	88	9	term	term	NOUN
arestyrurj-165	88	10	in	in	ADP
arestyrurj-165	88	11	our	our	PRON
arestyrurj-165	88	12	hyperplane	hyperplane	NOUN
arestyrurj-165	88	13	equation	equation	NOUN
arestyrurj-165	88	14	,	,	PUNCT
arestyrurj-165	88	15	as	as	SCONJ
arestyrurj-165	88	16	it	it	PRON
arestyrurj-165	88	17	can	can	AUX
arestyrurj-165	88	18	be	be	AUX
arestyrurj-165	88	19	modeled	model	VERB
arestyrurj-165	88	20	in	in	ADP
arestyrurj-165	88	21	𝑤	𝑤	ADP
arestyrurj-165	88	22	as	as	ADP
arestyrurj-165	88	23	a	a	DET
arestyrurj-165	88	24	column	column	NOUN
arestyrurj-165	88	25	vector	vector	NOUN
arestyrurj-165	88	26	.	.	PROPN
arestyrurj-165	88	27	3	3	NUM
arestyrurj-165	88	28	problem	problem	NOUN
arestyrurj-165	88	29	formulation	formulation	NOUN
arestyrurj-165	88	30	in	in	ADP
arestyrurj-165	88	31	this	this	DET
arestyrurj-165	88	32	section	section	NOUN
arestyrurj-165	88	33	,	,	PUNCT
arestyrurj-165	88	34	we	we	PRON
arestyrurj-165	88	35	propose	propose	VERB
arestyrurj-165	88	36	our	our	PRON
arestyrurj-165	88	37	tensor	tensor	NOUN
arestyrurj-165	88	38	-	-	PUNCT
arestyrurj-165	88	39	based	base	VERB
arestyrurj-165	88	40	classifiers	classifier	NOUN
arestyrurj-165	88	41	in	in	ADP
arestyrurj-165	88	42	the	the	DET
arestyrurj-165	88	43	form	form	NOUN
arestyrurj-165	88	44	of	of	ADP
arestyrurj-165	88	45	an	an	DET
arestyrurj-165	88	46	erm	erm	NOUN
arestyrurj-165	88	47	framework	framework	NOUN
arestyrurj-165	88	48	.	.	PUNCT
arestyrurj-165	89	1	in	in	ADP
arestyrurj-165	89	2	general	general	ADJ
arestyrurj-165	89	3	,	,	PUNCT
arestyrurj-165	89	4	we	we	PRON
arestyrurj-165	89	5	structure	structure	VERB
arestyrurj-165	89	6	our	our	PRON
arestyrurj-165	89	7	linear	linear	ADJ
arestyrurj-165	89	8	predictors	predictor	NOUN
arestyrurj-165	89	9	(	(	PUNCT
arestyrurj-165	89	10	𝑤	𝑤	X
arestyrurj-165	89	11	)	)	PUNCT
arestyrurj-165	89	12	to	to	PART
arestyrurj-165	89	13	admit	admit	VERB
arestyrurj-165	89	14	a	a	DET
arestyrurj-165	89	15	cp	cp	NOUN
arestyrurj-165	89	16	decomposition	decomposition	NOUN
arestyrurj-165	89	17	,	,	PUNCT
arestyrurj-165	89	18	in	in	ADP
arestyrurj-165	89	19	which	which	PRON
arestyrurj-165	89	20	we	we	PRON
arestyrurj-165	89	21	can	can	AUX
arestyrurj-165	89	22	reconstruct	reconstruct	VERB
arestyrurj-165	89	23	to	to	PART
arestyrurj-165	89	24	make	make	VERB
arestyrurj-165	89	25	classifications	classification	NOUN
arestyrurj-165	89	26	.	.	PUNCT
arestyrurj-165	90	1	we	we	PRON
arestyrurj-165	90	2	also	also	ADV
arestyrurj-165	90	3	discuss	discuss	VERB
arestyrurj-165	90	4	the	the	DET
arestyrurj-165	90	5	metrics	metric	NOUN
arestyrurj-165	90	6	that	that	PRON
arestyrurj-165	90	7	we	we	PRON
arestyrurj-165	90	8	will	will	AUX
arestyrurj-165	90	9	be	be	AUX
arestyrurj-165	90	10	investigating	investigate	VERB
arestyrurj-165	90	11	to	to	PART
arestyrurj-165	90	12	evaluate	evaluate	VERB
arestyrurj-165	90	13	the	the	DET
arestyrurj-165	90	14	performance	performance	NOUN
arestyrurj-165	90	15	of	of	ADP
arestyrurj-165	90	16	our	our	PRON
arestyrurj-165	90	17	models	model	NOUN
arestyrurj-165	90	18	.	.	PUNCT
arestyrurj-165	91	1	aresty	aresty	ADJ
arestyrurj-165	91	2	rutgers	rutgers	PROPN
arestyrurj-165	91	3	undergraduate	undergraduate	PROPN
arestyrurj-165	91	4	research	research	PROPN
arestyrurj-165	91	5	journal	journal	PROPN
arestyrurj-165	91	6	,	,	PUNCT
arestyrurj-165	91	7	volume	volume	NOUN
arestyrurj-165	91	8	i	i	PRON
arestyrurj-165	91	9	,	,	PUNCT
arestyrurj-165	91	10	issue	issue	VERB
arestyrurj-165	91	11	iii	iii	NUM
arestyrurj-165	91	12	i.	i.	PROPN
arestyrurj-165	91	13	candecomp	candecomp	PROPN
arestyrurj-165	91	14	/	/	SYM
arestyrurj-165	91	15	parafac	parafac	NOUN
arestyrurj-165	91	16	structured	structure	VERB
arestyrurj-165	91	17	classifiers	classifier	NOUN
arestyrurj-165	91	18	support	support	VERB
arestyrurj-165	91	19	vector	vector	NOUN
arestyrurj-165	91	20	machines	machine	NOUN
arestyrurj-165	91	21	consider	consider	VERB
arestyrurj-165	91	22	a	a	DET
arestyrurj-165	91	23	dataset	dataset	NOUN
arestyrurj-165	91	24	{	{	PUNCT
arestyrurj-165	91	25	(	(	PUNCT
arestyrurj-165	91	26	𝐗𝒊	𝐗𝒊	PROPN
arestyrurj-165	91	27	,	,	PUNCT
arestyrurj-165	91	28	𝑦	𝑦	NOUN
arestyrurj-165	91	29	)	)	PUNCT
arestyrurj-165	91	30	}	}	PUNCT
arestyrurj-165	91	31	,	,	PUNCT
arestyrurj-165	91	32	where	where	SCONJ
arestyrurj-165	91	33	𝐗𝒊	𝐗𝒊	PROPN
arestyrurj-165	91	34	∈	∈	NOUN
arestyrurj-165	91	35	ℝ	ℝ	PROPN
arestyrurj-165	91	36	×	×	NOUN
arestyrurj-165	91	37	…	…	SYM
arestyrurj-165	91	38	×	×	NOUN
arestyrurj-165	91	39	denotes	denote	VERB
arestyrurj-165	91	40	a	a	DET
arestyrurj-165	91	41	tensor	tensor	NOUN
arestyrurj-165	91	42	data	data	NOUN
arestyrurj-165	91	43	sample	sample	NOUN
arestyrurj-165	91	44	with	with	ADP
arestyrurj-165	91	45	𝑦	𝑦	PROPN
arestyrurj-165	91	46	∈	∈	NOUN
arestyrurj-165	91	47	{	{	PUNCT
arestyrurj-165	91	48	−1,1	−1,1	NOUN
arestyrurj-165	91	49	}	}	PUNCT
arestyrurj-165	91	50	.	.	PUNCT
arestyrurj-165	92	1	by	by	ADP
arestyrurj-165	92	2	imposing	impose	VERB
arestyrurj-165	92	3	the	the	DET
arestyrurj-165	92	4	constraints	constraint	NOUN
arestyrurj-165	92	5	from	from	ADP
arestyrurj-165	92	6	(	(	PUNCT
arestyrurj-165	92	7	1	1	X
arestyrurj-165	92	8	)	)	PUNCT
arestyrurj-165	92	9	onto	onto	ADP
arestyrurj-165	92	10	the	the	DET
arestyrurj-165	92	11	predictors	predictor	NOUN
arestyrurj-165	92	12	of	of	ADP
arestyrurj-165	92	13	(	(	PUNCT
arestyrurj-165	92	14	3	3	NUM
arestyrurj-165	92	15	)	)	PUNCT
arestyrurj-165	92	16	,	,	PUNCT
arestyrurj-165	92	17	we	we	PRON
arestyrurj-165	92	18	can	can	AUX
arestyrurj-165	92	19	formulate	formulate	VERB
arestyrurj-165	92	20	the	the	DET
arestyrurj-165	92	21	following	follow	VERB
arestyrurj-165	92	22	optimization	optimization	NOUN
arestyrurj-165	92	23	problem	problem	NOUN
arestyrurj-165	92	24	:	:	PUNCT
arestyrurj-165	92	25	the	the	DET
arestyrurj-165	92	26	traditional	traditional	ADJ
arestyrurj-165	92	27	erm	erm	PROPN
arestyrurj-165	92	28	problem	problem	NOUN
arestyrurj-165	92	29	for	for	ADP
arestyrurj-165	92	30	svm	svm	NOUN
arestyrurj-165	92	31	in	in	ADP
arestyrurj-165	92	32	(	(	PUNCT
arestyrurj-165	92	33	3	3	X
arestyrurj-165	92	34	)	)	PUNCT
arestyrurj-165	92	35	solves	solve	NOUN
arestyrurj-165	92	36	for	for	ADP
arestyrurj-165	92	37	one	one	NUM
arestyrurj-165	92	38	vector	vector	NOUN
arestyrurj-165	92	39	predictor	predictor	NOUN
arestyrurj-165	92	40	of	of	ADP
arestyrurj-165	92	41	dimensions	dimension	NOUN
arestyrurj-165	92	42	𝑤	𝑤	ADP
arestyrurj-165	92	43	∈	∈	PROPN
arestyrurj-165	92	44	ℝ	ℝ	PROPN
arestyrurj-165	92	45	×	×	NOUN
arestyrurj-165	92	46	…	…	SYM
arestyrurj-165	92	47	×	×	NOUN
arestyrurj-165	92	48	.	.	PUNCT
arestyrurj-165	93	1	the	the	DET
arestyrurj-165	93	2	problem	problem	NOUN
arestyrurj-165	93	3	in	in	ADP
arestyrurj-165	93	4	(	(	PUNCT
arestyrurj-165	93	5	5	5	NUM
arestyrurj-165	93	6	)	)	PUNCT
arestyrurj-165	93	7	,	,	PUNCT
arestyrurj-165	93	8	which	which	PRON
arestyrurj-165	93	9	we	we	PRON
arestyrurj-165	93	10	call	call	VERB
arestyrurj-165	93	11	“	"	PUNCT
arestyrurj-165	93	12	cp	cp	PROPN
arestyrurj-165	93	13	-	-	PUNCT
arestyrurj-165	93	14	svm	svm	NOUN
arestyrurj-165	93	15	”	"	PUNCT
arestyrurj-165	93	16	,	,	PUNCT
arestyrurj-165	93	17	solves	solve	NOUN
arestyrurj-165	93	18	for	for	ADP
arestyrurj-165	93	19	𝑁	𝑁	PROPN
arestyrurj-165	93	20	matrix	matrix	NOUN
arestyrurj-165	93	21	-	-	PUNCT
arestyrurj-165	93	22	valued	value	VERB
arestyrurj-165	93	23	predictors	predictor	NOUN
arestyrurj-165	93	24	of	of	ADP
arestyrurj-165	93	25	dimensions	dimension	NOUN
arestyrurj-165	93	26	𝑊𝒊	𝑊𝒊	ADP
arestyrurj-165	93	27	∈	∈	NOUN
arestyrurj-165	93	28	ℝ	ℝ	PROPN
arestyrurj-165	93	29	×	×	NOUN
arestyrurj-165	93	30	,	,	PUNCT
arestyrurj-165	93	31	for	for	ADP
arestyrurj-165	93	32	𝑖	𝑖	PRON
arestyrurj-165	93	33	=	=	SYM
arestyrurj-165	93	34	1	1	NUM
arestyrurj-165	93	35	,	,	PUNCT
arestyrurj-165	93	36	.	.	PUNCT
arestyrurj-165	93	37	.	.	PUNCT
arestyrurj-165	94	1	.	.	PUNCT
arestyrurj-165	95	1	,	,	PUNCT
arestyrurj-165	95	2	𝑁	𝑁	PROPN
arestyrurj-165	95	3	.	.	PUNCT
arestyrurj-165	96	1	as	as	ADP
arestyrurj-165	96	2	a	a	DET
arestyrurj-165	96	3	concrete	concrete	ADJ
arestyrurj-165	96	4	example	example	NOUN
arestyrurj-165	96	5	,	,	PUNCT
arestyrurj-165	96	6	let	let	VERB
arestyrurj-165	96	7	each	each	DET
arestyrurj-165	96	8	tensor	tensor	NOUN
arestyrurj-165	96	9	sample	sample	NOUN
arestyrurj-165	96	10	be	be	AUX
arestyrurj-165	96	11	dimensions	dimension	NOUN
arestyrurj-165	97	1	𝐗𝒊	𝐗𝒊	NOUN
arestyrurj-165	97	2	∈	∈	NOUN
arestyrurj-165	98	1	ℝ	ℝ	PROPN
arestyrurj-165	98	2	×	×	NOUN
arestyrurj-165	98	3	×	×	NOUN
arestyrurj-165	98	4	and	and	CCONJ
arestyrurj-165	98	5	𝑅	𝑅	NOUN
arestyrurj-165	98	6	=	=	NOUN
arestyrurj-165	98	7	3	3	NUM
arestyrurj-165	98	8	.	.	PUNCT
arestyrurj-165	99	1	the	the	DET
arestyrurj-165	99	2	traditional	traditional	ADJ
arestyrurj-165	99	3	problem	problem	NOUN
arestyrurj-165	99	4	would	would	AUX
arestyrurj-165	99	5	solve	solve	VERB
arestyrurj-165	99	6	for	for	ADP
arestyrurj-165	99	7	5	5	NUM
arestyrurj-165	99	8	×	×	NOUN
arestyrurj-165	99	9	5	5	NUM
arestyrurj-165	99	10	×	×	NOUN
arestyrurj-165	99	11	5	5	NUM
arestyrurj-165	99	12	=	=	SYM
arestyrurj-165	99	13	125	125	NUM
arestyrurj-165	99	14	coefficients	coefficient	NOUN
arestyrurj-165	99	15	,	,	PUNCT
arestyrurj-165	99	16	whereas	whereas	SCONJ
arestyrurj-165	99	17	the	the	DET
arestyrurj-165	99	18	structured	structured	ADJ
arestyrurj-165	99	19	problem	problem	NOUN
arestyrurj-165	99	20	would	would	AUX
arestyrurj-165	99	21	solve	solve	VERB
arestyrurj-165	99	22	for	for	ADP
arestyrurj-165	99	23	3	3	NUM
arestyrurj-165	99	24	×	×	NOUN
arestyrurj-165	99	25	(	(	PUNCT
arestyrurj-165	99	26	5	5	NUM
arestyrurj-165	99	27	×	×	NOUN
arestyrurj-165	99	28	3	3	NUM
arestyrurj-165	99	29	)	)	PUNCT
arestyrurj-165	99	30	=	=	NOUN
arestyrurj-165	99	31	45	45	NUM
arestyrurj-165	99	32	coefficients	coefficient	NOUN
arestyrurj-165	99	33	.	.	PUNCT
arestyrurj-165	100	1	as	as	ADP
arestyrurj-165	100	2	the	the	DET
arestyrurj-165	100	3	dimensions	dimension	NOUN
arestyrurj-165	100	4	increase	increase	NOUN
arestyrurj-165	100	5	,	,	PUNCT
arestyrurj-165	100	6	the	the	DET
arestyrurj-165	100	7	structured	structured	ADJ
arestyrurj-165	100	8	problem	problem	NOUN
arestyrurj-165	100	9	substantially	substantially	ADV
arestyrurj-165	100	10	reduces	reduce	VERB
arestyrurj-165	100	11	the	the	DET
arestyrurj-165	100	12	number	number	NOUN
arestyrurj-165	100	13	of	of	ADP
arestyrurj-165	100	14	parameters	parameter	NOUN
arestyrurj-165	100	15	/	/	SYM
arestyrurj-165	100	16	coefficients	coefficient	NOUN
arestyrurj-165	100	17	to	to	PART
arestyrurj-165	100	18	be	be	AUX
arestyrurj-165	100	19	estimated	estimate	VERB
arestyrurj-165	100	20	.	.	PUNCT
arestyrurj-165	101	1	logistic	logistic	ADJ
arestyrurj-165	101	2	regression	regression	NOUN
arestyrurj-165	101	3	similarly	similarly	ADV
arestyrurj-165	101	4	,	,	PUNCT
arestyrurj-165	101	5	consider	consider	VERB
arestyrurj-165	101	6	a	a	DET
arestyrurj-165	101	7	dataset	dataset	NOUN
arestyrurj-165	101	8	{	{	PUNCT
arestyrurj-165	101	9	(	(	PUNCT
arestyrurj-165	101	10	𝐗𝒊	𝐗𝒊	PROPN
arestyrurj-165	101	11	,	,	PUNCT
arestyrurj-165	101	12	𝑦	𝑦	NOUN
arestyrurj-165	101	13	)	)	PUNCT
arestyrurj-165	101	14	}	}	PUNCT
arestyrurj-165	101	15	,	,	PUNCT
arestyrurj-165	101	16	where	where	SCONJ
arestyrurj-165	101	17	𝐗𝒊	𝐗𝒊	PROPN
arestyrurj-165	101	18	∈	∈	NOUN
arestyrurj-165	101	19	ℝ	ℝ	PROPN
arestyrurj-165	101	20	×	×	NOUN
arestyrurj-165	101	21	…	…	SYM
arestyrurj-165	101	22	×	×	NOUN
arestyrurj-165	101	23	denotes	denote	VERB
arestyrurj-165	101	24	a	a	DET
arestyrurj-165	101	25	tensor	tensor	NOUN
arestyrurj-165	101	26	data	data	NOUN
arestyrurj-165	101	27	sample	sample	NOUN
arestyrurj-165	101	28	with	with	ADP
arestyrurj-165	101	29	𝑦	𝑦	PROPN
arestyrurj-165	101	30	∈	∈	NOUN
arestyrurj-165	101	31	{	{	PUNCT
arestyrurj-165	101	32	−1,1	−1,1	NOUN
arestyrurj-165	101	33	}	}	PUNCT
arestyrurj-165	101	34	.	.	PUNCT
arestyrurj-165	102	1	by	by	ADP
arestyrurj-165	102	2	imposing	impose	VERB
arestyrurj-165	102	3	the	the	DET
arestyrurj-165	102	4	constraints	constraint	NOUN
arestyrurj-165	102	5	from	from	ADP
arestyrurj-165	102	6	(	(	PUNCT
arestyrurj-165	102	7	1	1	X
arestyrurj-165	102	8	)	)	PUNCT
arestyrurj-165	102	9	onto	onto	ADP
arestyrurj-165	102	10	the	the	DET
arestyrurj-165	102	11	predictors	predictor	NOUN
arestyrurj-165	102	12	of	of	ADP
arestyrurj-165	102	13	(	(	PUNCT
arestyrurj-165	102	14	4	4	NUM
arestyrurj-165	102	15	)	)	PUNCT
arestyrurj-165	102	16	,	,	PUNCT
arestyrurj-165	102	17	we	we	PRON
arestyrurj-165	102	18	can	can	AUX
arestyrurj-165	102	19	solve	solve	VERB
arestyrurj-165	102	20	the	the	DET
arestyrurj-165	102	21	following	follow	VERB
arestyrurj-165	102	22	erm	erm	PROPN
arestyrurj-165	102	23	problem	problem	NOUN
arestyrurj-165	102	24	:	:	PUNCT
arestyrurj-165	102	25	this	this	DET
arestyrurj-165	102	26	new	new	ADJ
arestyrurj-165	102	27	framework	framework	NOUN
arestyrurj-165	102	28	,	,	PUNCT
arestyrurj-165	102	29	which	which	PRON
arestyrurj-165	102	30	we	we	PRON
arestyrurj-165	102	31	call	call	VERB
arestyrurj-165	102	32	“	"	PUNCT
arestyrurj-165	102	33	cplogit	cplogit	PROPN
arestyrurj-165	102	34	”	"	PUNCT
arestyrurj-165	102	35	,	,	PUNCT
arestyrurj-165	102	36	solves	solve	NOUN
arestyrurj-165	102	37	for	for	ADP
arestyrurj-165	102	38	fewer	few	ADJ
arestyrurj-165	102	39	parameters	parameter	NOUN
arestyrurj-165	102	40	,	,	PUNCT
arestyrurj-165	102	41	similar	similar	ADJ
arestyrurj-165	102	42	to	to	PART
arestyrurj-165	102	43	cpsvm	cpsvm	VERB
arestyrurj-165	102	44	.	.	PUNCT
arestyrurj-165	103	1	in	in	ADP
arestyrurj-165	103	2	practice	practice	NOUN
arestyrurj-165	103	3	,	,	PUNCT
arestyrurj-165	103	4	we	we	PRON
arestyrurj-165	103	5	solve	solve	VERB
arestyrurj-165	103	6	for	for	ADP
arestyrurj-165	103	7	the	the	DET
arestyrurj-165	103	8	weights	weight	NOUN
arestyrurj-165	103	9	using	use	VERB
arestyrurj-165	103	10	numerical	numerical	ADJ
arestyrurj-165	103	11	optimization	optimization	NOUN
arestyrurj-165	103	12	methods	method	NOUN
arestyrurj-165	103	13	such	such	ADJ
arestyrurj-165	103	14	as	as	ADP
arestyrurj-165	103	15	gradient	gradient	ADJ
arestyrurj-165	103	16	descent	descent	NOUN
arestyrurj-165	103	17	.	.	PUNCT
arestyrurj-165	104	1	however	however	ADV
arestyrurj-165	104	2	,	,	PUNCT
arestyrurj-165	104	3	solving	solve	VERB
arestyrurj-165	104	4	for	for	ADP
arestyrurj-165	104	5	the	the	DET
arestyrurj-165	104	6	weights	weight	NOUN
arestyrurj-165	104	7	in	in	ADP
arestyrurj-165	104	8	this	this	DET
arestyrurj-165	104	9	new	new	ADJ
arestyrurj-165	104	10	cp	cp	ADJ
arestyrurj-165	104	11	-	-	PUNCT
arestyrurj-165	104	12	structured	structured	ADJ
arestyrurj-165	104	13	paradigm	paradigm	NOUN
arestyrurj-165	104	14	is	be	AUX
arestyrurj-165	104	15	a	a	DET
arestyrurj-165	104	16	non	non	ADJ
arestyrurj-165	104	17	-	-	ADJ
arestyrurj-165	104	18	trivial	trivial	ADJ
arestyrurj-165	104	19	task	task	NOUN
arestyrurj-165	104	20	.	.	PUNCT
arestyrurj-165	105	1	in	in	ADP
arestyrurj-165	105	2	order	order	NOUN
arestyrurj-165	105	3	to	to	PART
arestyrurj-165	105	4	solve	solve	VERB
arestyrurj-165	105	5	for	for	ADP
arestyrurj-165	105	6	the	the	DET
arestyrurj-165	105	7	coefficients	coefficient	NOUN
arestyrurj-165	105	8	in	in	ADP
arestyrurj-165	105	9	(	(	PUNCT
arestyrurj-165	105	10	5	5	NUM
arestyrurj-165	105	11	)	)	PUNCT
arestyrurj-165	105	12	and	and	CCONJ
arestyrurj-165	105	13	(	(	PUNCT
arestyrurj-165	105	14	6	6	NUM
arestyrurj-165	105	15	)	)	PUNCT
arestyrurj-165	105	16	,	,	PUNCT
arestyrurj-165	105	17	we	we	PRON
arestyrurj-165	105	18	adopt	adopt	VERB
arestyrurj-165	105	19	an	an	DET
arestyrurj-165	105	20	alternating	alternate	VERB
arestyrurj-165	105	21	minimization	minimization	NOUN
arestyrurj-165	105	22	algorithm	algorithm	NOUN
arestyrurj-165	105	23	similar	similar	ADJ
arestyrurj-165	105	24	to	to	ADP
arestyrurj-165	105	25	the	the	DET
arestyrurj-165	105	26	block	block	NOUN
arestyrurj-165	105	27	relaxation	relaxation	NOUN
arestyrurj-165	105	28	algorithm	algorithm	NOUN
arestyrurj-165	105	29	proposed	propose	VERB
arestyrurj-165	105	30	in	in	ADP
arestyrurj-165	105	31	zhou	zhou	PROPN
arestyrurj-165	105	32	et	et	PROPN
arestyrurj-165	105	33	al.[21	al.[21	PROPN
arestyrurj-165	105	34	]	]	PUNCT
arestyrurj-165	105	35	at	at	ADP
arestyrurj-165	105	36	each	each	DET
arestyrurj-165	105	37	iteration	iteration	NOUN
arestyrurj-165	105	38	,	,	PUNCT
arestyrurj-165	105	39	we	we	PRON
arestyrurj-165	105	40	update	update	VERB
arestyrurj-165	105	41	block	block	NOUN
arestyrurj-165	105	42	𝑊𝒊	𝑊𝒊	PROPN
arestyrurj-165	105	43	,	,	PUNCT
arestyrurj-165	105	44	while	while	SCONJ
arestyrurj-165	105	45	keeping	keep	VERB
arestyrurj-165	105	46	the	the	DET
arestyrurj-165	105	47	rest	rest	NOUN
arestyrurj-165	105	48	of	of	ADP
arestyrurj-165	105	49	the	the	DET
arestyrurj-165	105	50	blocks	block	NOUN
arestyrurj-165	105	51	fixed	fix	VERB
arestyrurj-165	105	52	.	.	PUNCT
arestyrurj-165	106	1	to	to	PART
arestyrurj-165	106	2	see	see	VERB
arestyrurj-165	106	3	this	this	PRON
arestyrurj-165	106	4	,	,	PUNCT
arestyrurj-165	106	5	when	when	SCONJ
arestyrurj-165	106	6	updating	update	VERB
arestyrurj-165	106	7	𝑊𝒊	𝑊𝒊	PROPN
arestyrurj-165	106	8	∈	∈	PROPN
arestyrurj-165	106	9	ℝ	ℝ	PROPN
arestyrurj-165	106	10	×	×	NOUN
arestyrurj-165	106	11	,	,	PUNCT
arestyrurj-165	106	12	we	we	PRON
arestyrurj-165	106	13	can	can	AUX
arestyrurj-165	106	14	rewrite	rewrite	VERB
arestyrurj-165	106	15	the	the	DET
arestyrurj-165	106	16	inner	inner	ADJ
arestyrurj-165	106	17	product	product	NOUN
arestyrurj-165	106	18	in	in	ADP
arestyrurj-165	106	19	(	(	PUNCT
arestyrurj-165	106	20	5	5	NUM
arestyrurj-165	106	21	)	)	PUNCT
arestyrurj-165	106	22	and	and	CCONJ
arestyrurj-165	106	23	(	(	PUNCT
arestyrurj-165	106	24	6	6	NUM
arestyrurj-165	106	25	)	)	PUNCT
arestyrurj-165	106	26	with	with	ADP
arestyrurj-165	106	27	the	the	DET
arestyrurj-165	106	28	properties	property	NOUN
arestyrurj-165	106	29	mentioned	mention	VERB
arestyrurj-165	106	30	in	in	ADP
arestyrurj-165	106	31	(	(	PUNCT
arestyrurj-165	106	32	2	2	NUM
arestyrurj-165	106	33	):	):	PUNCT
arestyrurj-165	106	34	this	this	DET
arestyrurj-165	106	35	alternating	alternate	VERB
arestyrurj-165	106	36	minimization	minimization	NOUN
arestyrurj-165	106	37	algorithm	algorithm	NOUN
arestyrurj-165	106	38	is	be	AUX
arestyrurj-165	106	39	summarized	summarize	VERB
arestyrurj-165	106	40	in	in	ADP
arestyrurj-165	106	41	algorithm	algorithm	NOUN
arestyrurj-165	106	42	1	1	NUM
arestyrurj-165	106	43	,	,	PUNCT
arestyrurj-165	106	44	in	in	ADP
arestyrurj-165	106	45	which	which	PRON
arestyrurj-165	106	46	ℓ	ℓ	SYM
arestyrurj-165	106	47	(	(	PUNCT
arestyrurj-165	106	48	·	·	PUNCT
arestyrurj-165	106	49	)	)	PUNCT
arestyrurj-165	106	50	represents	represent	VERB
arestyrurj-165	106	51	the	the	DET
arestyrurj-165	106	52	erm	erm	PROPN
arestyrurj-165	106	53	problem	problem	NOUN
arestyrurj-165	106	54	to	to	PART
arestyrurj-165	106	55	be	be	AUX
arestyrurj-165	106	56	minimized	minimize	VERB
arestyrurj-165	106	57	,	,	PUNCT
arestyrurj-165	106	58	𝜃	𝜃	PRON
arestyrurj-165	106	59	represents	represent	VERB
arestyrurj-165	106	60	a	a	DET
arestyrurj-165	106	61	collection	collection	NOUN
arestyrurj-165	106	62	of	of	ADP
arestyrurj-165	106	63	all	all	DET
arestyrurj-165	106	64	the	the	DET
arestyrurj-165	106	65	parameters	parameter	NOUN
arestyrurj-165	106	66	,	,	PUNCT
arestyrurj-165	106	67	and	and	CCONJ
arestyrurj-165	106	68	λ	λ	PROPN
arestyrurj-165	106	69	is	be	AUX
arestyrurj-165	106	70	the	the	DET
arestyrurj-165	106	71	regularization	regularization	NOUN
arestyrurj-165	106	72	parameter	parameter	NOUN
arestyrurj-165	106	73	.	.	PUNCT
arestyrurj-165	107	1	the	the	DET
arestyrurj-165	107	2	parameter	parameter	PROPN
arestyrurj-165	107	3	λ	λ	PROPN
arestyrurj-165	107	4	was	be	AUX
arestyrurj-165	107	5	tuned	tune	VERB
arestyrurj-165	107	6	by	by	ADP
arestyrurj-165	107	7	hand	hand	NOUN
arestyrurj-165	107	8	,	,	PUNCT
arestyrurj-165	107	9	but	but	CCONJ
arestyrurj-165	107	10	can	can	AUX
arestyrurj-165	107	11	also	also	ADV
arestyrurj-165	107	12	be	be	AUX
arestyrurj-165	107	13	determined	determine	VERB
arestyrurj-165	107	14	through	through	ADP
arestyrurj-165	107	15	cross	cross	NOUN
arestyrurj-165	107	16	validation	validation	NOUN
arestyrurj-165	107	17	.	.	PUNCT
arestyrurj-165	108	1	to	to	PART
arestyrurj-165	108	2	understand	understand	VERB
arestyrurj-165	108	3	the	the	DET
arestyrurj-165	108	4	cp	cp	PROPN
arestyrurj-165	108	5	structured	structure	VERB
arestyrurj-165	108	6	algorithm	algorithm	NOUN
arestyrurj-165	108	7	,	,	PUNCT
arestyrurj-165	108	8	consider	consider	VERB
arestyrurj-165	108	9	the	the	DET
arestyrurj-165	108	10	loss	loss	NOUN
arestyrurj-165	108	11	function	function	NOUN
arestyrurj-165	108	12	in	in	ADP
arestyrurj-165	108	13	(	(	PUNCT
arestyrurj-165	108	14	5	5	NUM
arestyrurj-165	108	15	)	)	PUNCT
arestyrurj-165	108	16	with	with	ADP
arestyrurj-165	108	17	𝑁	𝑁	PROPN
arestyrurj-165	108	18	=	=	SYM
arestyrurj-165	108	19	3	3	NUM
arestyrurj-165	108	20	.	.	PUNCT
arestyrurj-165	109	1	when	when	SCONJ
arestyrurj-165	109	2	updating	update	VERB
arestyrurj-165	109	3	𝑊𝟐	𝑊𝟐	PROPN
arestyrurj-165	109	4	,	,	PUNCT
arestyrurj-165	109	5	we	we	PRON
arestyrurj-165	109	6	rewrite	rewrite	VERB
arestyrurj-165	109	7	the	the	DET
arestyrurj-165	109	8	inner	inner	ADJ
arestyrurj-165	109	9	product	product	NOUN
arestyrurj-165	109	10	〈	〈	PROPN
arestyrurj-165	109	11	∑	∑	PROPN
arestyrurj-165	109	12	𝑊	𝑊	PROPN
arestyrurj-165	109	13	(	(	PUNCT
arestyrurj-165	109	14	)	)	PUNCT
arestyrurj-165	109	15	○	○	PROPN
arestyrurj-165	109	16	𝑊	𝑊	PROPN
arestyrurj-165	109	17	(	(	PUNCT
arestyrurj-165	109	18	)	)	PUNCT
arestyrurj-165	109	19	○	○	PROPN
arestyrurj-165	109	20	𝑊	𝑊	PROPN
arestyrurj-165	109	21	(	(	PUNCT
arestyrurj-165	109	22	)	)	PUNCT
arestyrurj-165	109	23	,	,	PUNCT
arestyrurj-165	109	24	𝐗𝒊	𝐗𝒊	VERB
arestyrurj-165	109	25	〉	〉	NOUN
arestyrurj-165	109	26	as	as	ADP
arestyrurj-165	109	27	〈	〈	NOUN
arestyrurj-165	109	28	𝑊	𝑊	PROPN
arestyrurj-165	109	29	,	,	PUNCT
arestyrurj-165	109	30	𝐗	𝐗	PROPN
arestyrurj-165	109	31	(	(	PUNCT
arestyrurj-165	109	32	)	)	PUNCT
arestyrurj-165	109	33	(	(	PUNCT
arestyrurj-165	109	34	𝑊	𝑊	PROPN
arestyrurj-165	109	35	⊙	⊙	NOUN
arestyrurj-165	109	36	𝑊	𝑊	PROPN
arestyrurj-165	109	37	)	)	PUNCT
arestyrurj-165	109	38	〉	〉	NOUN
arestyrurj-165	109	39	.	.	PUNCT
arestyrurj-165	110	1	note	note	VERB
arestyrurj-165	110	2	that	that	SCONJ
arestyrurj-165	110	3	this	this	DET
arestyrurj-165	110	4	equation	equation	NOUN
arestyrurj-165	110	5	follows	follow	VERB
arestyrurj-165	110	6	from	from	ADP
arestyrurj-165	110	7	the	the	DET
arestyrurj-165	110	8	property	property	NOUN
arestyrurj-165	110	9	of	of	ADP
arestyrurj-165	110	10	tensor	tensor	NOUN
arestyrurj-165	110	11	algebra	algebra	NOUN
arestyrurj-165	110	12	as	as	SCONJ
arestyrurj-165	110	13	shown	show	VERB
arestyrurj-165	110	14	in	in	ADP
arestyrurj-165	110	15	(	(	PUNCT
arestyrurj-165	110	16	2	2	NUM
arestyrurj-165	110	17	)	)	PUNCT
arestyrurj-165	110	18	.	.	PUNCT
arestyrurj-165	111	1	we	we	PRON
arestyrurj-165	111	2	perform	perform	VERB
arestyrurj-165	111	3	this	this	DET
arestyrurj-165	111	4	algorithm	algorithm	NOUN
arestyrurj-165	111	5	for	for	ADP
arestyrurj-165	111	6	all	all	DET
arestyrurj-165	111	7	the	the	DET
arestyrurj-165	111	8	factor	factor	NOUN
arestyrurj-165	111	9	matrices	matrix	NOUN
arestyrurj-165	111	10	until	until	SCONJ
arestyrurj-165	111	11	the	the	DET
arestyrurj-165	111	12	stopping	stopping	NOUN
arestyrurj-165	111	13	criteria	criterion	NOUN
arestyrurj-165	111	14	is	be	AUX
arestyrurj-165	111	15	met	meet	VERB
arestyrurj-165	111	16	.	.	PUNCT
arestyrurj-165	112	1	aresty	aresty	PROPN
arestyrurj-165	112	2	rutgers	rutgers	PROPN
arestyrurj-165	112	3	undergraduate	undergraduate	PROPN
arestyrurj-165	112	4	research	research	PROPN
arestyrurj-165	112	5	journal	journal	PROPN
arestyrurj-165	112	6	,	,	PUNCT
arestyrurj-165	112	7	volume	volume	NOUN
arestyrurj-165	112	8	i	i	PRON
arestyrurj-165	112	9	,	,	PUNCT
arestyrurj-165	112	10	issue	issue	VERB
arestyrurj-165	112	11	iii	iii	NUM
arestyrurj-165	112	12	the	the	DET
arestyrurj-165	112	13	alternating	alternate	VERB
arestyrurj-165	112	14	minimization	minimization	NOUN
arestyrurj-165	112	15	algorithm	algorithm	NOUN
arestyrurj-165	112	16	is	be	AUX
arestyrurj-165	112	17	useful	useful	ADJ
arestyrurj-165	112	18	for	for	ADP
arestyrurj-165	112	19	several	several	ADJ
arestyrurj-165	112	20	reasons	reason	NOUN
arestyrurj-165	112	21	.	.	PUNCT
arestyrurj-165	113	1	first	first	ADV
arestyrurj-165	113	2	,	,	PUNCT
arestyrurj-165	113	3	in	in	ADP
arestyrurj-165	113	4	practice	practice	NOUN
arestyrurj-165	113	5	,	,	PUNCT
arestyrurj-165	113	6	this	this	DET
arestyrurj-165	113	7	algorithm	algorithm	NOUN
arestyrurj-165	113	8	almost	almost	ADV
arestyrurj-165	113	9	always	always	ADV
arestyrurj-165	113	10	converges	converge	VERB
arestyrurj-165	113	11	to	to	ADP
arestyrurj-165	113	12	at	at	ADP
arestyrurj-165	113	13	least	least	ADJ
arestyrurj-165	113	14	a	a	DET
arestyrurj-165	113	15	local	local	ADJ
arestyrurj-165	113	16	minimum.[1,20,21	minimum.[1,20,21	NOUN
arestyrurj-165	113	17	]	]	PUNCT
arestyrurj-165	113	18	to	to	PART
arestyrurj-165	113	19	find	find	VERB
arestyrurj-165	113	20	the	the	DET
arestyrurj-165	113	21	best	good	ADJ
arestyrurj-165	113	22	solution	solution	NOUN
arestyrurj-165	113	23	,	,	PUNCT
arestyrurj-165	113	24	the	the	DET
arestyrurj-165	113	25	algorithm	algorithm	NOUN
arestyrurj-165	113	26	can	can	AUX
arestyrurj-165	113	27	be	be	AUX
arestyrurj-165	113	28	ran	run	VERB
arestyrurj-165	113	29	several	several	ADJ
arestyrurj-165	113	30	times	time	NOUN
arestyrurj-165	113	31	with	with	ADP
arestyrurj-165	113	32	different	different	ADJ
arestyrurj-165	113	33	initial	initial	ADJ
arestyrurj-165	113	34	factor	factor	NOUN
arestyrurj-165	113	35	matrices	matrix	NOUN
arestyrurj-165	113	36	.	.	PUNCT
arestyrurj-165	114	1	second	second	ADJ
arestyrurj-165	114	2	,	,	PUNCT
arestyrurj-165	114	3	the	the	DET
arestyrurj-165	114	4	low	low	ADJ
arestyrurj-165	114	5	rank	rank	NOUN
arestyrurj-165	114	6	optimization	optimization	NOUN
arestyrurj-165	114	7	problem	problem	NOUN
arestyrurj-165	114	8	over	over	ADP
arestyrurj-165	114	9	the	the	DET
arestyrurj-165	114	10	factor	factor	NOUN
arestyrurj-165	114	11	matrices	matrix	NOUN
arestyrurj-165	114	12	is	be	AUX
arestyrurj-165	114	13	non	non	ADJ
arestyrurj-165	114	14	-	-	NOUN
arestyrurj-165	114	15	convex.[2	convex.[2	NOUN
arestyrurj-165	114	16	]	]	PUNCT
arestyrurj-165	114	17	thus	thus	ADV
arestyrurj-165	114	18	,	,	PUNCT
arestyrurj-165	114	19	this	this	DET
arestyrurj-165	114	20	problem	problem	NOUN
arestyrurj-165	114	21	becomes	become	VERB
arestyrurj-165	114	22	difficult	difficult	ADJ
arestyrurj-165	114	23	to	to	PART
arestyrurj-165	114	24	solve	solve	VERB
arestyrurj-165	114	25	using	use	VERB
arestyrurj-165	114	26	common	common	ADJ
arestyrurj-165	114	27	unconstrained	unconstrained	ADJ
arestyrurj-165	114	28	solvers	solver	NOUN
arestyrurj-165	114	29	,	,	PUNCT
arestyrurj-165	114	30	such	such	ADJ
arestyrurj-165	114	31	as	as	ADP
arestyrurj-165	114	32	gradient	gradient	ADJ
arestyrurj-165	114	33	descent	descent	NOUN
arestyrurj-165	114	34	.	.	PUNCT
arestyrurj-165	115	1	in	in	ADP
arestyrurj-165	115	2	literature	literature	NOUN
arestyrurj-165	115	3	,	,	PUNCT
arestyrurj-165	115	4	there	there	PRON
arestyrurj-165	115	5	are	be	VERB
arestyrurj-165	115	6	two	two	NUM
arestyrurj-165	115	7	ways	way	NOUN
arestyrurj-165	115	8	to	to	PART
arestyrurj-165	115	9	handle	handle	VERB
arestyrurj-165	115	10	the	the	DET
arestyrurj-165	115	11	non	non	NOUN
arestyrurj-165	115	12	-	-	NOUN
arestyrurj-165	115	13	convexity	convexity	NOUN
arestyrurj-165	115	14	of	of	ADP
arestyrurj-165	115	15	this	this	DET
arestyrurj-165	115	16	optimization	optimization	NOUN
arestyrurj-165	115	17	problem	problem	NOUN
arestyrurj-165	115	18	.	.	PUNCT
arestyrurj-165	116	1	one	one	NUM
arestyrurj-165	116	2	way	way	NOUN
arestyrurj-165	116	3	is	be	AUX
arestyrurj-165	116	4	to	to	PART
arestyrurj-165	116	5	relax	relax	VERB
arestyrurj-165	116	6	the	the	DET
arestyrurj-165	116	7	rank	rank	NOUN
arestyrurj-165	116	8	constraint	constraint	NOUN
arestyrurj-165	116	9	by	by	ADP
arestyrurj-165	116	10	adding	add	VERB
arestyrurj-165	116	11	a	a	DET
arestyrurj-165	116	12	convex	convex	ADJ
arestyrurj-165	116	13	regularization	regularization	NOUN
arestyrurj-165	116	14	term	term	NOUN
arestyrurj-165	116	15	that	that	PRON
arestyrurj-165	116	16	induces	induce	VERB
arestyrurj-165	116	17	low	low	ADJ
arestyrurj-165	116	18	rank	rank	NOUN
arestyrurj-165	116	19	(	(	PUNCT
arestyrurj-165	116	20	e.g.	e.g.	ADV
arestyrurj-165	116	21	trace	trace	NOUN
arestyrurj-165	116	22	norm	norm	NOUN
arestyrurj-165	116	23	,	,	PUNCT
arestyrurj-165	116	24	nuclear	nuclear	ADJ
arestyrurj-165	116	25	norm).[16,19	norm).[16,19	NOUN
arestyrurj-165	116	26	]	]	PUNCT
arestyrurj-165	116	27	the	the	DET
arestyrurj-165	116	28	other	other	ADJ
arestyrurj-165	116	29	solution	solution	NOUN
arestyrurj-165	116	30	is	be	AUX
arestyrurj-165	116	31	to	to	PART
arestyrurj-165	116	32	employ	employ	VERB
arestyrurj-165	116	33	this	this	DET
arestyrurj-165	116	34	alternating	alternate	VERB
arestyrurj-165	116	35	minimization	minimization	NOUN
arestyrurj-165	116	36	algorithm	algorithm	NOUN
arestyrurj-165	116	37	,	,	PUNCT
arestyrurj-165	116	38	as	as	ADP
arestyrurj-165	116	39	the	the	DET
arestyrurj-165	116	40	optimization	optimization	NOUN
arestyrurj-165	116	41	over	over	ADP
arestyrurj-165	116	42	one	one	NUM
arestyrurj-165	116	43	matrix	matrix	NOUN
arestyrurj-165	116	44	,	,	PUNCT
arestyrurj-165	116	45	while	while	SCONJ
arestyrurj-165	116	46	holding	hold	VERB
arestyrurj-165	116	47	the	the	DET
arestyrurj-165	116	48	others	other	NOUN
arestyrurj-165	116	49	fixed	fix	VERB
arestyrurj-165	116	50	is	be	AUX
arestyrurj-165	116	51	convex	convex	ADJ
arestyrurj-165	116	52	.	.	PUNCT
arestyrurj-165	117	1	we	we	PRON
arestyrurj-165	117	2	chose	choose	VERB
arestyrurj-165	117	3	to	to	PART
arestyrurj-165	117	4	explore	explore	VERB
arestyrurj-165	117	5	this	this	DET
arestyrurj-165	117	6	procedure	procedure	NOUN
arestyrurj-165	117	7	following	follow	VERB
arestyrurj-165	117	8	zhou	zhou	PROPN
arestyrurj-165	117	9	et	et	PROPN
arestyrurj-165	117	10	al	al	PROPN
arestyrurj-165	117	11	.	.	PROPN
arestyrurj-165	117	12	,[21	,[21	PROPN
arestyrurj-165	117	13	]	]	PUNCT
arestyrurj-165	117	14	as	as	SCONJ
arestyrurj-165	117	15	the	the	DET
arestyrurj-165	117	16	algorithm	algorithm	NOUN
arestyrurj-165	117	17	is	be	AUX
arestyrurj-165	117	18	straightforward	straightforward	ADJ
arestyrurj-165	117	19	to	to	PART
arestyrurj-165	117	20	implement	implement	VERB
arestyrurj-165	117	21	using	use	VERB
arestyrurj-165	117	22	statistical	statistical	ADJ
arestyrurj-165	117	23	software	software	NOUN
arestyrurj-165	117	24	such	such	ADJ
arestyrurj-165	117	25	as	as	ADP
arestyrurj-165	117	26	matlab	matlab	PROPN
arestyrurj-165	117	27	or	or	CCONJ
arestyrurj-165	117	28	python	python	PROPN
arestyrurj-165	117	29	.	.	PUNCT
arestyrurj-165	118	1	ii	ii	PROPN
arestyrurj-165	118	2	.	.	PUNCT
arestyrurj-165	119	1	performance	performance	NOUN
arestyrurj-165	119	2	metrics	metric	NOUN
arestyrurj-165	119	3	we	we	PRON
arestyrurj-165	119	4	evaluate	evaluate	VERB
arestyrurj-165	119	5	the	the	DET
arestyrurj-165	119	6	performance	performance	NOUN
arestyrurj-165	119	7	of	of	ADP
arestyrurj-165	119	8	our	our	PRON
arestyrurj-165	119	9	models	model	NOUN
arestyrurj-165	119	10	using	use	VERB
arestyrurj-165	119	11	several	several	ADJ
arestyrurj-165	119	12	measures	measure	NOUN
arestyrurj-165	119	13	with	with	ADP
arestyrurj-165	119	14	different	different	ADJ
arestyrurj-165	119	15	sample	sample	NOUN
arestyrurj-165	119	16	sizes	size	NOUN
arestyrurj-165	119	17	.	.	PUNCT
arestyrurj-165	120	1	the	the	DET
arestyrurj-165	120	2	following	follow	VERB
arestyrurj-165	120	3	four	four	NUM
arestyrurj-165	120	4	metrics	metric	NOUN
arestyrurj-165	120	5	help	help	NOUN
arestyrurj-165	120	6	determine	determine	VERB
arestyrurj-165	120	7	the	the	DET
arestyrurj-165	120	8	measure	measure	NOUN
arestyrurj-165	120	9	of	of	ADP
arestyrurj-165	120	10	“	"	PUNCT
arestyrurj-165	120	11	closeness	closeness	NOUN
arestyrurj-165	120	12	”	"	PUNCT
arestyrurj-165	120	13	between	between	ADP
arestyrurj-165	120	14	the	the	DET
arestyrurj-165	120	15	true	true	ADJ
arestyrurj-165	120	16	and	and	CCONJ
arestyrurj-165	120	17	estimated	estimated	ADJ
arestyrurj-165	120	18	predictors	predictor	NOUN
arestyrurj-165	120	19	.	.	PUNCT
arestyrurj-165	121	1	1	1	X
arestyrurj-165	121	2	.	.	X
arestyrurj-165	121	3	the	the	DET
arestyrurj-165	121	4	mean	mean	ADJ
arestyrurj-165	121	5	squared	square	VERB
arestyrurj-165	121	6	error	error	NOUN
arestyrurj-165	121	7	(	(	PUNCT
arestyrurj-165	121	8	mse	mse	NOUN
arestyrurj-165	121	9	)	)	PUNCT
arestyrurj-165	121	10	for	for	ADP
arestyrurj-165	121	11	𝑛	𝑛	DET
arestyrurj-165	121	12	data	data	NOUN
arestyrurj-165	121	13	samples	sample	NOUN
arestyrurj-165	121	14	and	and	CCONJ
arestyrurj-165	121	15	true	true	ADJ
arestyrurj-165	121	16	predictor	predictor	NOUN
arestyrurj-165	121	17	𝑊	𝑊	PROPN
arestyrurj-165	121	18	is	be	AUX
arestyrurj-165	121	19	computed	compute	VERB
arestyrurj-165	121	20	as	as	ADP
arestyrurj-165	121	21	where	where	SCONJ
arestyrurj-165	121	22	𝑊	𝑊	PROPN
arestyrurj-165	121	23	is	be	AUX
arestyrurj-165	121	24	the	the	DET
arestyrurj-165	121	25	estimated	estimate	VERB
arestyrurj-165	121	26	predictor	predictor	NOUN
arestyrurj-165	121	27	from	from	ADP
arestyrurj-165	121	28	solving	solve	VERB
arestyrurj-165	121	29	the	the	DET
arestyrurj-165	121	30	erm	erm	PROPN
arestyrurj-165	121	31	problem	problem	NOUN
arestyrurj-165	121	32	.	.	PUNCT
arestyrurj-165	122	1	2	2	X
arestyrurj-165	122	2	.	.	X
arestyrurj-165	122	3	the	the	DET
arestyrurj-165	122	4	cosine	cosine	NOUN
arestyrurj-165	122	5	distance	distance	NOUN
arestyrurj-165	122	6	(	(	PUNCT
arestyrurj-165	122	7	or	or	CCONJ
arestyrurj-165	122	8	similarity)[12	similarity)[12	NOUN
arestyrurj-165	122	9	]	]	PUNCT
arestyrurj-165	122	10	for	for	ADP
arestyrurj-165	122	11	true	true	ADJ
arestyrurj-165	122	12	predictor	predictor	NOUN
arestyrurj-165	122	13	𝑊	𝑊	PROPN
arestyrurj-165	122	14	is	be	AUX
arestyrurj-165	122	15	computed	compute	VERB
arestyrurj-165	122	16	as	as	ADP
arestyrurj-165	122	17	where	where	SCONJ
arestyrurj-165	122	18	𝑊	𝑊	PROPN
arestyrurj-165	122	19	is	be	AUX
arestyrurj-165	122	20	the	the	DET
arestyrurj-165	122	21	reconstructed	reconstructed	ADJ
arestyrurj-165	122	22	predictor	predictor	NOUN
arestyrurj-165	122	23	from	from	ADP
arestyrurj-165	122	24	solving	solve	VERB
arestyrurj-165	122	25	the	the	DET
arestyrurj-165	122	26	erm	erm	PROPN
arestyrurj-165	122	27	problem	problem	NOUN
arestyrurj-165	122	28	.	.	PUNCT
arestyrurj-165	123	1	mathematically	mathematically	ADV
arestyrurj-165	123	2	,	,	PUNCT
arestyrurj-165	123	3	the	the	DET
arestyrurj-165	123	4	cosine	cosine	NOUN
arestyrurj-165	123	5	similarity	similarity	NOUN
arestyrurj-165	123	6	measures	measure	VERB
arestyrurj-165	123	7	the	the	DET
arestyrurj-165	123	8	cosine	cosine	NOUN
arestyrurj-165	123	9	of	of	ADP
arestyrurj-165	123	10	the	the	DET
arestyrurj-165	123	11	angle	angle	NOUN
arestyrurj-165	123	12	between	between	ADP
arestyrurj-165	123	13	two	two	NUM
arestyrurj-165	123	14	vectors	vector	NOUN
arestyrurj-165	123	15	projected	project	VERB
arestyrurj-165	123	16	in	in	ADP
arestyrurj-165	123	17	a	a	DET
arestyrurj-165	123	18	𝑛-dimensional	𝑛-dimensional	ADJ
arestyrurj-165	123	19	space	space	NOUN
arestyrurj-165	123	20	.	.	PUNCT
arestyrurj-165	124	1	as	as	SCONJ
arestyrurj-165	124	2	the	the	DET
arestyrurj-165	124	3	angle	angle	NOUN
arestyrurj-165	124	4	,	,	PUNCT
arestyrurj-165	124	5	𝜃	𝜃	NOUN
arestyrurj-165	124	6	,	,	PUNCT
arestyrurj-165	124	7	between	between	ADP
arestyrurj-165	124	8	the	the	DET
arestyrurj-165	124	9	two	two	NUM
arestyrurj-165	124	10	vectors	vector	NOUN
arestyrurj-165	124	11	becomes	become	VERB
arestyrurj-165	124	12	smaller	small	ADJ
arestyrurj-165	124	13	,	,	PUNCT
arestyrurj-165	124	14	the	the	DET
arestyrurj-165	124	15	cosine	cosine	NOUN
arestyrurj-165	124	16	similarity	similarity	NOUN
arestyrurj-165	124	17	will	will	AUX
arestyrurj-165	124	18	approach	approach	VERB
arestyrurj-165	124	19	a	a	DET
arestyrurj-165	124	20	value	value	NOUN
arestyrurj-165	124	21	of	of	ADP
arestyrurj-165	124	22	1	1	NUM
arestyrurj-165	124	23	.	.	PUNCT
arestyrurj-165	125	1	as	as	SCONJ
arestyrurj-165	125	2	the	the	DET
arestyrurj-165	125	3	angles	angle	NOUN
arestyrurj-165	125	4	become	become	VERB
arestyrurj-165	125	5	farther	far	ADV
arestyrurj-165	125	6	apart	apart	ADV
arestyrurj-165	125	7	(	(	PUNCT
arestyrurj-165	125	8	perpendicular	perpendicular	NOUN
arestyrurj-165	125	9	)	)	PUNCT
arestyrurj-165	125	10	,	,	PUNCT
arestyrurj-165	125	11	the	the	DET
arestyrurj-165	125	12	cosine	cosine	NOUN
arestyrurj-165	125	13	similarity	similarity	NOUN
arestyrurj-165	125	14	will	will	AUX
arestyrurj-165	125	15	approach	approach	VERB
arestyrurj-165	125	16	a	a	DET
arestyrurj-165	125	17	value	value	NOUN
arestyrurj-165	125	18	of	of	ADP
arestyrurj-165	125	19	0	0	NUM
arestyrurj-165	125	20	.	.	NOUN
arestyrurj-165	126	1	3	3	NUM
arestyrurj-165	126	2	.	.	X
arestyrurj-165	127	1	the	the	DET
arestyrurj-165	127	2	reconstruction	reconstruction	NOUN
arestyrurj-165	127	3	error	error	NOUN
arestyrurj-165	127	4	for	for	ADP
arestyrurj-165	127	5	true	true	ADJ
arestyrurj-165	127	6	predictor	predictor	NOUN
arestyrurj-165	127	7	𝑊	𝑊	PROPN
arestyrurj-165	127	8	and	and	CCONJ
arestyrurj-165	127	9	estimated	estimate	VERB
arestyrurj-165	127	10	tensor	tensor	NOUN
arestyrurj-165	127	11	predictor	predictor	NOUN
arestyrurj-165	127	12	𝑊	𝑊	PROPN
arestyrurj-165	127	13	is	be	AUX
arestyrurj-165	127	14	defined	define	VERB
arestyrurj-165	127	15	as	as	ADP
arestyrurj-165	127	16	where	where	SCONJ
arestyrurj-165	127	17	||	||	NOUN
arestyrurj-165	127	18	·	·	PUNCT
arestyrurj-165	127	19	||	||	NUM
arestyrurj-165	127	20	denotes	denote	VERB
arestyrurj-165	127	21	the	the	DET
arestyrurj-165	127	22	frobenius	frobenius	PROPN
arestyrurj-165	127	23	norm	norm	NOUN
arestyrurj-165	127	24	,	,	PUNCT
arestyrurj-165	127	25	a	a	DET
arestyrurj-165	127	26	matrix	matrix	NOUN
arestyrurj-165	127	27	generalization	generalization	NOUN
arestyrurj-165	127	28	of	of	ADP
arestyrurj-165	127	29	the	the	DET
arestyrurj-165	127	30	ℓ	ℓ	PROPN
arestyrurj-165	127	31	norm	norm	NOUN
arestyrurj-165	127	32	.	.	PUNCT
arestyrurj-165	128	1	4	4	X
arestyrurj-165	128	2	.	.	X
arestyrurj-165	128	3	the	the	DET
arestyrurj-165	128	4	classification	classification	NOUN
arestyrurj-165	128	5	accuracy	accuracy	NOUN
arestyrurj-165	128	6	for	for	ADP
arestyrurj-165	128	7	𝑛	𝑛	DET
arestyrurj-165	128	8	test	test	NOUN
arestyrurj-165	128	9	samples	sample	NOUN
arestyrurj-165	128	10	is	be	AUX
arestyrurj-165	128	11	simply	simply	ADV
arestyrurj-165	128	12	defined	define	VERB
arestyrurj-165	128	13	as	as	ADP
arestyrurj-165	128	14	the	the	DET
arestyrurj-165	128	15	following	following	NOUN
arestyrurj-165	128	16	:	:	PUNCT
arestyrurj-165	128	17	after	after	ADP
arestyrurj-165	128	18	solving	solve	VERB
arestyrurj-165	128	19	for	for	ADP
arestyrurj-165	128	20	𝑊	𝑊	PROPN
arestyrurj-165	128	21	,	,	PUNCT
arestyrurj-165	128	22	we	we	PRON
arestyrurj-165	128	23	make	make	VERB
arestyrurj-165	128	24	predictions	prediction	NOUN
arestyrurj-165	128	25	on	on	ADP
arestyrurj-165	128	26	test	test	NOUN
arestyrurj-165	128	27	data	datum	NOUN
arestyrurj-165	128	28	and	and	CCONJ
arestyrurj-165	128	29	compare	compare	VERB
arestyrurj-165	128	30	𝑦	𝑦	NOUN
arestyrurj-165	128	31	to	to	ADP
arestyrurj-165	128	32	the	the	DET
arestyrurj-165	128	33	true	true	ADJ
arestyrurj-165	128	34	𝑦	𝑦	NOUN
arestyrurj-165	128	35	.	.	PUNCT
arestyrurj-165	129	1	before	before	ADP
arestyrurj-165	129	2	comparing	compare	VERB
arestyrurj-165	129	3	the	the	DET
arestyrurj-165	129	4	labels	label	NOUN
arestyrurj-165	129	5	,	,	PUNCT
arestyrurj-165	129	6	we	we	PRON
arestyrurj-165	129	7	use	use	VERB
arestyrurj-165	129	8	the	the	DET
arestyrurj-165	129	9	sign	sign	NOUN
arestyrurj-165	129	10	function	function	NOUN
arestyrurj-165	129	11	to	to	PART
arestyrurj-165	129	12	quantize	quantize	VERB
arestyrurj-165	129	13	our	our	PRON
arestyrurj-165	129	14	values	value	NOUN
arestyrurj-165	129	15	to	to	ADP
arestyrurj-165	129	16	𝑦	𝑦	PROPN
arestyrurj-165	129	17	∈	∈	NOUN
arestyrurj-165	129	18	{	{	PUNCT
arestyrurj-165	129	19	−1,1	−1,1	NOUN
arestyrurj-165	129	20	}	}	PUNCT
arestyrurj-165	129	21	.	.	PUNCT
arestyrurj-165	130	1	4	4	NUM
arestyrurj-165	130	2	experiments	experiment	NOUN
arestyrurj-165	130	3	we	we	PRON
arestyrurj-165	130	4	used	use	VERB
arestyrurj-165	130	5	two	two	NUM
arestyrurj-165	130	6	types	type	NOUN
arestyrurj-165	130	7	of	of	ADP
arestyrurj-165	130	8	data	datum	NOUN
arestyrurj-165	130	9	for	for	ADP
arestyrurj-165	130	10	our	our	PRON
arestyrurj-165	130	11	experiments	experiment	NOUN
arestyrurj-165	130	12	:	:	PUNCT
arestyrurj-165	130	13	synthetic	synthetic	ADJ
arestyrurj-165	130	14	data	datum	NOUN
arestyrurj-165	130	15	and	and	CCONJ
arestyrurj-165	130	16	the	the	DET
arestyrurj-165	130	17	modified	modified	ADJ
arestyrurj-165	130	18	national	national	PROPN
arestyrurj-165	130	19	institute	institute	PROPN
arestyrurj-165	130	20	of	of	ADP
arestyrurj-165	130	21	standards	standard	NOUN
arestyrurj-165	130	22	and	and	CCONJ
arestyrurj-165	130	23	technology	technology	NOUN
arestyrurj-165	130	24	(	(	PUNCT
arestyrurj-165	130	25	mnist	mnist	NOUN
arestyrurj-165	130	26	)	)	PUNCT
arestyrurj-165	130	27	database.[9	database.[9	NOUN
arestyrurj-165	130	28	]	]	PUNCT
arestyrurj-165	130	29	the	the	DET
arestyrurj-165	130	30	mnist	mnist	NOUN
arestyrurj-165	130	31	database	database	NOUN
arestyrurj-165	130	32	is	be	AUX
arestyrurj-165	130	33	a	a	DET
arestyrurj-165	130	34	benchmark	benchmark	ADJ
arestyrurj-165	130	35	dataset	dataset	NOUN
arestyrurj-165	130	36	used	use	VERB
arestyrurj-165	130	37	widely	widely	ADV
arestyrurj-165	130	38	in	in	ADP
arestyrurj-165	130	39	machine	machine	NOUN
arestyrurj-165	130	40	learning	learning	NOUN
arestyrurj-165	130	41	that	that	PRON
arestyrurj-165	130	42	consists	consist	VERB
arestyrurj-165	130	43	of	of	ADP
arestyrurj-165	130	44	60,000	60,000	NUM
arestyrurj-165	130	45	samples	sample	NOUN
arestyrurj-165	130	46	of	of	ADP
arestyrurj-165	130	47	handwritten	handwritten	ADJ
arestyrurj-165	130	48	digits	digit	NOUN
arestyrurj-165	130	49	from	from	ADP
arestyrurj-165	130	50	0	0	NUM
arestyrurj-165	130	51	to	to	ADP
arestyrurj-165	130	52	9	9	NUM
arestyrurj-165	130	53	.	.	PUNCT
arestyrurj-165	131	1	the	the	DET
arestyrurj-165	131	2	objective	objective	NOUN
arestyrurj-165	131	3	of	of	ADP
arestyrurj-165	131	4	both	both	DET
arestyrurj-165	131	5	experiments	experiment	NOUN
arestyrurj-165	131	6	is	be	AUX
arestyrurj-165	131	7	to	to	PART
arestyrurj-165	131	8	compare	compare	VERB
arestyrurj-165	131	9	the	the	DET
arestyrurj-165	131	10	performance	performance	NOUN
arestyrurj-165	131	11	between	between	ADP
arestyrurj-165	131	12	the	the	DET
arestyrurj-165	131	13	cp	cp	NOUN
arestyrurj-165	131	14	-	-	PUNCT
arestyrurj-165	131	15	structured	structured	ADJ
arestyrurj-165	131	16	algorithms	algorithm	NOUN
arestyrurj-165	131	17	and	and	CCONJ
arestyrurj-165	131	18	the	the	DET
arestyrurj-165	131	19	traditional	traditional	ADJ
arestyrurj-165	131	20	algorithms	algorithm	NOUN
arestyrurj-165	131	21	,	,	PUNCT
arestyrurj-165	131	22	which	which	PRON
arestyrurj-165	131	23	were	be	AUX
arestyrurj-165	131	24	implemented	implement	VERB
arestyrurj-165	131	25	using	use	VERB
arestyrurj-165	131	26	software	software	NOUN
arestyrurj-165	131	27	packages	package	NOUN
arestyrurj-165	131	28	tensorly[7	tensorly[7	NUM
arestyrurj-165	131	29	]	]	PUNCT
arestyrurj-165	131	30	and	and	CCONJ
arestyrurj-165	131	31	scipy.[17	scipy.[17	VERB
arestyrurj-165	131	32	]	]	PUNCT
arestyrurj-165	131	33	for	for	ADP
arestyrurj-165	131	34	all	all	DET
arestyrurj-165	131	35	experiments	experiment	NOUN
arestyrurj-165	131	36	,	,	PUNCT
arestyrurj-165	131	37	we	we	PRON
arestyrurj-165	131	38	use	use	VERB
arestyrurj-165	131	39	a	a	DET
arestyrurj-165	131	40	python	python	NOUN
arestyrurj-165	131	41	environment	environment	NOUN
arestyrurj-165	131	42	on	on	ADP
arestyrurj-165	131	43	a	a	DET
arestyrurj-165	131	44	macbook	macbook	NOUN
arestyrurj-165	131	45	pro	pro	ADJ
arestyrurj-165	131	46	with	with	ADP
arestyrurj-165	131	47	2.2	2.2	NUM
arestyrurj-165	131	48	ghz	ghz	NOUN
arestyrurj-165	131	49	intel	intel	NOUN
arestyrurj-165	131	50	core	core	NOUN
arestyrurj-165	131	51	i7	i7	NOUN
arestyrurj-165	131	52	and	and	CCONJ
arestyrurj-165	131	53	16	16	NUM
arestyrurj-165	131	54	gb	gb	NOUN
arestyrurj-165	131	55	ram	ram	NOUN
arestyrurj-165	131	56	.	.	PUNCT
arestyrurj-165	132	1	i.	i.	PROPN
arestyrurj-165	132	2	synthetic	synthetic	PROPN
arestyrurj-165	132	3	data	datum	NOUN
arestyrurj-165	132	4	for	for	ADP
arestyrurj-165	132	5	synthetic	synthetic	ADJ
arestyrurj-165	132	6	data	datum	NOUN
arestyrurj-165	132	7	,	,	PUNCT
arestyrurj-165	132	8	we	we	PRON
arestyrurj-165	132	9	generated	generate	VERB
arestyrurj-165	132	10	univariate	univariate	ADJ
arestyrurj-165	132	11	𝑦	𝑦	NOUN
arestyrurj-165	132	12	responses	response	NOUN
arestyrurj-165	132	13	with	with	ADP
arestyrurj-165	132	14	different	different	ADJ
arestyrurj-165	132	15	sample	sample	NOUN
arestyrurj-165	132	16	sizes	size	NOUN
arestyrurj-165	132	17	according	accord	VERB
arestyrurj-165	132	18	to	to	ADP
arestyrurj-165	132	19	the	the	DET
arestyrurj-165	132	20	following	following	ADJ
arestyrurj-165	132	21	model	model	NOUN
arestyrurj-165	132	22	:	:	PUNCT
arestyrurj-165	132	23	where	where	SCONJ
arestyrurj-165	132	24	𝑋	𝑋	PROPN
arestyrurj-165	132	25	is	be	AUX
arestyrurj-165	132	26	drawn	draw	VERB
arestyrurj-165	132	27	independently	independently	ADV
arestyrurj-165	132	28	and	and	CCONJ
arestyrurj-165	132	29	identically	identically	ADV
arestyrurj-165	132	30	distributed	distribute	VERB
arestyrurj-165	132	31	(	(	PUNCT
arestyrurj-165	132	32	iid	iid	NOUN
arestyrurj-165	132	33	)	)	PUNCT
arestyrurj-165	132	34	from	from	ADP
arestyrurj-165	132	35	𝒩(0,1	𝒩(0,1	ADV
arestyrurj-165	132	36	)	)	PUNCT
arestyrurj-165	132	37	,	,	PUNCT
arestyrurj-165	132	38	𝜖	𝜖	PROPN
arestyrurj-165	132	39	is	be	AUX
arestyrurj-165	132	40	a	a	DET
arestyrurj-165	132	41	noise	noise	NOUN
arestyrurj-165	132	42	term	term	NOUN
arestyrurj-165	132	43	drawn	draw	VERB
arestyrurj-165	132	44	iid	iid	NOUN
arestyrurj-165	132	45	from	from	ADP
arestyrurj-165	132	46	𝒩(0,1	𝒩(0,1	ADV
arestyrurj-165	132	47	)	)	PUNCT
arestyrurj-165	132	48	,	,	PUNCT
arestyrurj-165	132	49	and	and	CCONJ
arestyrurj-165	132	50	𝑊	𝑊	PROPN
arestyrurj-165	132	51	is	be	AUX
arestyrurj-165	132	52	the	the	DET
arestyrurj-165	132	53	fixed	fix	VERB
arestyrurj-165	132	54	predictor	predictor	NOUN
arestyrurj-165	132	55	as	as	SCONJ
arestyrurj-165	132	56	shown	show	VERB
arestyrurj-165	132	57	in	in	ADP
arestyrurj-165	132	58	figure	figure	NOUN
arestyrurj-165	132	59	4	4	NUM
arestyrurj-165	132	60	.	.	PUNCT
arestyrurj-165	133	1	the	the	DET
arestyrurj-165	133	2	objective	objective	NOUN
arestyrurj-165	133	3	was	be	AUX
arestyrurj-165	133	4	to	to	PART
arestyrurj-165	133	5	observe	observe	VERB
arestyrurj-165	133	6	if	if	SCONJ
arestyrurj-165	133	7	our	our	PRON
arestyrurj-165	133	8	models	model	NOUN
arestyrurj-165	133	9	defined	define	VERB
arestyrurj-165	133	10	in	in	ADP
arestyrurj-165	133	11	(	(	PUNCT
arestyrurj-165	133	12	5	5	NUM
arestyrurj-165	133	13	)	)	PUNCT
arestyrurj-165	133	14	and	and	CCONJ
arestyrurj-165	133	15	(	(	PUNCT
arestyrurj-165	133	16	6	6	NUM
arestyrurj-165	133	17	)	)	PUNCT
arestyrurj-165	133	18	can	can	AUX
arestyrurj-165	133	19	identify	identify	VERB
arestyrurj-165	133	20	the	the	DET
arestyrurj-165	133	21	true	true	ADJ
arestyrurj-165	133	22	signal	signal	NOUN
arestyrurj-165	133	23	𝑊	𝑊	PROPN
arestyrurj-165	133	24	given	give	VERB
arestyrurj-165	133	25	(	(	PUNCT
arestyrurj-165	133	26	𝑋	𝑋	PROPN
arestyrurj-165	133	27	,	,	PUNCT
arestyrurj-165	133	28	𝑦	𝑦	NOUN
arestyrurj-165	133	29	)	)	PUNCT
arestyrurj-165	133	30	.	.	PUNCT
arestyrurj-165	134	1	aresty	aresty	PROPN
arestyrurj-165	134	2	rutgers	rutgers	PROPN
arestyrurj-165	134	3	undergraduate	undergraduate	PROPN
arestyrurj-165	134	4	research	research	PROPN
arestyrurj-165	134	5	journal	journal	PROPN
arestyrurj-165	134	6	,	,	PUNCT
arestyrurj-165	134	7	volume	volume	NOUN
arestyrurj-165	134	8	i	i	PRON
arestyrurj-165	134	9	,	,	PUNCT
arestyrurj-165	134	10	issue	issue	NOUN
arestyrurj-165	134	11	iii	iii	NUM
arestyrurj-165	134	12	performance	performance	NOUN
arestyrurj-165	134	13	comparison	comparison	NOUN
arestyrurj-165	134	14	to	to	PART
arestyrurj-165	134	15	measure	measure	VERB
arestyrurj-165	134	16	the	the	DET
arestyrurj-165	134	17	“	"	PUNCT
arestyrurj-165	134	18	closeness	closeness	NOUN
arestyrurj-165	134	19	”	"	PUNCT
arestyrurj-165	134	20	and	and	CCONJ
arestyrurj-165	134	21	classification	classification	NOUN
arestyrurj-165	134	22	accuracy	accuracy	NOUN
arestyrurj-165	134	23	between	between	ADP
arestyrurj-165	134	24	the	the	DET
arestyrurj-165	134	25	true	true	ADJ
arestyrurj-165	134	26	model	model	NOUN
arestyrurj-165	134	27	and	and	CCONJ
arestyrurj-165	134	28	the	the	DET
arestyrurj-165	134	29	predicted	predict	VERB
arestyrurj-165	134	30	model	model	NOUN
arestyrurj-165	134	31	,	,	PUNCT
arestyrurj-165	134	32	we	we	PRON
arestyrurj-165	134	33	use	use	VERB
arestyrurj-165	134	34	performance	performance	NOUN
arestyrurj-165	134	35	metrics	metric	NOUN
arestyrurj-165	134	36	defined	define	VERB
arestyrurj-165	134	37	in	in	ADP
arestyrurj-165	134	38	(	(	PUNCT
arestyrurj-165	134	39	7	7	NUM
arestyrurj-165	134	40	)	)	PUNCT
arestyrurj-165	134	41	,	,	PUNCT
arestyrurj-165	134	42	(	(	PUNCT
arestyrurj-165	134	43	8)	8)	NUM
arestyrurj-165	134	44	,	,	PUNCT
arestyrurj-165	134	45	(	(	PUNCT
arestyrurj-165	134	46	9	9	NUM
arestyrurj-165	134	47	)	)	PUNCT
arestyrurj-165	134	48	,	,	PUNCT
arestyrurj-165	134	49	and	and	CCONJ
arestyrurj-165	134	50	(	(	PUNCT
arestyrurj-165	134	51	10	10	NUM
arestyrurj-165	134	52	)	)	PUNCT
arestyrurj-165	134	53	,	,	PUNCT
arestyrurj-165	134	54	we	we	PRON
arestyrurj-165	134	55	compute	compute	VERB
arestyrurj-165	134	56	these	these	DET
arestyrurj-165	134	57	metrics	metric	NOUN
arestyrurj-165	134	58	at	at	ADP
arestyrurj-165	134	59	different	different	ADJ
arestyrurj-165	134	60	sample	sample	NOUN
arestyrurj-165	134	61	sizes	size	NOUN
arestyrurj-165	134	62	and	and	CCONJ
arestyrurj-165	134	63	show	show	VERB
arestyrurj-165	134	64	that	that	SCONJ
arestyrurj-165	134	65	as	as	ADP
arestyrurj-165	134	66	the	the	DET
arestyrurj-165	134	67	number	number	NOUN
arestyrurj-165	134	68	of	of	ADP
arestyrurj-165	134	69	samples	sample	NOUN
arestyrurj-165	134	70	increases	increase	NOUN
arestyrurj-165	134	71	,	,	PUNCT
arestyrurj-165	134	72	the	the	DET
arestyrurj-165	134	73	performance	performance	NOUN
arestyrurj-165	134	74	of	of	ADP
arestyrurj-165	134	75	the	the	DET
arestyrurj-165	134	76	traditional	traditional	ADJ
arestyrurj-165	134	77	vector	vector	NOUN
arestyrurj-165	134	78	approach	approach	NOUN
arestyrurj-165	134	79	converges	converge	VERB
arestyrurj-165	134	80	to	to	ADP
arestyrurj-165	134	81	the	the	DET
arestyrurj-165	134	82	performance	performance	NOUN
arestyrurj-165	134	83	of	of	ADP
arestyrurj-165	134	84	the	the	DET
arestyrurj-165	134	85	cp	cp	PROPN
arestyrurj-165	134	86	structured	structure	VERB
arestyrurj-165	134	87	model	model	NOUN
arestyrurj-165	134	88	.	.	PUNCT
arestyrurj-165	135	1	these	these	DET
arestyrurj-165	135	2	results	result	NOUN
arestyrurj-165	135	3	are	be	AUX
arestyrurj-165	135	4	displayed	display	VERB
arestyrurj-165	135	5	in	in	ADP
arestyrurj-165	135	6	figures	figure	NOUN
arestyrurj-165	135	7	5	5	NUM
arestyrurj-165	135	8	and	and	CCONJ
arestyrurj-165	135	9	6	6	NUM
arestyrurj-165	135	10	.	.	PUNCT
arestyrurj-165	136	1	in	in	ADP
arestyrurj-165	136	2	figure	figure	NOUN
arestyrurj-165	136	3	5	5	NUM
arestyrurj-165	136	4	,	,	PUNCT
arestyrurj-165	136	5	we	we	PRON
arestyrurj-165	136	6	can	can	AUX
arestyrurj-165	136	7	visually	visually	ADV
arestyrurj-165	136	8	see	see	VERB
arestyrurj-165	136	9	that	that	SCONJ
arestyrurj-165	136	10	the	the	DET
arestyrurj-165	136	11	predictors	predictor	NOUN
arestyrurj-165	136	12	from	from	ADP
arestyrurj-165	136	13	our	our	PRON
arestyrurj-165	136	14	method	method	NOUN
arestyrurj-165	136	15	solves	solve	NOUN
arestyrurj-165	136	16	for	for	ADP
arestyrurj-165	136	17	the	the	DET
arestyrurj-165	136	18	true	true	ADJ
arestyrurj-165	136	19	predictors	predictor	NOUN
arestyrurj-165	136	20	more	more	ADV
arestyrurj-165	136	21	accurately	accurately	ADV
arestyrurj-165	136	22	.	.	PUNCT
arestyrurj-165	137	1	for	for	ADP
arestyrurj-165	137	2	example	example	NOUN
arestyrurj-165	137	3	,	,	PUNCT
arestyrurj-165	137	4	in	in	ADP
arestyrurj-165	137	5	the	the	DET
arestyrurj-165	137	6	case	case	NOUN
arestyrurj-165	137	7	of	of	ADP
arestyrurj-165	137	8	𝑛	𝑛	NOUN
arestyrurj-165	137	9	=	=	SYM
arestyrurj-165	137	10	500	500	NUM
arestyrurj-165	137	11	from	from	ADP
arestyrurj-165	137	12	row	row	NOUN
arestyrurj-165	137	13	1	1	NUM
arestyrurj-165	137	14	,	,	PUNCT
arestyrurj-165	137	15	the	the	DET
arestyrurj-165	137	16	“	"	PUNCT
arestyrurj-165	137	17	cross	cross	ADJ
arestyrurj-165	137	18	”	"	PUNCT
arestyrurj-165	137	19	figure	figure	NOUN
arestyrurj-165	137	20	is	be	AUX
arestyrurj-165	137	21	more	more	ADV
arestyrurj-165	137	22	accurately	accurately	ADV
arestyrurj-165	137	23	portrayed	portray	VERB
arestyrurj-165	137	24	using	use	VERB
arestyrurj-165	137	25	the	the	DET
arestyrurj-165	137	26	cp	cp	PROPN
arestyrurj-165	137	27	method	method	NOUN
arestyrurj-165	137	28	(	(	PUNCT
arestyrurj-165	137	29	right	right	ADJ
arestyrurj-165	137	30	)	)	PUNCT
arestyrurj-165	137	31	than	than	ADP
arestyrurj-165	137	32	the	the	DET
arestyrurj-165	137	33	traditional	traditional	ADJ
arestyrurj-165	137	34	method	method	NOUN
arestyrurj-165	137	35	(	(	PUNCT
arestyrurj-165	137	36	middle	middle	NOUN
arestyrurj-165	137	37	)	)	PUNCT
arestyrurj-165	137	38	.	.	PUNCT
arestyrurj-165	138	1	this	this	PRON
arestyrurj-165	138	2	would	would	AUX
arestyrurj-165	138	3	allow	allow	VERB
arestyrurj-165	138	4	us	we	PRON
arestyrurj-165	138	5	to	to	PART
arestyrurj-165	138	6	make	make	VERB
arestyrurj-165	138	7	more	more	ADV
arestyrurj-165	138	8	accurate	accurate	ADJ
arestyrurj-165	138	9	predictions	prediction	NOUN
arestyrurj-165	138	10	,	,	PUNCT
arestyrurj-165	138	11	as	as	SCONJ
arestyrurj-165	138	12	the	the	DET
arestyrurj-165	138	13	estimated	estimate	VERB
arestyrurj-165	138	14	weights	weight	NOUN
arestyrurj-165	138	15	more	more	ADV
arestyrurj-165	138	16	closely	closely	ADV
arestyrurj-165	138	17	follow	follow	VERB
arestyrurj-165	138	18	the	the	DET
arestyrurj-165	138	19	true	true	ADJ
arestyrurj-165	138	20	weights	weight	NOUN
arestyrurj-165	138	21	.	.	PUNCT
arestyrurj-165	139	1	in	in	ADP
arestyrurj-165	139	2	figure	figure	NOUN
arestyrurj-165	139	3	6	6	NUM
arestyrurj-165	139	4	,	,	PUNCT
arestyrurj-165	139	5	we	we	PRON
arestyrurj-165	139	6	can	can	AUX
arestyrurj-165	139	7	see	see	VERB
arestyrurj-165	139	8	that	that	SCONJ
arestyrurj-165	139	9	the	the	DET
arestyrurj-165	139	10	mse	mse	NOUN
arestyrurj-165	139	11	for	for	ADP
arestyrurj-165	139	12	both	both	DET
arestyrurj-165	139	13	algorithms	algorithm	NOUN
arestyrurj-165	139	14	is	be	AUX
arestyrurj-165	139	15	relatively	relatively	ADV
arestyrurj-165	139	16	the	the	DET
arestyrurj-165	139	17	same	same	ADJ
arestyrurj-165	139	18	throughout	throughout	ADP
arestyrurj-165	139	19	all	all	DET
arestyrurj-165	139	20	sample	sample	NOUN
arestyrurj-165	139	21	sizes	size	NOUN
arestyrurj-165	139	22	.	.	PUNCT
arestyrurj-165	140	1	for	for	ADP
arestyrurj-165	140	2	the	the	DET
arestyrurj-165	140	3	cosine	cosine	NOUN
arestyrurj-165	140	4	distance	distance	NOUN
arestyrurj-165	140	5	,	,	PUNCT
arestyrurj-165	140	6	we	we	PRON
arestyrurj-165	140	7	can	can	AUX
arestyrurj-165	140	8	see	see	VERB
arestyrurj-165	140	9	that	that	SCONJ
arestyrurj-165	140	10	the	the	DET
arestyrurj-165	140	11	cp	cp	PROPN
arestyrurj-165	140	12	structured	structured	ADJ
arestyrurj-165	140	13	algorithm	algorithm	NOUN
arestyrurj-165	140	14	approaches	approach	VERB
arestyrurj-165	140	15	a	a	DET
arestyrurj-165	140	16	value	value	NOUN
arestyrurj-165	140	17	of	of	ADP
arestyrurj-165	140	18	1	1	NUM
arestyrurj-165	140	19	very	very	ADV
arestyrurj-165	140	20	quickly	quickly	ADV
arestyrurj-165	140	21	,	,	PUNCT
arestyrurj-165	140	22	which	which	PRON
arestyrurj-165	140	23	indicates	indicate	VERB
arestyrurj-165	140	24	that	that	SCONJ
arestyrurj-165	140	25	there	there	PRON
arestyrurj-165	140	26	is	be	VERB
arestyrurj-165	140	27	a	a	DET
arestyrurj-165	140	28	strong	strong	ADJ
arestyrurj-165	140	29	similarity	similarity	NOUN
arestyrurj-165	140	30	between	between	ADP
arestyrurj-165	140	31	the	the	DET
arestyrurj-165	140	32	estimated	estimate	VERB
arestyrurj-165	140	33	and	and	CCONJ
arestyrurj-165	140	34	the	the	DET
arestyrurj-165	140	35	true	true	ADJ
arestyrurj-165	140	36	coefficients	coefficient	NOUN
arestyrurj-165	140	37	.	.	PUNCT
arestyrurj-165	141	1	the	the	DET
arestyrurj-165	141	2	reconstruction	reconstruction	NOUN
arestyrurj-165	141	3	error	error	NOUN
arestyrurj-165	141	4	and	and	CCONJ
arestyrurj-165	141	5	classification	classification	NOUN
arestyrurj-165	141	6	accuracy	accuracy	NOUN
arestyrurj-165	141	7	both	both	PRON
arestyrurj-165	141	8	generally	generally	ADV
arestyrurj-165	141	9	have	have	VERB
arestyrurj-165	141	10	gaps	gap	NOUN
arestyrurj-165	141	11	in	in	ADP
arestyrurj-165	141	12	the	the	DET
arestyrurj-165	141	13	figures	figure	NOUN
arestyrurj-165	141	14	,	,	PUNCT
arestyrurj-165	141	15	but	but	CCONJ
arestyrurj-165	141	16	lessen	lessen	VERB
arestyrurj-165	141	17	as	as	SCONJ
arestyrurj-165	141	18	the	the	DET
arestyrurj-165	141	19	sample	sample	NOUN
arestyrurj-165	141	20	sizes	size	NOUN
arestyrurj-165	141	21	increase	increase	VERB
arestyrurj-165	141	22	.	.	PUNCT
arestyrurj-165	142	1	we	we	PRON
arestyrurj-165	142	2	can	can	AUX
arestyrurj-165	142	3	conclude	conclude	VERB
arestyrurj-165	142	4	that	that	SCONJ
arestyrurj-165	142	5	these	these	DET
arestyrurj-165	142	6	results	result	NOUN
arestyrurj-165	142	7	depend	depend	VERB
arestyrurj-165	142	8	on	on	ADP
arestyrurj-165	142	9	the	the	DET
arestyrurj-165	142	10	sample	sample	NOUN
arestyrurj-165	142	11	size	size	NOUN
arestyrurj-165	142	12	,	,	PUNCT
arestyrurj-165	142	13	as	as	SCONJ
arestyrurj-165	142	14	more	more	ADJ
arestyrurj-165	142	15	samples	sample	NOUN
arestyrurj-165	142	16	can	can	AUX
arestyrurj-165	142	17	decrease	decrease	VERB
arestyrurj-165	142	18	the	the	DET
arestyrurj-165	142	19	number	number	NOUN
arestyrurj-165	142	20	of	of	ADP
arestyrurj-165	142	21	hyperplanes	hyperplane	NOUN
arestyrurj-165	142	22	that	that	PRON
arestyrurj-165	142	23	separates	separate	VERB
arestyrurj-165	142	24	the	the	DET
arestyrurj-165	142	25	data	datum	NOUN
arestyrurj-165	142	26	,	,	PUNCT
arestyrurj-165	142	27	predicting	predict	VERB
arestyrurj-165	142	28	coefficients	coefficient	NOUN
arestyrurj-165	142	29	closer	close	ADV
arestyrurj-165	142	30	to	to	ADP
arestyrurj-165	142	31	the	the	DET
arestyrurj-165	142	32	true	true	ADJ
arestyrurj-165	142	33	model	model	NOUN
arestyrurj-165	142	34	.	.	PUNCT
arestyrurj-165	143	1	based	base	VERB
arestyrurj-165	143	2	on	on	ADP
arestyrurj-165	143	3	the	the	DET
arestyrurj-165	143	4	trends	trend	NOUN
arestyrurj-165	143	5	of	of	ADP
arestyrurj-165	143	6	the	the	DET
arestyrurj-165	143	7	graphs	graph	NOUN
arestyrurj-165	143	8	in	in	ADP
arestyrurj-165	143	9	figure	figure	NOUN
arestyrurj-165	143	10	6	6	NUM
arestyrurj-165	143	11	,	,	PUNCT
arestyrurj-165	143	12	we	we	PRON
arestyrurj-165	143	13	also	also	ADV
arestyrurj-165	143	14	hypothesize	hypothesize	VERB
arestyrurj-165	143	15	that	that	SCONJ
arestyrurj-165	143	16	if	if	SCONJ
arestyrurj-165	143	17	the	the	DET
arestyrurj-165	143	18	variance	variance	NOUN
arestyrurj-165	143	19	of	of	ADP
arestyrurj-165	143	20	the	the	DET
arestyrurj-165	143	21	noise	noise	NOUN
arestyrurj-165	143	22	(	(	PUNCT
arestyrurj-165	143	23	𝜖	𝜖	NOUN
arestyrurj-165	143	24	)	)	PUNCT
arestyrurj-165	143	25	distribution	distribution	NOUN
arestyrurj-165	143	26	was	be	AUX
arestyrurj-165	143	27	higher	high	ADJ
arestyrurj-165	143	28	,	,	PUNCT
arestyrurj-165	143	29	the	the	DET
arestyrurj-165	143	30	cp	cp	NOUN
arestyrurj-165	143	31	structured	structured	ADJ
arestyrurj-165	143	32	algorithms	algorithm	NOUN
arestyrurj-165	143	33	would	would	AUX
arestyrurj-165	143	34	also	also	ADV
arestyrurj-165	143	35	perform	perform	VERB
arestyrurj-165	143	36	better	well	ADJ
arestyrurj-165	143	37	than	than	ADP
arestyrurj-165	143	38	the	the	DET
arestyrurj-165	143	39	traditional	traditional	ADJ
arestyrurj-165	143	40	method	method	NOUN
arestyrurj-165	143	41	.	.	PUNCT
arestyrurj-165	144	1	results	result	NOUN
arestyrurj-165	144	2	with	with	ADP
arestyrurj-165	144	3	pca	pca	PROPN
arestyrurj-165	144	4	the	the	DET
arestyrurj-165	144	5	cp	cp	PROPN
arestyrurj-165	144	6	structured	structured	ADJ
arestyrurj-165	144	7	algorithm	algorithm	NOUN
arestyrurj-165	144	8	significantly	significantly	ADV
arestyrurj-165	144	9	reduces	reduce	VERB
arestyrurj-165	144	10	the	the	DET
arestyrurj-165	144	11	number	number	NOUN
arestyrurj-165	144	12	of	of	ADP
arestyrurj-165	144	13	predictors	predictor	NOUN
arestyrurj-165	144	14	to	to	PART
arestyrurj-165	144	15	be	be	AUX
arestyrurj-165	144	16	estimated	estimate	VERB
arestyrurj-165	144	17	.	.	PUNCT
arestyrurj-165	145	1	to	to	PART
arestyrurj-165	145	2	solve	solve	VERB
arestyrurj-165	145	3	for	for	ADP
arestyrurj-165	145	4	less	less	ADJ
arestyrurj-165	145	5	coefficients	coefficient	NOUN
arestyrurj-165	145	6	using	use	VERB
arestyrurj-165	145	7	the	the	DET
arestyrurj-165	145	8	traditional	traditional	ADJ
arestyrurj-165	145	9	method	method	NOUN
arestyrurj-165	145	10	,	,	PUNCT
arestyrurj-165	145	11	we	we	PRON
arestyrurj-165	145	12	can	can	AUX
arestyrurj-165	145	13	perform	perform	VERB
arestyrurj-165	145	14	principal	principal	ADJ
arestyrurj-165	145	15	component	component	NOUN
arestyrurj-165	145	16	analysis	analysis	NOUN
arestyrurj-165	145	17	(	(	PUNCT
arestyrurj-165	145	18	pca	pca	NOUN
arestyrurj-165	145	19	)	)	PUNCT
arestyrurj-165	145	20	on	on	ADP
arestyrurj-165	145	21	the	the	DET
arestyrurj-165	145	22	dataset	dataset	NOUN
arestyrurj-165	145	23	before	before	ADP
arestyrurj-165	145	24	using	use	VERB
arestyrurj-165	145	25	the	the	DET
arestyrurj-165	145	26	algorithm	algorithm	NOUN
arestyrurj-165	145	27	.	.	PUNCT
arestyrurj-165	146	1	we	we	PRON
arestyrurj-165	146	2	use	use	VERB
arestyrurj-165	146	3	pca	pca	NOUN
arestyrurj-165	146	4	on	on	ADP
arestyrurj-165	146	5	𝑋	𝑋	PROPN
arestyrurj-165	146	6	with	with	ADP
arestyrurj-165	146	7	an	an	DET
arestyrurj-165	146	8	energy	energy	NOUN
arestyrurj-165	146	9	capture	capture	NOUN
arestyrurj-165	146	10	of	of	ADP
arestyrurj-165	146	11	95	95	NUM
arestyrurj-165	146	12	%	%	NOUN
arestyrurj-165	146	13	,	,	PUNCT
arestyrurj-165	146	14	which	which	PRON
arestyrurj-165	146	15	reduces	reduce	VERB
arestyrurj-165	146	16	the	the	DET
arestyrurj-165	146	17	number	number	NOUN
arestyrurj-165	146	18	of	of	ADP
arestyrurj-165	146	19	coefficients	coefficient	NOUN
arestyrurj-165	146	20	from	from	ADP
arestyrurj-165	146	21	225	225	NUM
arestyrurj-165	146	22	to	to	ADP
arestyrurj-165	146	23	189	189	NUM
arestyrurj-165	146	24	.	.	PUNCT
arestyrurj-165	147	1	however	however	ADV
arestyrurj-165	147	2	,	,	PUNCT
arestyrurj-165	147	3	even	even	ADV
arestyrurj-165	147	4	with	with	ADP
arestyrurj-165	147	5	this	this	DET
arestyrurj-165	147	6	minimal	minimal	ADJ
arestyrurj-165	147	7	reduction	reduction	NOUN
arestyrurj-165	147	8	,	,	PUNCT
arestyrurj-165	147	9	we	we	PRON
arestyrurj-165	147	10	can	can	AUX
arestyrurj-165	147	11	see	see	VERB
arestyrurj-165	147	12	in	in	ADP
arestyrurj-165	147	13	figure	figure	NOUN
arestyrurj-165	147	14	6	6	NUM
arestyrurj-165	147	15	that	that	SCONJ
arestyrurj-165	147	16	there	there	PRON
arestyrurj-165	147	17	is	be	VERB
arestyrurj-165	147	18	a	a	DET
arestyrurj-165	147	19	notable	notable	ADJ
arestyrurj-165	147	20	decrease	decrease	NOUN
arestyrurj-165	147	21	in	in	ADP
arestyrurj-165	147	22	performance	performance	NOUN
arestyrurj-165	147	23	throughout	throughout	ADP
arestyrurj-165	147	24	most	most	ADJ
arestyrurj-165	147	25	metrics	metric	NOUN
arestyrurj-165	147	26	.	.	PUNCT
arestyrurj-165	148	1	the	the	DET
arestyrurj-165	148	2	mse	mse	PROPN
arestyrurj-165	148	3	seems	seem	VERB
arestyrurj-165	148	4	unaffected	unaffected	ADJ
arestyrurj-165	148	5	,	,	PUNCT
arestyrurj-165	148	6	but	but	CCONJ
arestyrurj-165	148	7	the	the	DET
arestyrurj-165	148	8	other	other	ADJ
arestyrurj-165	148	9	three	three	NUM
arestyrurj-165	148	10	metrics	metric	NOUN
arestyrurj-165	148	11	start	start	VERB
arestyrurj-165	148	12	to	to	PART
arestyrurj-165	148	13	see	see	VERB
arestyrurj-165	148	14	a	a	DET
arestyrurj-165	148	15	gap	gap	NOUN
arestyrurj-165	148	16	between	between	ADP
arestyrurj-165	148	17	the	the	DET
arestyrurj-165	148	18	traditional	traditional	ADJ
arestyrurj-165	148	19	method	method	NOUN
arestyrurj-165	148	20	with	with	ADP
arestyrurj-165	148	21	no	no	DET
arestyrurj-165	148	22	pca	pca	NOUN
arestyrurj-165	148	23	and	and	CCONJ
arestyrurj-165	148	24	the	the	DET
arestyrurj-165	148	25	cp	cp	PROPN
arestyrurj-165	148	26	structured	structure	VERB
arestyrurj-165	148	27	algorithm	algorithm	NOUN
arestyrurj-165	148	28	.	.	PUNCT
arestyrurj-165	149	1	a	a	DET
arestyrurj-165	149	2	possible	possible	ADJ
arestyrurj-165	149	3	explanation	explanation	NOUN
arestyrurj-165	149	4	for	for	ADP
arestyrurj-165	149	5	this	this	DET
arestyrurj-165	149	6	phenomenon	phenomenon	NOUN
arestyrurj-165	149	7	is	be	AUX
arestyrurj-165	149	8	that	that	SCONJ
arestyrurj-165	149	9	pca	pca	PROPN
arestyrurj-165	149	10	does	do	AUX
arestyrurj-165	149	11	not	not	PART
arestyrurj-165	149	12	capture	capture	VERB
arestyrurj-165	149	13	tensor	tensor	NOUN
arestyrurj-165	149	14	data	datum	NOUN
arestyrurj-165	149	15	efficiently	efficiently	ADV
arestyrurj-165	149	16	in	in	ADP
arestyrurj-165	149	17	lower	low	ADJ
arestyrurj-165	149	18	dimensional	dimensional	ADJ
arestyrurj-165	149	19	space	space	NOUN
arestyrurj-165	149	20	.	.	PUNCT
arestyrurj-165	150	1	if	if	SCONJ
arestyrurj-165	150	2	we	we	PRON
arestyrurj-165	150	3	were	be	AUX
arestyrurj-165	150	4	to	to	PART
arestyrurj-165	150	5	decrease	decrease	VERB
arestyrurj-165	150	6	the	the	DET
arestyrurj-165	150	7	energy	energy	NOUN
arestyrurj-165	150	8	capture	capture	NOUN
arestyrurj-165	150	9	,	,	PUNCT
arestyrurj-165	150	10	the	the	DET
arestyrurj-165	150	11	gap	gap	NOUN
arestyrurj-165	150	12	in	in	ADP
arestyrurj-165	150	13	performance	performance	NOUN
arestyrurj-165	150	14	would	would	AUX
arestyrurj-165	150	15	grow	grow	VERB
arestyrurj-165	150	16	larger	large	ADJ
arestyrurj-165	150	17	even	even	ADV
arestyrurj-165	150	18	for	for	ADP
arestyrurj-165	150	19	a	a	DET
arestyrurj-165	150	20	bigger	big	ADJ
arestyrurj-165	150	21	sample	sample	NOUN
arestyrurj-165	150	22	size	size	NOUN
arestyrurj-165	150	23	.	.	PUNCT
arestyrurj-165	151	1	we	we	PRON
arestyrurj-165	151	2	predict	predict	VERB
arestyrurj-165	151	3	that	that	SCONJ
arestyrurj-165	151	4	as	as	ADP
arestyrurj-165	151	5	the	the	DET
arestyrurj-165	151	6	dimensions	dimension	NOUN
arestyrurj-165	151	7	of	of	ADP
arestyrurj-165	151	8	the	the	DET
arestyrurj-165	151	9	data	data	NOUN
arestyrurj-165	151	10	increases	increase	NOUN
arestyrurj-165	151	11	,	,	PUNCT
arestyrurj-165	151	12	pca	pca	PROPN
arestyrurj-165	151	13	would	would	AUX
arestyrurj-165	151	14	not	not	PART
arestyrurj-165	151	15	be	be	AUX
arestyrurj-165	151	16	an	an	DET
arestyrurj-165	151	17	efficient	efficient	ADJ
arestyrurj-165	151	18	feature	feature	NOUN
arestyrurj-165	151	19	learning	learn	VERB
arestyrurj-165	151	20	method	method	NOUN
arestyrurj-165	151	21	for	for	ADP
arestyrurj-165	151	22	parameter	parameter	NOUN
arestyrurj-165	151	23	reduction	reduction	NOUN
arestyrurj-165	151	24	,	,	PUNCT
arestyrurj-165	151	25	favoring	favor	VERB
arestyrurj-165	151	26	the	the	DET
arestyrurj-165	151	27	cp	cp	PROPN
arestyrurj-165	151	28	structured	structure	VERB
arestyrurj-165	151	29	methods	method	NOUN
arestyrurj-165	151	30	.	.	PUNCT
arestyrurj-165	152	1	figure	figure	VERB
arestyrurj-165	152	2	4	4	NUM
arestyrurj-165	152	3	:	:	SYM
arestyrurj-165	152	4	two	two	NUM
arestyrurj-165	152	5	15	15	NUM
arestyrurj-165	152	6	×	×	NOUN
arestyrurj-165	152	7	15	15	NUM
arestyrurj-165	152	8	images	image	NOUN
arestyrurj-165	152	9	used	use	VERB
arestyrurj-165	152	10	as	as	ADP
arestyrurj-165	152	11	true	true	ADJ
arestyrurj-165	152	12	predictors	predictor	NOUN
arestyrurj-165	152	13	𝑊	𝑊	PRON
arestyrurj-165	152	14	to	to	PART
arestyrurj-165	152	15	generate	generate	VERB
arestyrurj-165	152	16	synthetic	synthetic	ADJ
arestyrurj-165	152	17	data	datum	NOUN
arestyrurj-165	152	18	figure	figure	NOUN
arestyrurj-165	152	19	5	5	NUM
arestyrurj-165	152	20	:	:	PUNCT
arestyrurj-165	152	21	reconstructed	reconstruct	VERB
arestyrurj-165	152	22	predictors	predictor	NOUN
arestyrurj-165	152	23	from	from	ADP
arestyrurj-165	152	24	both	both	DET
arestyrurj-165	152	25	algorithms	algorithm	NOUN
arestyrurj-165	152	26	:	:	PUNCT
arestyrurj-165	152	27	left	leave	VERB
arestyrurj-165	152	28	–	–	PUNCT
arestyrurj-165	152	29	true	true	ADJ
arestyrurj-165	152	30	predictor	predictor	NOUN
arestyrurj-165	152	31	,	,	PUNCT
arestyrurj-165	152	32	middle	middle	ADJ
arestyrurj-165	152	33	–	–	PUNCT
arestyrurj-165	152	34	reconstructed	reconstructed	ADJ
arestyrurj-165	152	35	predictor	predictor	NOUN
arestyrurj-165	152	36	from	from	ADP
arestyrurj-165	152	37	traditional	traditional	ADJ
arestyrurj-165	152	38	method	method	NOUN
arestyrurj-165	152	39	with	with	ADP
arestyrurj-165	152	40	increasing	increase	VERB
arestyrurj-165	152	41	sample	sample	NOUN
arestyrurj-165	152	42	sizes	size	NOUN
arestyrurj-165	152	43	(	(	PUNCT
arestyrurj-165	152	44	𝑛	𝑛	PROPN
arestyrurj-165	152	45	=	=	SYM
arestyrurj-165	152	46	500,1000,1500	500,1000,1500	NOUN
arestyrurj-165	152	47	)	)	PUNCT
arestyrurj-165	152	48	,	,	PUNCT
arestyrurj-165	152	49	right	right	ADJ
arestyrurj-165	152	50	–	–	PUNCT
arestyrurj-165	152	51	reconstructed	reconstruct	VERB
arestyrurj-165	152	52	predictor	predictor	NOUN
arestyrurj-165	152	53	from	from	ADP
arestyrurj-165	152	54	cp	cp	ADJ
arestyrurj-165	152	55	-	-	PUNCT
arestyrurj-165	152	56	structured	structure	VERB
arestyrurj-165	152	57	logistic	logistic	ADJ
arestyrurj-165	152	58	regression	regression	NOUN
arestyrurj-165	152	59	with	with	ADP
arestyrurj-165	152	60	increasing	increase	VERB
arestyrurj-165	152	61	sample	sample	NOUN
arestyrurj-165	152	62	sizes	size	NOUN
arestyrurj-165	152	63	(	(	PUNCT
arestyrurj-165	152	64	𝑛	𝑛	PROPN
arestyrurj-165	152	65	=	=	SYM
arestyrurj-165	152	66	500,1000,1500	500,1000,1500	NOUN
arestyrurj-165	152	67	)	)	PUNCT
arestyrurj-165	152	68	aresty	aresty	ADJ
arestyrurj-165	152	69	rutgers	rutgers	PROPN
arestyrurj-165	152	70	undergraduate	undergraduate	PROPN
arestyrurj-165	152	71	research	research	PROPN
arestyrurj-165	152	72	journal	journal	PROPN
arestyrurj-165	152	73	,	,	PUNCT
arestyrurj-165	152	74	volume	volume	NOUN
arestyrurj-165	152	75	i	i	PRON
arestyrurj-165	152	76	,	,	PUNCT
arestyrurj-165	152	77	issue	issue	PROPN
arestyrurj-165	152	78	iii	iii	PROPN
arestyrurj-165	152	79	ii	ii	PROPN
arestyrurj-165	152	80	.	.	PUNCT
arestyrurj-165	153	1	mnist	mnist	PROPN
arestyrurj-165	153	2	data	data	VERB
arestyrurj-165	153	3	the	the	DET
arestyrurj-165	153	4	objective	objective	NOUN
arestyrurj-165	153	5	of	of	ADP
arestyrurj-165	153	6	the	the	DET
arestyrurj-165	153	7	mnist	mnist	NOUN
arestyrurj-165	153	8	dataset	dataset	PROPN
arestyrurj-165	153	9	experiment	experiment	NOUN
arestyrurj-165	153	10	was	be	AUX
arestyrurj-165	153	11	to	to	PART
arestyrurj-165	153	12	observe	observe	VERB
arestyrurj-165	153	13	which	which	DET
arestyrurj-165	153	14	algorithm	algorithm	NOUN
arestyrurj-165	153	15	would	would	AUX
arestyrurj-165	153	16	be	be	AUX
arestyrurj-165	153	17	more	more	ADV
arestyrurj-165	153	18	efficient	efficient	ADJ
arestyrurj-165	153	19	to	to	PART
arestyrurj-165	153	20	use	use	VERB
arestyrurj-165	153	21	when	when	SCONJ
arestyrurj-165	153	22	the	the	DET
arestyrurj-165	153	23	true	true	ADJ
arestyrurj-165	153	24	predictor	predictor	NOUN
arestyrurj-165	153	25	exhibited	exhibit	VERB
arestyrurj-165	153	26	an	an	DET
arestyrurj-165	153	27	“	"	PUNCT
arestyrurj-165	153	28	approximate	approximate	ADJ
arestyrurj-165	153	29	”	"	PUNCT
arestyrurj-165	153	30	low	low	ADJ
arestyrurj-165	153	31	rank	rank	NOUN
arestyrurj-165	153	32	structure	structure	NOUN
arestyrurj-165	153	33	.	.	PUNCT
arestyrurj-165	154	1	in	in	ADP
arestyrurj-165	154	2	the	the	DET
arestyrurj-165	154	3	previous	previous	ADJ
arestyrurj-165	154	4	experiment	experiment	NOUN
arestyrurj-165	154	5	,	,	PUNCT
arestyrurj-165	154	6	the	the	DET
arestyrurj-165	154	7	two	two	NUM
arestyrurj-165	154	8	images	image	NOUN
arestyrurj-165	154	9	used	use	VERB
arestyrurj-165	154	10	as	as	ADP
arestyrurj-165	154	11	the	the	DET
arestyrurj-165	154	12	true	true	ADJ
arestyrurj-165	154	13	predictor	predictor	NOUN
arestyrurj-165	154	14	had	have	VERB
arestyrurj-165	154	15	an	an	DET
arestyrurj-165	154	16	exact	exact	ADJ
arestyrurj-165	154	17	low	low	ADJ
arestyrurj-165	154	18	rank	rank	NOUN
arestyrurj-165	154	19	structure	structure	NOUN
arestyrurj-165	154	20	,	,	PUNCT
arestyrurj-165	154	21	as	as	SCONJ
arestyrurj-165	154	22	it	it	PRON
arestyrurj-165	154	23	could	could	AUX
arestyrurj-165	154	24	easily	easily	ADV
arestyrurj-165	154	25	be	be	AUX
arestyrurj-165	154	26	computed	compute	VERB
arestyrurj-165	154	27	through	through	ADP
arestyrurj-165	154	28	an	an	DET
arestyrurj-165	154	29	outer	outer	ADJ
arestyrurj-165	154	30	product	product	NOUN
arestyrurj-165	154	31	of	of	ADP
arestyrurj-165	154	32	two	two	NUM
arestyrurj-165	154	33	matrices	matrix	NOUN
arestyrurj-165	154	34	.	.	PUNCT
arestyrurj-165	155	1	similar	similar	ADJ
arestyrurj-165	155	2	to	to	ADP
arestyrurj-165	155	3	the	the	DET
arestyrurj-165	155	4	synthetic	synthetic	ADJ
arestyrurj-165	155	5	data	data	NOUN
arestyrurj-165	155	6	setup	setup	NOUN
arestyrurj-165	155	7	,	,	PUNCT
arestyrurj-165	155	8	we	we	PRON
arestyrurj-165	155	9	generated	generate	VERB
arestyrurj-165	155	10	univariate	univariate	ADJ
arestyrurj-165	155	11	𝑦	𝑦	NOUN
arestyrurj-165	155	12	responses	response	NOUN
arestyrurj-165	155	13	with	with	ADP
arestyrurj-165	155	14	sample	sample	NOUN
arestyrurj-165	155	15	size	size	NOUN
arestyrurj-165	155	16	𝑛	𝑛	PROPN
arestyrurj-165	156	1	=	=	NOUN
arestyrurj-165	156	2	750	750	NUM
arestyrurj-165	156	3	with	with	ADP
arestyrurj-165	156	4	the	the	DET
arestyrurj-165	156	5	model	model	NOUN
arestyrurj-165	156	6	defined	define	VERB
arestyrurj-165	156	7	in	in	ADP
arestyrurj-165	156	8	(	(	PUNCT
arestyrurj-165	156	9	11	11	NUM
arestyrurj-165	156	10	)	)	PUNCT
arestyrurj-165	156	11	.	.	PUNCT
arestyrurj-165	157	1	however	however	ADV
arestyrurj-165	157	2	,	,	PUNCT
arestyrurj-165	157	3	for	for	ADP
arestyrurj-165	157	4	the	the	DET
arestyrurj-165	157	5	true	true	ADJ
arestyrurj-165	157	6	predictor	predictor	NOUN
arestyrurj-165	157	7	,	,	PUNCT
arestyrurj-165	157	8	𝑊	𝑊	PROPN
arestyrurj-165	157	9	,	,	PUNCT
arestyrurj-165	157	10	we	we	PRON
arestyrurj-165	157	11	chose	choose	VERB
arestyrurj-165	157	12	a	a	DET
arestyrurj-165	157	13	“	"	PUNCT
arestyrurj-165	157	14	1	1	NUM
arestyrurj-165	157	15	”	"	PUNCT
arestyrurj-165	157	16	from	from	ADP
arestyrurj-165	157	17	the	the	DET
arestyrurj-165	157	18	mnist	mnist	NOUN
arestyrurj-165	157	19	dataset	dataset	NOUN
arestyrurj-165	157	20	,	,	PUNCT
arestyrurj-165	157	21	as	as	SCONJ
arestyrurj-165	157	22	it	it	PRON
arestyrurj-165	157	23	exhibits	exhibit	VERB
arestyrurj-165	157	24	“	"	PUNCT
arestyrurj-165	157	25	approximate	approximate	ADJ
arestyrurj-165	157	26	”	"	PUNCT
arestyrurj-165	157	27	low	low	ADJ
arestyrurj-165	157	28	rank	rank	NOUN
arestyrurj-165	157	29	structure	structure	NOUN
arestyrurj-165	157	30	.	.	PUNCT
arestyrurj-165	158	1	we	we	PRON
arestyrurj-165	158	2	compared	compare	VERB
arestyrurj-165	158	3	the	the	DET
arestyrurj-165	158	4	cp	cp	NOUN
arestyrurj-165	158	5	-	-	ADJ
arestyrurj-165	158	6	structued	structue	VERB
arestyrurj-165	158	7	algorithms	algorithm	NOUN
arestyrurj-165	158	8	to	to	ADP
arestyrurj-165	158	9	the	the	DET
arestyrurj-165	158	10	traditional	traditional	ADJ
arestyrurj-165	158	11	algorithms	algorithms	NOUN
arestyrurj-165	158	12	using	use	VERB
arestyrurj-165	158	13	different	different	ADJ
arestyrurj-165	158	14	rank	rank	NOUN
arestyrurj-165	158	15	values	value	NOUN
arestyrurj-165	158	16	.	.	PUNCT
arestyrurj-165	159	1	these	these	DET
arestyrurj-165	159	2	results	result	NOUN
arestyrurj-165	159	3	are	be	AUX
arestyrurj-165	159	4	shown	show	VERB
arestyrurj-165	159	5	in	in	ADP
arestyrurj-165	159	6	table	table	NOUN
arestyrurj-165	159	7	1	1	NUM
arestyrurj-165	159	8	.	.	PUNCT
arestyrurj-165	159	9	performance	performance	NOUN
arestyrurj-165	159	10	comparison	comparison	NOUN
arestyrurj-165	159	11	we	we	PRON
arestyrurj-165	159	12	use	use	VERB
arestyrurj-165	159	13	the	the	DET
arestyrurj-165	159	14	same	same	ADJ
arestyrurj-165	159	15	performance	performance	NOUN
arestyrurj-165	159	16	metrics	metric	NOUN
arestyrurj-165	159	17	defined	define	VERB
arestyrurj-165	159	18	for	for	ADP
arestyrurj-165	159	19	the	the	DET
arestyrurj-165	159	20	previous	previous	ADJ
arestyrurj-165	159	21	experiment	experiment	NOUN
arestyrurj-165	159	22	and	and	CCONJ
arestyrurj-165	159	23	display	display	VERB
arestyrurj-165	159	24	the	the	DET
arestyrurj-165	159	25	results	result	NOUN
arestyrurj-165	159	26	in	in	ADP
arestyrurj-165	159	27	table	table	NOUN
arestyrurj-165	159	28	1	1	NUM
arestyrurj-165	159	29	.	.	PUNCT
arestyrurj-165	159	30	from	from	ADP
arestyrurj-165	159	31	this	this	DET
arestyrurj-165	159	32	table	table	NOUN
arestyrurj-165	159	33	,	,	PUNCT
arestyrurj-165	159	34	we	we	PRON
arestyrurj-165	159	35	can	can	AUX
arestyrurj-165	159	36	conclude	conclude	VERB
arestyrurj-165	159	37	that	that	SCONJ
arestyrurj-165	159	38	both	both	PRON
arestyrurj-165	159	39	cp	cp	NUM
arestyrurj-165	159	40	structured	structure	VERB
arestyrurj-165	159	41	algorithms	algorithm	NOUN
arestyrurj-165	159	42	gave	give	VERB
arestyrurj-165	159	43	favorable	favorable	ADJ
arestyrurj-165	159	44	results	result	NOUN
arestyrurj-165	159	45	when	when	SCONJ
arestyrurj-165	159	46	the	the	DET
arestyrurj-165	159	47	cp	cp	PROPN
arestyrurj-165	159	48	rank	rank	NOUN
arestyrurj-165	159	49	was	be	AUX
arestyrurj-165	159	50	2	2	NUM
arestyrurj-165	159	51	.	.	PUNCT
arestyrurj-165	160	1	this	this	PRON
arestyrurj-165	160	2	shows	show	VERB
arestyrurj-165	160	3	that	that	SCONJ
arestyrurj-165	160	4	we	we	PRON
arestyrurj-165	160	5	can	can	AUX
arestyrurj-165	160	6	approximate	approximate	VERB
arestyrurj-165	160	7	a	a	DET
arestyrurj-165	160	8	”	"	PUNCT
arestyrurj-165	160	9	1	1	NUM
arestyrurj-165	160	10	”	"	PUNCT
arestyrurj-165	160	11	from	from	ADP
arestyrurj-165	160	12	the	the	DET
arestyrurj-165	160	13	mnist	mnist	NOUN
arestyrurj-165	160	14	dataset	dataset	VERB
arestyrurj-165	160	15	with	with	ADP
arestyrurj-165	160	16	matrices	matrix	NOUN
arestyrurj-165	160	17	of	of	ADP
arestyrurj-165	160	18	rank	rank	NOUN
arestyrurj-165	160	19	2	2	NUM
arestyrurj-165	160	20	.	.	PUNCT
arestyrurj-165	161	1	however	however	ADV
arestyrurj-165	161	2	in	in	ADP
arestyrurj-165	161	3	all	all	DET
arestyrurj-165	161	4	cases	case	NOUN
arestyrurj-165	161	5	from	from	ADP
arestyrurj-165	161	6	rank	rank	NOUN
arestyrurj-165	161	7	1	1	NUM
arestyrurj-165	161	8	figure	figure	NOUN
arestyrurj-165	161	9	6	6	NUM
arestyrurj-165	161	10	:	:	PUNCT
arestyrurj-165	161	11	variation	variation	NOUN
arestyrurj-165	161	12	of	of	ADP
arestyrurj-165	161	13	performance	performance	NOUN
arestyrurj-165	161	14	(	(	PUNCT
arestyrurj-165	161	15	y	y	NOUN
arestyrurj-165	161	16	-	-	PUNCT
arestyrurj-165	161	17	axis	axis	NOUN
arestyrurj-165	161	18	)	)	PUNCT
arestyrurj-165	161	19	with	with	ADP
arestyrurj-165	161	20	different	different	ADJ
arestyrurj-165	161	21	sample	sample	NOUN
arestyrurj-165	161	22	sizes	size	NOUN
arestyrurj-165	161	23	(	(	PUNCT
arestyrurj-165	161	24	x	x	NOUN
arestyrurj-165	161	25	-	-	NOUN
arestyrurj-165	161	26	axis	axis	ADJ
arestyrurj-165	161	27	)	)	PUNCT
arestyrurj-165	161	28	for	for	ADP
arestyrurj-165	161	29	svm	svm	NOUN
arestyrurj-165	161	30	and	and	CCONJ
arestyrurj-165	161	31	logit	logit	PROPN
arestyrurj-165	161	32	.	.	PUNCT
arestyrurj-165	162	1	columns	column	NOUN
arestyrurj-165	162	2	1	1	NUM
arestyrurj-165	162	3	-	-	SYM
arestyrurj-165	162	4	4	4	NUM
arestyrurj-165	162	5	represent	represent	VERB
arestyrurj-165	162	6	plots	plot	NOUN
arestyrurj-165	162	7	for	for	ADP
arestyrurj-165	162	8	the	the	DET
arestyrurj-165	162	9	mse	mse	NOUN
arestyrurj-165	162	10	,	,	PUNCT
arestyrurj-165	162	11	cosine	cosine	NOUN
arestyrurj-165	162	12	distance	distance	NOUN
arestyrurj-165	162	13	,	,	PUNCT
arestyrurj-165	162	14	reconstruction	reconstruction	NOUN
arestyrurj-165	162	15	error	error	NOUN
arestyrurj-165	162	16	,	,	PUNCT
arestyrurj-165	162	17	and	and	CCONJ
arestyrurj-165	162	18	classification	classification	NOUN
arestyrurj-165	162	19	accuracy	accuracy	NOUN
arestyrurj-165	162	20	,	,	PUNCT
arestyrurj-165	162	21	respectively	respectively	ADV
arestyrurj-165	162	22	.	.	PUNCT
arestyrurj-165	163	1	row	row	NOUN
arestyrurj-165	163	2	1	1	NUM
arestyrurj-165	163	3	,	,	PUNCT
arestyrurj-165	163	4	2	2	NUM
arestyrurj-165	163	5	:	:	PUNCT
arestyrurj-165	163	6	performance	performance	NOUN
arestyrurj-165	163	7	metrics	metric	NOUN
arestyrurj-165	163	8	for	for	ADP
arestyrurj-165	163	9	logit	logit	NOUN
arestyrurj-165	163	10	with	with	ADP
arestyrurj-165	163	11	predictors	predictor	NOUN
arestyrurj-165	163	12	as	as	ADP
arestyrurj-165	163	13	cross	cross	NOUN
arestyrurj-165	163	14	and	and	CCONJ
arestyrurj-165	163	15	square	square	ADJ
arestyrurj-165	163	16	,	,	PUNCT
arestyrurj-165	163	17	respectively	respectively	ADV
arestyrurj-165	163	18	.	.	PUNCT
arestyrurj-165	163	19	row	row	NOUN
arestyrurj-165	163	20	3	3	NUM
arestyrurj-165	163	21	,	,	PUNCT
arestyrurj-165	163	22	4	4	NUM
arestyrurj-165	163	23	:	:	PUNCT
arestyrurj-165	163	24	performance	performance	NOUN
arestyrurj-165	163	25	metrics	metric	NOUN
arestyrurj-165	163	26	for	for	ADP
arestyrurj-165	163	27	svm	svm	NOUN
arestyrurj-165	163	28	with	with	ADP
arestyrurj-165	163	29	predictors	predictor	NOUN
arestyrurj-165	163	30	as	as	ADP
arestyrurj-165	163	31	cross	cross	NOUN
arestyrurj-165	163	32	and	and	CCONJ
arestyrurj-165	163	33	square	square	ADJ
arestyrurj-165	163	34	,	,	PUNCT
arestyrurj-165	163	35	respectively	respectively	ADV
arestyrurj-165	163	36	.	.	PUNCT
arestyrurj-165	164	1	predictors	predictor	NOUN
arestyrurj-165	164	2	of	of	ADP
arestyrurj-165	164	3	cross	cross	NOUN
arestyrurj-165	164	4	and	and	CCONJ
arestyrurj-165	164	5	square	square	NOUN
arestyrurj-165	164	6	is	be	AUX
arestyrurj-165	164	7	as	as	SCONJ
arestyrurj-165	164	8	shown	show	VERB
arestyrurj-165	164	9	in	in	ADP
arestyrurj-165	164	10	figure	figure	NOUN
arestyrurj-165	164	11	4	4	NUM
arestyrurj-165	164	12	aresty	aresty	ADJ
arestyrurj-165	164	13	rutgers	rutgers	PROPN
arestyrurj-165	164	14	undergraduate	undergraduate	PROPN
arestyrurj-165	164	15	research	research	PROPN
arestyrurj-165	164	16	journal	journal	PROPN
arestyrurj-165	164	17	,	,	PUNCT
arestyrurj-165	164	18	volume	volume	NOUN
arestyrurj-165	164	19	i	i	PRON
arestyrurj-165	164	20	,	,	PUNCT
arestyrurj-165	164	21	issue	issue	VERB
arestyrurj-165	164	22	iii	iii	NUM
arestyrurj-165	164	23	to	to	ADP
arestyrurj-165	164	24	3	3	NUM
arestyrurj-165	164	25	,	,	PUNCT
arestyrurj-165	164	26	the	the	DET
arestyrurj-165	164	27	structured	structured	ADJ
arestyrurj-165	164	28	algorithms	algorithm	NOUN
arestyrurj-165	164	29	gave	give	VERB
arestyrurj-165	164	30	more	more	ADV
arestyrurj-165	164	31	favorable	favorable	ADJ
arestyrurj-165	164	32	results	result	NOUN
arestyrurj-165	164	33	.	.	PUNCT
arestyrurj-165	165	1	this	this	PRON
arestyrurj-165	165	2	proves	prove	VERB
arestyrurj-165	165	3	to	to	PART
arestyrurj-165	165	4	show	show	VERB
arestyrurj-165	165	5	that	that	SCONJ
arestyrurj-165	165	6	if	if	SCONJ
arestyrurj-165	165	7	the	the	DET
arestyrurj-165	165	8	true	true	ADJ
arestyrurj-165	165	9	predictor	predictor	NOUN
arestyrurj-165	165	10	exhibits	exhibit	VERB
arestyrurj-165	165	11	an	an	DET
arestyrurj-165	165	12	approximate	approximate	ADJ
arestyrurj-165	165	13	low	low	ADJ
arestyrurj-165	165	14	rank	rank	NOUN
arestyrurj-165	165	15	structure	structure	NOUN
arestyrurj-165	165	16	,	,	PUNCT
arestyrurj-165	165	17	it	it	PRON
arestyrurj-165	165	18	may	may	AUX
arestyrurj-165	165	19	be	be	AUX
arestyrurj-165	165	20	beneficial	beneficial	ADJ
arestyrurj-165	165	21	to	to	PART
arestyrurj-165	165	22	use	use	VERB
arestyrurj-165	165	23	the	the	DET
arestyrurj-165	165	24	structured	structured	ADJ
arestyrurj-165	165	25	algorithms	algorithm	NOUN
arestyrurj-165	165	26	for	for	ADP
arestyrurj-165	165	27	classification	classification	NOUN
arestyrurj-165	165	28	.	.	PUNCT
arestyrurj-165	166	1	5	5	NUM
arestyrurj-165	166	2	conclusion	conclusion	NOUN
arestyrurj-165	166	3	in	in	ADP
arestyrurj-165	166	4	this	this	DET
arestyrurj-165	166	5	paper	paper	NOUN
arestyrurj-165	166	6	,	,	PUNCT
arestyrurj-165	166	7	we	we	PRON
arestyrurj-165	166	8	explored	explore	VERB
arestyrurj-165	166	9	tensor	tensor	NOUN
arestyrurj-165	166	10	-	-	PUNCT
arestyrurj-165	166	11	based	base	VERB
arestyrurj-165	166	12	classification	classification	NOUN
arestyrurj-165	166	13	models	model	NOUN
arestyrurj-165	166	14	using	use	VERB
arestyrurj-165	166	15	a	a	DET
arestyrurj-165	166	16	tensor	tensor	NOUN
arestyrurj-165	166	17	decomposition	decomposition	NOUN
arestyrurj-165	166	18	.	.	PUNCT
arestyrurj-165	167	1	we	we	PRON
arestyrurj-165	167	2	proposed	propose	VERB
arestyrurj-165	167	3	two	two	NUM
arestyrurj-165	167	4	algorithms	algorithm	NOUN
arestyrurj-165	167	5	that	that	PRON
arestyrurj-165	167	6	imposed	impose	VERB
arestyrurj-165	167	7	a	a	DET
arestyrurj-165	167	8	candecomp	candecomp	NOUN
arestyrurj-165	167	9	/	/	SYM
arestyrurj-165	167	10	parafac	parafac	NOUN
arestyrurj-165	167	11	factorization	factorization	NOUN
arestyrurj-165	167	12	structure	structure	NOUN
arestyrurj-165	167	13	on	on	ADP
arestyrurj-165	167	14	the	the	DET
arestyrurj-165	167	15	predictors	predictor	NOUN
arestyrurj-165	167	16	of	of	ADP
arestyrurj-165	167	17	traditional	traditional	ADJ
arestyrurj-165	167	18	classification	classification	NOUN
arestyrurj-165	167	19	algorithms	algorithm	NOUN
arestyrurj-165	167	20	:	:	PUNCT
arestyrurj-165	167	21	support	support	NOUN
arestyrurj-165	167	22	vector	vector	NOUN
arestyrurj-165	167	23	machines	machine	NOUN
arestyrurj-165	167	24	and	and	CCONJ
arestyrurj-165	167	25	logistic	logistic	ADJ
arestyrurj-165	167	26	regression	regression	NOUN
arestyrurj-165	167	27	.	.	PUNCT
arestyrurj-165	168	1	imposing	impose	VERB
arestyrurj-165	168	2	these	these	DET
arestyrurj-165	168	3	techniques	technique	NOUN
arestyrurj-165	168	4	on	on	ADP
arestyrurj-165	168	5	traditional	traditional	ADJ
arestyrurj-165	168	6	algorithms	algorithm	NOUN
arestyrurj-165	168	7	allowed	allow	VERB
arestyrurj-165	168	8	us	we	PRON
arestyrurj-165	168	9	to	to	PART
arestyrurj-165	168	10	exploit	exploit	VERB
arestyrurj-165	168	11	the	the	DET
arestyrurj-165	168	12	structure	structure	NOUN
arestyrurj-165	168	13	of	of	ADP
arestyrurj-165	168	14	the	the	DET
arestyrurj-165	168	15	data	datum	NOUN
arestyrurj-165	168	16	,	,	PUNCT
arestyrurj-165	168	17	enabling	enable	VERB
arestyrurj-165	168	18	efficient	efficient	ADJ
arestyrurj-165	168	19	learning	learning	NOUN
arestyrurj-165	168	20	with	with	ADP
arestyrurj-165	168	21	fewer	few	ADJ
arestyrurj-165	168	22	parameters	parameter	NOUN
arestyrurj-165	168	23	.	.	PUNCT
arestyrurj-165	169	1	we	we	PRON
arestyrurj-165	169	2	showed	show	VERB
arestyrurj-165	169	3	with	with	ADP
arestyrurj-165	169	4	different	different	ADJ
arestyrurj-165	169	5	performance	performance	NOUN
arestyrurj-165	169	6	metrics	metric	NOUN
arestyrurj-165	169	7	that	that	PRON
arestyrurj-165	169	8	our	our	PRON
arestyrurj-165	169	9	proposed	propose	VERB
arestyrurj-165	169	10	method	method	NOUN
arestyrurj-165	169	11	increased	increase	VERB
arestyrurj-165	169	12	accuracy	accuracy	NOUN
arestyrurj-165	169	13	and	and	CCONJ
arestyrurj-165	169	14	overall	overall	ADV
arestyrurj-165	169	15	solved	solve	VERB
arestyrurj-165	169	16	a	a	DET
arestyrurj-165	169	17	more	more	ADV
arestyrurj-165	169	18	accurate	accurate	ADJ
arestyrurj-165	169	19	estimation	estimation	NOUN
arestyrurj-165	169	20	of	of	ADP
arestyrurj-165	169	21	the	the	DET
arestyrurj-165	169	22	weights	weight	NOUN
arestyrurj-165	169	23	.	.	PUNCT
arestyrurj-165	170	1	the	the	DET
arestyrurj-165	170	2	experiments	experiment	NOUN
arestyrurj-165	170	3	showed	show	VERB
arestyrurj-165	170	4	that	that	SCONJ
arestyrurj-165	170	5	the	the	DET
arestyrurj-165	170	6	cp	cp	PROPN
arestyrurj-165	170	7	algorithm	algorithm	NOUN
arestyrurj-165	170	8	performed	perform	VERB
arestyrurj-165	170	9	best	well	ADV
arestyrurj-165	170	10	when	when	SCONJ
arestyrurj-165	170	11	the	the	DET
arestyrurj-165	170	12	true	true	ADJ
arestyrurj-165	170	13	predictor	predictor	NOUN
arestyrurj-165	170	14	had	have	VERB
arestyrurj-165	170	15	either	either	CCONJ
arestyrurj-165	170	16	an	an	DET
arestyrurj-165	170	17	approximate	approximate	ADJ
arestyrurj-165	170	18	or	or	CCONJ
arestyrurj-165	170	19	exact	exact	ADJ
arestyrurj-165	170	20	low	low	ADJ
arestyrurj-165	170	21	rank	rank	NOUN
arestyrurj-165	170	22	structure	structure	NOUN
arestyrurj-165	170	23	.	.	PUNCT
arestyrurj-165	171	1	we	we	PRON
arestyrurj-165	171	2	also	also	ADV
arestyrurj-165	171	3	showed	show	VERB
arestyrurj-165	171	4	that	that	SCONJ
arestyrurj-165	171	5	solving	solve	VERB
arestyrurj-165	171	6	for	for	ADP
arestyrurj-165	171	7	fewer	few	ADJ
arestyrurj-165	171	8	parameters	parameter	NOUN
arestyrurj-165	171	9	using	use	VERB
arestyrurj-165	171	10	pca	pca	NOUN
arestyrurj-165	171	11	compromised	compromise	VERB
arestyrurj-165	171	12	the	the	DET
arestyrurj-165	171	13	performance	performance	NOUN
arestyrurj-165	171	14	of	of	ADP
arestyrurj-165	171	15	the	the	DET
arestyrurj-165	171	16	traditional	traditional	ADJ
arestyrurj-165	171	17	method	method	NOUN
arestyrurj-165	171	18	.	.	PUNCT
arestyrurj-165	172	1	we	we	PRON
arestyrurj-165	172	2	predict	predict	VERB
arestyrurj-165	172	3	that	that	SCONJ
arestyrurj-165	172	4	pca	pca	PROPN
arestyrurj-165	172	5	would	would	AUX
arestyrurj-165	172	6	not	not	PART
arestyrurj-165	172	7	generalize	generalize	VERB
arestyrurj-165	172	8	well	well	ADV
arestyrurj-165	172	9	to	to	ADP
arestyrurj-165	172	10	data	datum	NOUN
arestyrurj-165	172	11	with	with	ADP
arestyrurj-165	172	12	multidimensional	multidimensional	ADJ
arestyrurj-165	172	13	structure	structure	NOUN
arestyrurj-165	172	14	,	,	PUNCT
arestyrurj-165	172	15	favoring	favor	VERB
arestyrurj-165	172	16	the	the	DET
arestyrurj-165	172	17	cp	cp	NOUN
arestyrurj-165	172	18	structured	structured	ADJ
arestyrurj-165	172	19	algorithms	algorithm	NOUN
arestyrurj-165	172	20	.	.	PUNCT
arestyrurj-165	173	1	however	however	ADV
arestyrurj-165	173	2	,	,	PUNCT
arestyrurj-165	173	3	we	we	PRON
arestyrurj-165	173	4	believe	believe	VERB
arestyrurj-165	173	5	that	that	SCONJ
arestyrurj-165	173	6	it	it	PRON
arestyrurj-165	173	7	would	would	AUX
arestyrurj-165	173	8	be	be	AUX
arestyrurj-165	173	9	interesting	interesting	ADJ
arestyrurj-165	173	10	if	if	SCONJ
arestyrurj-165	173	11	one	one	PRON
arestyrurj-165	173	12	could	could	AUX
arestyrurj-165	173	13	show	show	VERB
arestyrurj-165	173	14	when	when	SCONJ
arestyrurj-165	173	15	pca	pca	PROPN
arestyrurj-165	173	16	could	could	AUX
arestyrurj-165	173	17	be	be	AUX
arestyrurj-165	173	18	better	well	ADJ
arestyrurj-165	173	19	than	than	ADP
arestyrurj-165	173	20	using	use	VERB
arestyrurj-165	173	21	cp	cp	NUM
arestyrurj-165	173	22	structure	structure	NOUN
arestyrurj-165	173	23	.	.	PUNCT
arestyrurj-165	174	1	this	this	PRON
arestyrurj-165	174	2	could	could	AUX
arestyrurj-165	174	3	possibly	possibly	ADV
arestyrurj-165	174	4	be	be	AUX
arestyrurj-165	174	5	a	a	DET
arestyrurj-165	174	6	case	case	NOUN
arestyrurj-165	174	7	when	when	SCONJ
arestyrurj-165	174	8	the	the	DET
arestyrurj-165	174	9	data	datum	NOUN
arestyrurj-165	174	10	in	in	ADP
arestyrurj-165	174	11	question	question	NOUN
arestyrurj-165	174	12	is	be	AUX
arestyrurj-165	174	13	known	know	VERB
arestyrurj-165	174	14	to	to	PART
arestyrurj-165	174	15	be	be	AUX
arestyrurj-165	174	16	linear	linear	ADJ
arestyrurj-165	174	17	,	,	PUNCT
arestyrurj-165	174	18	as	as	SCONJ
arestyrurj-165	174	19	pca	pca	PROPN
arestyrurj-165	174	20	is	be	AUX
arestyrurj-165	174	21	a	a	DET
arestyrurj-165	174	22	linear	linear	ADJ
arestyrurj-165	174	23	feature	feature	NOUN
arestyrurj-165	174	24	learning	learning	NOUN
arestyrurj-165	174	25	method	method	NOUN
arestyrurj-165	174	26	.	.	PUNCT
arestyrurj-165	175	1	one	one	NUM
arestyrurj-165	175	2	potential	potential	ADJ
arestyrurj-165	175	3	example	example	NOUN
arestyrurj-165	175	4	is	be	AUX
arestyrurj-165	175	5	using	use	VERB
arestyrurj-165	175	6	structured	structured	ADJ
arestyrurj-165	175	7	data	datum	NOUN
arestyrurj-165	175	8	for	for	ADP
arestyrurj-165	175	9	prediction	prediction	NOUN
arestyrurj-165	175	10	when	when	SCONJ
arestyrurj-165	175	11	it	it	PRON
arestyrurj-165	175	12	is	be	AUX
arestyrurj-165	175	13	known	know	VERB
arestyrurj-165	175	14	a	a	DET
arestyrurj-165	175	15	priori	priori	ADV
arestyrurj-165	175	16	that	that	SCONJ
arestyrurj-165	175	17	the	the	DET
arestyrurj-165	175	18	features	feature	NOUN
arestyrurj-165	175	19	have	have	VERB
arestyrurj-165	175	20	a	a	DET
arestyrurj-165	175	21	linear	linear	ADJ
arestyrurj-165	175	22	relationship	relationship	NOUN
arestyrurj-165	175	23	.	.	PUNCT
arestyrurj-165	176	1	however	however	ADV
arestyrurj-165	176	2	,	,	PUNCT
arestyrurj-165	176	3	due	due	ADP
arestyrurj-165	176	4	to	to	ADP
arestyrurj-165	176	5	time	time	NOUN
arestyrurj-165	176	6	constraints	constraint	NOUN
arestyrurj-165	176	7	,	,	PUNCT
arestyrurj-165	176	8	we	we	PRON
arestyrurj-165	176	9	were	be	AUX
arestyrurj-165	176	10	not	not	PART
arestyrurj-165	176	11	able	able	ADJ
arestyrurj-165	176	12	to	to	PART
arestyrurj-165	176	13	explore	explore	VERB
arestyrurj-165	176	14	this	this	DET
arestyrurj-165	176	15	possibility	possibility	NOUN
arestyrurj-165	176	16	in	in	ADP
arestyrurj-165	176	17	detail	detail	NOUN
arestyrurj-165	176	18	.	.	PUNCT
arestyrurj-165	177	1	we	we	PRON
arestyrurj-165	177	2	also	also	ADV
arestyrurj-165	177	3	think	think	VERB
arestyrurj-165	177	4	it	it	PRON
arestyrurj-165	177	5	would	would	AUX
arestyrurj-165	177	6	be	be	AUX
arestyrurj-165	177	7	interesting	interesting	ADJ
arestyrurj-165	177	8	to	to	PART
arestyrurj-165	177	9	test	test	VERB
arestyrurj-165	177	10	these	these	DET
arestyrurj-165	177	11	algorithms	algorithm	NOUN
arestyrurj-165	177	12	on	on	ADP
arestyrurj-165	177	13	more	more	ADJ
arestyrurj-165	177	14	datasets	dataset	NOUN
arestyrurj-165	177	15	.	.	PUNCT
arestyrurj-165	178	1	in	in	ADP
arestyrurj-165	178	2	addition	addition	NOUN
arestyrurj-165	178	3	,	,	PUNCT
arestyrurj-165	178	4	we	we	PRON
arestyrurj-165	178	5	believe	believe	VERB
arestyrurj-165	178	6	an	an	DET
arestyrurj-165	178	7	exciting	exciting	ADJ
arestyrurj-165	178	8	direction	direction	NOUN
arestyrurj-165	178	9	for	for	ADP
arestyrurj-165	178	10	future	future	ADJ
arestyrurj-165	178	11	research	research	NOUN
arestyrurj-165	178	12	is	be	AUX
arestyrurj-165	178	13	to	to	PART
arestyrurj-165	178	14	exploit	exploit	VERB
arestyrurj-165	178	15	tensor	tensor	NOUN
arestyrurj-165	178	16	decompositions	decomposition	NOUN
arestyrurj-165	178	17	in	in	ADP
arestyrurj-165	178	18	other	other	ADJ
arestyrurj-165	178	19	learning	learning	NOUN
arestyrurj-165	178	20	problems	problem	NOUN
arestyrurj-165	178	21	such	such	ADJ
arestyrurj-165	178	22	as	as	ADP
arestyrurj-165	178	23	deep	deep	ADJ
arestyrurj-165	178	24	learning	learning	NOUN
arestyrurj-165	178	25	.	.	PUNCT
arestyrurj-165	179	1	however	however	ADV
arestyrurj-165	179	2	,	,	PUNCT
arestyrurj-165	179	3	it	it	PRON
arestyrurj-165	179	4	is	be	AUX
arestyrurj-165	179	5	not	not	PART
arestyrurj-165	179	6	clear	clear	ADJ
arestyrurj-165	179	7	how	how	SCONJ
arestyrurj-165	179	8	one	one	PRON
arestyrurj-165	179	9	would	would	AUX
arestyrurj-165	179	10	approach	approach	VERB
arestyrurj-165	179	11	this	this	DET
arestyrurj-165	179	12	problem	problem	NOUN
arestyrurj-165	179	13	,	,	PUNCT
arestyrurj-165	179	14	as	as	SCONJ
arestyrurj-165	179	15	deep	deep	ADJ
arestyrurj-165	179	16	learning	learning	NOUN
arestyrurj-165	179	17	algorithms	algorithm	NOUN
arestyrurj-165	179	18	have	have	VERB
arestyrurj-165	179	19	nonconvex	nonconvex	NOUN
arestyrurj-165	179	20	loss	loss	NOUN
arestyrurj-165	179	21	functions	function	NOUN
arestyrurj-165	179	22	.	.	PUNCT
arestyrurj-165	180	1	we	we	PRON
arestyrurj-165	180	2	leave	leave	VERB
arestyrurj-165	180	3	this	this	PRON
arestyrurj-165	180	4	up	up	ADP
arestyrurj-165	180	5	to	to	ADP
arestyrurj-165	180	6	the	the	DET
arestyrurj-165	180	7	audience	audience	NOUN
arestyrurj-165	180	8	to	to	PART
arestyrurj-165	180	9	investigate	investigate	VERB
arestyrurj-165	180	10	for	for	ADP
arestyrurj-165	180	11	future	future	ADJ
arestyrurj-165	180	12	exploration.∎	exploration.∎	NOUN
arestyrurj-165	180	13	method	method	NOUN
arestyrurj-165	180	14	mse	mse	PROPN
arestyrurj-165	180	15	cos	cos	PROPN
arestyrurj-165	180	16	distance	distance	NOUN
arestyrurj-165	180	17	reconstruction	reconstruction	NOUN
arestyrurj-165	180	18	error	error	NOUN
arestyrurj-165	180	19	svm	svm	NOUN
arestyrurj-165	180	20	0.00128	0.00128	NUM
arestyrurj-165	180	21	0.51832	0.51832	NUM
arestyrurj-165	180	22	0.00053	0.00053	NUM
arestyrurj-165	180	23	cp	cp	NOUN
arestyrurj-165	180	24	-	-	ADJ
arestyrurj-165	180	25	svm	svm	ADJ
arestyrurj-165	180	26	(	(	PUNCT
arestyrurj-165	180	27	r=1	r=1	NOUN
arestyrurj-165	180	28	)	)	PUNCT
arestyrurj-165	180	29	0.00088	0.00088	NUM
arestyrurj-165	180	30	0.66727	0.66727	NUM
arestyrurj-165	180	31	0.00044	0.00044	NUM
arestyrurj-165	180	32	cp	cp	NOUN
arestyrurj-165	180	33	-	-	PUNCT
arestyrurj-165	180	34	svm	svm	PROPN
arestyrurj-165	180	35	(	(	PUNCT
arestyrurj-165	180	36	r=2	r=2	PROPN
arestyrurj-165	180	37	)	)	PUNCT
arestyrurj-165	180	38	0.00026	0.00026	NUM
arestyrurj-165	180	39	0.90259	0.90259	NUM
arestyrurj-165	180	40	0.00024	0.00024	NUM
arestyrurj-165	180	41	cp	cp	NOUN
arestyrurj-165	180	42	-	-	ADJ
arestyrurj-165	180	43	svm	svm	ADJ
arestyrurj-165	180	44	(	(	PUNCT
arestyrurj-165	180	45	r=3	r=3	PROPN
arestyrurj-165	180	46	)	)	PUNCT
arestyrurj-165	180	47	0.00039	0.00039	NUM
arestyrurj-165	180	48	0.85099	0.85099	NUM
arestyrurj-165	180	49	0.00029	0.00029	NUM
arestyrurj-165	180	50	logit	logit	NOUN
arestyrurj-165	180	51	0.00120	0.00120	NUM
arestyrurj-165	180	52	0.54759	0.54759	NUM
arestyrurj-165	180	53	0.00051	0.00051	NUM
arestyrurj-165	180	54	cp	cp	PROPN
arestyrurj-165	180	55	-	-	PUNCT
arestyrurj-165	180	56	logit	logit	PROPN
arestyrurj-165	180	57	(	(	PUNCT
arestyrurj-165	180	58	r=1	r=1	NOUN
arestyrurj-165	180	59	)	)	PUNCT
arestyrurj-165	180	60	0.00089	0.00089	NUM
arestyrurj-165	180	61	0.66483	0.66483	NUM
arestyrurj-165	180	62	0.00044	0.00044	NUM
arestyrurj-165	180	63	cp	cp	PROPN
arestyrurj-165	180	64	-	-	PUNCT
arestyrurj-165	180	65	logit	logit	PROPN
arestyrurj-165	180	66	(	(	PUNCT
arestyrurj-165	180	67	r=2	r=2	PROPN
arestyrurj-165	180	68	)	)	PUNCT
arestyrurj-165	180	69	0.00028	0.00028	NUM
arestyrurj-165	180	70	0.89590	0.89590	NUM
arestyrurj-165	180	71	0.00024	0.00024	NUM
arestyrurj-165	180	72	cp	cp	NOUN
arestyrurj-165	180	73	-	-	PUNCT
arestyrurj-165	180	74	logit	logit	PROPN
arestyrurj-165	180	75	(	(	PUNCT
arestyrurj-165	180	76	r=3	r=3	PROPN
arestyrurj-165	180	77	)	)	PUNCT
arestyrurj-165	180	78	0.00033	0.00033	NUM
arestyrurj-165	180	79	0.87807	0.87807	NUM
arestyrurj-165	180	80	0.00026	0.00026	NUM
arestyrurj-165	180	81	table	table	NOUN
arestyrurj-165	180	82	1	1	NUM
arestyrurj-165	180	83	:	:	PUNCT
arestyrurj-165	180	84	performance	performance	NOUN
arestyrurj-165	180	85	metrics	metric	NOUN
arestyrurj-165	180	86	between	between	ADP
arestyrurj-165	180	87	the	the	DET
arestyrurj-165	180	88	traditional	traditional	ADJ
arestyrurj-165	180	89	and	and	CCONJ
arestyrurj-165	180	90	structured	structured	ADJ
arestyrurj-165	180	91	algorithms	algorithm	NOUN
arestyrurj-165	180	92	for	for	ADP
arestyrurj-165	180	93	the	the	DET
arestyrurj-165	180	94	mnist	mnist	NOUN
arestyrurj-165	180	95	dataset	dataset	NOUN
arestyrurj-165	180	96	experiment	experiment	NOUN
arestyrurj-165	180	97	.	.	PUNCT
arestyrurj-165	181	1	the	the	DET
arestyrurj-165	181	2	bolded	bolde	VERB
arestyrurj-165	181	3	values	value	NOUN
arestyrurj-165	181	4	represent	represent	VERB
arestyrurj-165	181	5	the	the	DET
arestyrurj-165	181	6	“	"	PUNCT
arestyrurj-165	181	7	best	good	ADJ
arestyrurj-165	181	8	”	"	PUNCT
arestyrurj-165	181	9	performance	performance	NOUN
arestyrurj-165	181	10	throughout	throughout	ADP
arestyrurj-165	181	11	each	each	DET
arestyrurj-165	181	12	method	method	NOUN
arestyrurj-165	181	13	,	,	PUNCT
arestyrurj-165	181	14	where	where	SCONJ
arestyrurj-165	181	15	𝑅	𝑅	PROPN
arestyrurj-165	181	16	represents	represent	VERB
arestyrurj-165	181	17	the	the	DET
arestyrurj-165	181	18	rank	rank	NOUN
arestyrurj-165	181	19	of	of	ADP
arestyrurj-165	181	20	the	the	DET
arestyrurj-165	181	21	cp	cp	PROPN
arestyrurj-165	181	22	structured	structured	ADJ
arestyrurj-165	181	23	algorithm	algorithm	NOUN
arestyrurj-165	181	24	for	for	ADP
arestyrurj-165	181	25	each	each	DET
arestyrurj-165	181	26	experiment	experiment	NOUN
arestyrurj-165	181	27	.	.	PUNCT
arestyrurj-165	182	1	aresty	aresty	ADJ
arestyrurj-165	182	2	rutgers	rutgers	PROPN
arestyrurj-165	182	3	undergraduate	undergraduate	PROPN
arestyrurj-165	182	4	research	research	PROPN
arestyrurj-165	182	5	journal	journal	PROPN
arestyrurj-165	182	6	,	,	PUNCT
arestyrurj-165	182	7	volume	volume	NOUN
arestyrurj-165	182	8	i	i	PRON
arestyrurj-165	182	9	,	,	PUNCT
arestyrurj-165	182	10	issue	issue	VERB
arestyrurj-165	182	11	iii	iii	NUM
arestyrurj-165	182	12	6	6	NUM
arestyrurj-165	182	13	references	reference	NOUN
arestyrurj-165	182	14	[	[	X
arestyrurj-165	182	15	1	1	NUM
arestyrurj-165	182	16	]	]	X
arestyrurj-165	182	17	bezdek	bezdek	PROPN
arestyrurj-165	182	18	,	,	PUNCT
arestyrurj-165	182	19	j.	j.	PROPN
arestyrurj-165	182	20	&	&	CCONJ
arestyrurj-165	182	21	hathaway	hathaway	PROPN
arestyrurj-165	182	22	,	,	PUNCT
arestyrurj-165	182	23	r.	r.	PROPN
arestyrurj-165	182	24	(	(	PUNCT
arestyrurj-165	182	25	2003	2003	NUM
arestyrurj-165	182	26	)	)	PUNCT
arestyrurj-165	182	27	.	.	PUNCT
arestyrurj-165	183	1	convergence	convergence	NOUN
arestyrurj-165	183	2	of	of	ADP
arestyrurj-165	183	3	alternating	alternate	VERB
arestyrurj-165	183	4	optimization	optimization	NOUN
arestyrurj-165	183	5	.	.	PUNCT
arestyrurj-165	184	1	neural	neural	ADJ
arestyrurj-165	184	2	,	,	PUNCT
arestyrurj-165	184	3	parallel	parallel	ADJ
arestyrurj-165	184	4	&	&	CCONJ
arestyrurj-165	184	5	scientific	scientific	ADJ
arestyrurj-165	184	6	computations	computation	NOUN
arestyrurj-165	184	7	.	.	PUNCT
arestyrurj-165	185	1	11	11	NUM
arestyrurj-165	185	2	.	.	X
arestyrurj-165	185	3	351	351	NUM
arestyrurj-165	185	4	-	-	SYM
arestyrurj-165	185	5	368	368	NUM
arestyrurj-165	185	6	.	.	PUNCT
arestyrurj-165	186	1	[	[	X
arestyrurj-165	186	2	2	2	NUM
arestyrurj-165	186	3	]	]	PUNCT
arestyrurj-165	186	4	candès	candès	NOUN
arestyrurj-165	186	5	,	,	PUNCT
arestyrurj-165	186	6	e.	e.	PROPN
arestyrurj-165	186	7	j.	j.	PROPN
arestyrurj-165	186	8	,	,	PUNCT
arestyrurj-165	186	9	&	&	CCONJ
arestyrurj-165	186	10	recht	recht	PROPN
arestyrurj-165	186	11	,	,	PUNCT
arestyrurj-165	186	12	b.	b.	PROPN
arestyrurj-165	186	13	(	(	PUNCT
arestyrurj-165	186	14	2009	2009	NUM
arestyrurj-165	186	15	)	)	PUNCT
arestyrurj-165	186	16	.	.	PUNCT
arestyrurj-165	187	1	exact	exact	ADJ
arestyrurj-165	187	2	matrix	matrix	NOUN
arestyrurj-165	187	3	completion	completion	NOUN
arestyrurj-165	187	4	via	via	ADP
arestyrurj-165	187	5	convex	convex	PROPN
arestyrurj-165	187	6	optimization	optimization	NOUN
arestyrurj-165	187	7	.	.	PUNCT
arestyrurj-165	188	1	foundations	foundation	NOUN
arestyrurj-165	188	2	of	of	ADP
arestyrurj-165	188	3	computational	computational	ADJ
arestyrurj-165	188	4	mathematics	mathematic	NOUN
arestyrurj-165	188	5	,	,	PUNCT
arestyrurj-165	188	6	9(6	9(6	NUM
arestyrurj-165	188	7	)	)	PUNCT
arestyrurj-165	188	8	,	,	PUNCT
arestyrurj-165	188	9	717–772	717–772	NUM
arestyrurj-165	188	10	.	.	PUNCT
arestyrurj-165	189	1	[	[	X
arestyrurj-165	189	2	3	3	NUM
arestyrurj-165	189	3	]	]	X
arestyrurj-165	189	4	de	de	X
arestyrurj-165	189	5	luis	luis	X
arestyrurj-165	189	6	-	-	PUNCT
arestyrurj-165	189	7	garcía	garcía	NOUN
arestyrurj-165	189	8	,	,	PUNCT
arestyrurj-165	189	9	r.	r.	PROPN
arestyrurj-165	189	10	,	,	PUNCT
arestyrurj-165	189	11	westin	westin	PROPN
arestyrurj-165	189	12	,	,	PUNCT
arestyrurj-165	189	13	c.-f	c.-f	NOUN
arestyrurj-165	189	14	.	.	PUNCT
arestyrurj-165	189	15	,	,	PUNCT
arestyrurj-165	189	16	&	&	CCONJ
arestyrurj-165	189	17	alberola	alberola	PROPN
arestyrurj-165	189	18	-	-	PUNCT
arestyrurj-165	189	19	lópez	lópez	PROPN
arestyrurj-165	189	20	,	,	PUNCT
arestyrurj-165	189	21	c.	c.	PROPN
arestyrurj-165	189	22	(	(	PUNCT
arestyrurj-165	189	23	2010	2010	NUM
arestyrurj-165	189	24	)	)	PUNCT
arestyrurj-165	189	25	.	.	PUNCT
arestyrurj-165	190	1	gaussian	gaussian	ADJ
arestyrurj-165	190	2	mixtures	mixture	NOUN
arestyrurj-165	190	3	on	on	ADP
arestyrurj-165	190	4	tensor	tensor	NOUN
arestyrurj-165	190	5	fields	field	NOUN
arestyrurj-165	190	6	for	for	ADP
arestyrurj-165	190	7	segmentation	segmentation	NOUN
arestyrurj-165	190	8	:	:	PUNCT
arestyrurj-165	190	9	applications	application	NOUN
arestyrurj-165	190	10	to	to	ADP
arestyrurj-165	190	11	medical	medical	ADJ
arestyrurj-165	190	12	imaging	imaging	NOUN
arestyrurj-165	190	13	.	.	PUNCT
arestyrurj-165	191	1	computerized	computerized	ADJ
arestyrurj-165	191	2	medical	medical	ADJ
arestyrurj-165	191	3	imaging	imaging	NOUN
arestyrurj-165	191	4	and	and	CCONJ
arestyrurj-165	191	5	graphics	graphic	NOUN
arestyrurj-165	191	6	,	,	PUNCT
arestyrurj-165	191	7	35(1	35(1	NUM
arestyrurj-165	191	8	)	)	PUNCT
arestyrurj-165	191	9	,	,	PUNCT
arestyrurj-165	191	10	16–30	16–30	NUM
arestyrurj-165	191	11	.	.	PUNCT
arestyrurj-165	192	1	[	[	X
arestyrurj-165	192	2	4	4	NUM
arestyrurj-165	192	3	]	]	X
arestyrurj-165	192	4	james	james	PROPN
arestyrurj-165	192	5	,	,	PUNCT
arestyrurj-165	192	6	g.	g.	PROPN
arestyrurj-165	192	7	,	,	PUNCT
arestyrurj-165	192	8	witten	witten	PROPN
arestyrurj-165	192	9	,	,	PUNCT
arestyrurj-165	192	10	d.	d.	PROPN
arestyrurj-165	192	11	,	,	PUNCT
arestyrurj-165	192	12	hastie	hastie	PROPN
arestyrurj-165	192	13	,	,	PUNCT
arestyrurj-165	192	14	t.	t.	PROPN
arestyrurj-165	192	15	,	,	PUNCT
arestyrurj-165	192	16	&	&	CCONJ
arestyrurj-165	192	17	tibshirani	tibshirani	PROPN
arestyrurj-165	192	18	,	,	PUNCT
arestyrurj-165	192	19	r.	r.	PROPN
arestyrurj-165	192	20	(	(	PUNCT
arestyrurj-165	192	21	2013	2013	NUM
arestyrurj-165	192	22	)	)	PUNCT
arestyrurj-165	192	23	.	.	PUNCT
arestyrurj-165	193	1	an	an	DET
arestyrurj-165	193	2	introduction	introduction	NOUN
arestyrurj-165	193	3	to	to	ADP
arestyrurj-165	193	4	statistical	statistical	ADJ
arestyrurj-165	193	5	learning	learning	NOUN
arestyrurj-165	193	6	with	with	ADP
arestyrurj-165	193	7	applications	application	NOUN
arestyrurj-165	193	8	in	in	ADP
arestyrurj-165	193	9	r	r	NOUN
arestyrurj-165	193	10	(	(	PUNCT
arestyrurj-165	193	11	1st	1st	ADJ
arestyrurj-165	193	12	ed	ed	NOUN
arestyrurj-165	193	13	.	.	PUNCT
arestyrurj-165	193	14	2013	2013	NUM
arestyrurj-165	193	15	.	.	PUNCT
arestyrurj-165	193	16	)	)	PUNCT
arestyrurj-165	193	17	.	.	PUNCT
arestyrurj-165	194	1	springer	springer	PROPN
arestyrurj-165	194	2	new	new	PROPN
arestyrurj-165	194	3	york	york	PROPN
arestyrurj-165	194	4	.	.	PUNCT
arestyrurj-165	195	1	[	[	X
arestyrurj-165	195	2	5	5	NUM
arestyrurj-165	195	3	]	]	X
arestyrurj-165	195	4	jia	jia	PROPN
arestyrurj-165	195	5	,	,	PUNCT
arestyrurj-165	195	6	c.	c.	PROPN
arestyrurj-165	195	7	,	,	PUNCT
arestyrurj-165	195	8	kong	kong	PROPN
arestyrurj-165	195	9	,	,	PUNCT
arestyrurj-165	195	10	y.	y.	PROPN
arestyrurj-165	195	11	,	,	PUNCT
arestyrurj-165	195	12	ding	ding	NOUN
arestyrurj-165	195	13	,	,	PUNCT
arestyrurj-165	195	14	z.	z.	PROPN
arestyrurj-165	195	15	,	,	PUNCT
arestyrurj-165	195	16	&	&	CCONJ
arestyrurj-165	195	17	fu	fu	PROPN
arestyrurj-165	195	18	,	,	PUNCT
arestyrurj-165	195	19	y.	y.	PROPN
arestyrurj-165	195	20	(	(	PUNCT
arestyrurj-165	195	21	2014	2014	NUM
arestyrurj-165	195	22	)	)	PUNCT
arestyrurj-165	195	23	.	.	PUNCT
arestyrurj-165	196	1	latent	latent	NOUN
arestyrurj-165	196	2	tensor	tensor	NOUN
arestyrurj-165	196	3	transfer	transfer	NOUN
arestyrurj-165	196	4	learning	learning	NOUN
arestyrurj-165	196	5	for	for	ADP
arestyrurj-165	196	6	rgb	rgb	PROPN
arestyrurj-165	196	7	-	-	PROPN
arestyrurj-165	196	8	d	d	PROPN
arestyrurj-165	196	9	action	action	NOUN
arestyrurj-165	196	10	recognition	recognition	NOUN
arestyrurj-165	196	11	.	.	PUNCT
arestyrurj-165	197	1	proceedings	proceeding	NOUN
arestyrurj-165	197	2	of	of	ADP
arestyrurj-165	197	3	the	the	DET
arestyrurj-165	197	4	22nd	22nd	PROPN
arestyrurj-165	197	5	acm	acm	PROPN
arestyrurj-165	197	6	international	international	ADJ
arestyrurj-165	197	7	conference	conference	NOUN
arestyrurj-165	197	8	on	on	ADP
arestyrurj-165	197	9	multimedia	multimedia	NOUN
arestyrurj-165	197	10	,	,	PUNCT
arestyrurj-165	197	11	87–96	87–96	NUM
arestyrurj-165	197	12	.	.	PUNCT
arestyrurj-165	198	1	[	[	X
arestyrurj-165	198	2	6	6	NUM
arestyrurj-165	198	3	]	]	SYM
arestyrurj-165	198	4	kolda	kolda	NOUN
arestyrurj-165	198	5	,	,	PUNCT
arestyrurj-165	198	6	t.	t.	PROPN
arestyrurj-165	198	7	g.	g.	PROPN
arestyrurj-165	198	8	,	,	PUNCT
arestyrurj-165	198	9	&	&	CCONJ
arestyrurj-165	198	10	bader	bader	PROPN
arestyrurj-165	198	11	,	,	PUNCT
arestyrurj-165	198	12	b.	b.	PROPN
arestyrurj-165	198	13	w.	w.	PROPN
arestyrurj-165	198	14	(	(	PUNCT
arestyrurj-165	198	15	2009	2009	NUM
arestyrurj-165	198	16	)	)	PUNCT
arestyrurj-165	198	17	.	.	PUNCT
arestyrurj-165	199	1	tensor	tensor	NOUN
arestyrurj-165	199	2	decompositions	decomposition	NOUN
arestyrurj-165	199	3	and	and	CCONJ
arestyrurj-165	199	4	applications	application	NOUN
arestyrurj-165	199	5	.	.	PUNCT
arestyrurj-165	200	1	siam	siam	PROPN
arestyrurj-165	200	2	review	review	PROPN
arestyrurj-165	200	3	,	,	PUNCT
arestyrurj-165	200	4	51(3	51(3	NUM
arestyrurj-165	200	5	)	)	PUNCT
arestyrurj-165	200	6	,	,	PUNCT
arestyrurj-165	200	7	455–500	455–500	NUM
arestyrurj-165	200	8	.	.	PUNCT
arestyrurj-165	201	1	[	[	X
arestyrurj-165	201	2	7	7	NUM
arestyrurj-165	201	3	]	]	X
arestyrurj-165	201	4	kossaifi	kossaifi	PROPN
arestyrurj-165	201	5	,	,	PUNCT
arestyrurj-165	201	6	j.	j.	PROPN
arestyrurj-165	201	7	,	,	PUNCT
arestyrurj-165	201	8	panagakis	panagakis	PROPN
arestyrurj-165	201	9	,	,	PUNCT
arestyrurj-165	201	10	y.	y.	PROPN
arestyrurj-165	201	11	,	,	PUNCT
arestyrurj-165	201	12	anandkumar	anandkumar	PROPN
arestyrurj-165	201	13	,	,	PUNCT
arestyrurj-165	201	14	a.	a.	NOUN
arestyrurj-165	201	15	,	,	PUNCT
arestyrurj-165	201	16	&	&	CCONJ
arestyrurj-165	201	17	pantic	pantic	PROPN
arestyrurj-165	201	18	,	,	PUNCT
arestyrurj-165	201	19	m.	m.	NOUN
arestyrurj-165	201	20	(	(	PUNCT
arestyrurj-165	201	21	2019	2019	NUM
arestyrurj-165	201	22	)	)	PUNCT
arestyrurj-165	201	23	.	.	PUNCT
arestyrurj-165	202	1	tensorly	tensorly	ADV
arestyrurj-165	202	2	:	:	PUNCT
arestyrurj-165	202	3	tensor	tensor	NOUN
arestyrurj-165	202	4	learning	learning	NOUN
arestyrurj-165	202	5	in	in	ADP
arestyrurj-165	202	6	python	python	PROPN
arestyrurj-165	202	7	.	.	PUNCT
arestyrurj-165	203	1	journal	journal	PROPN
arestyrurj-165	203	2	of	of	ADP
arestyrurj-165	203	3	machine	machine	NOUN
arestyrurj-165	203	4	learning	learn	VERB
arestyrurj-165	203	5	research	research	NOUN
arestyrurj-165	203	6	,	,	PUNCT
arestyrurj-165	203	7	20	20	NUM
arestyrurj-165	203	8	.	.	PUNCT
arestyrurj-165	204	1	[	[	X
arestyrurj-165	204	2	8	8	NUM
arestyrurj-165	204	3	]	]	X
arestyrurj-165	204	4	kreimer	kreimer	X
arestyrurj-165	204	5	,	,	PUNCT
arestyrurj-165	204	6	n.	n.	PROPN
arestyrurj-165	204	7	,	,	PUNCT
arestyrurj-165	204	8	stanton	stanton	PROPN
arestyrurj-165	204	9	,	,	PUNCT
arestyrurj-165	204	10	a.	a.	PROPN
arestyrurj-165	204	11	,	,	PUNCT
arestyrurj-165	204	12	&	&	CCONJ
arestyrurj-165	204	13	sacchi	sacchi	PROPN
arestyrurj-165	204	14	,	,	PUNCT
arestyrurj-165	204	15	m.	m.	PROPN
arestyrurj-165	204	16	d.	d.	PROPN
arestyrurj-165	204	17	(	(	PUNCT
arestyrurj-165	204	18	2013	2013	NUM
arestyrurj-165	204	19	)	)	PUNCT
arestyrurj-165	204	20	.	.	PUNCT
arestyrurj-165	205	1	tensor	tensor	NOUN
arestyrurj-165	205	2	completion	completion	NOUN
arestyrurj-165	205	3	based	base	VERB
arestyrurj-165	205	4	on	on	ADP
arestyrurj-165	205	5	nuclear	nuclear	ADJ
arestyrurj-165	205	6	norm	norm	NOUN
arestyrurj-165	205	7	minimization	minimization	NOUN
arestyrurj-165	205	8	for	for	ADP
arestyrurj-165	205	9	5d	5d	NUM
arestyrurj-165	205	10	seismic	seismic	ADJ
arestyrurj-165	205	11	data	datum	NOUN
arestyrurj-165	205	12	reconstruction	reconstruction	NOUN
arestyrurj-165	205	13	.	.	PUNCT
arestyrurj-165	206	1	geophysics	geophysic	NOUN
arestyrurj-165	206	2	,	,	PUNCT
arestyrurj-165	206	3	78(6	78(6	NOUN
arestyrurj-165	206	4	)	)	PUNCT
arestyrurj-165	206	5	,	,	PUNCT
arestyrurj-165	206	6	v273	v273	PROPN
arestyrurj-165	206	7	–	–	PUNCT
arestyrurj-165	206	8	v284	v284	NUM
arestyrurj-165	206	9	.	.	PUNCT
arestyrurj-165	207	1	[	[	X
arestyrurj-165	207	2	9	9	NUM
arestyrurj-165	207	3	]	]	SYM
arestyrurj-165	207	4	lecun	lecun	ADJ
arestyrurj-165	207	5	,	,	PUNCT
arestyrurj-165	207	6	y.	y.	PROPN
arestyrurj-165	207	7	,	,	PUNCT
arestyrurj-165	207	8	bottou	bottou	PROPN
arestyrurj-165	207	9	,	,	PUNCT
arestyrurj-165	207	10	l.	l.	PROPN
arestyrurj-165	207	11	,	,	PUNCT
arestyrurj-165	207	12	bengio	bengio	PROPN
arestyrurj-165	207	13	,	,	PUNCT
arestyrurj-165	207	14	y.	y.	PROPN
arestyrurj-165	207	15	,	,	PUNCT
arestyrurj-165	207	16	&	&	CCONJ
arestyrurj-165	207	17	haffner	haffner	PROPN
arestyrurj-165	207	18	,	,	PUNCT
arestyrurj-165	207	19	p.	p.	NOUN
arestyrurj-165	207	20	(	(	PUNCT
arestyrurj-165	207	21	1998	1998	NUM
arestyrurj-165	207	22	)	)	PUNCT
arestyrurj-165	207	23	.	.	PUNCT
arestyrurj-165	208	1	gradient	gradient	NOUN
arestyrurj-165	208	2	-	-	PUNCT
arestyrurj-165	208	3	based	base	VERB
arestyrurj-165	208	4	learning	learning	NOUN
arestyrurj-165	208	5	applied	apply	VERB
arestyrurj-165	208	6	to	to	ADP
arestyrurj-165	208	7	document	document	NOUN
arestyrurj-165	208	8	recognition	recognition	NOUN
arestyrurj-165	208	9	.	.	PUNCT
arestyrurj-165	209	1	proceedings	proceeding	NOUN
arestyrurj-165	209	2	of	of	ADP
arestyrurj-165	209	3	the	the	DET
arestyrurj-165	209	4	ieee	ieee	NOUN
arestyrurj-165	209	5	,	,	PUNCT
arestyrurj-165	209	6	86(11	86(11	NUM
arestyrurj-165	209	7	)	)	PUNCT
arestyrurj-165	209	8	,	,	PUNCT
arestyrurj-165	209	9	2278–2324	2278–2324	NUM
arestyrurj-165	209	10	.	.	PUNCT
arestyrurj-165	210	1	[	[	X
arestyrurj-165	210	2	10	10	NUM
arestyrurj-165	210	3	]	]	X
arestyrurj-165	210	4	li	li	PROPN
arestyrurj-165	210	5	,	,	PUNCT
arestyrurj-165	210	6	x.	x.	PROPN
arestyrurj-165	210	7	,	,	PUNCT
arestyrurj-165	210	8	xu	xu	PROPN
arestyrurj-165	210	9	,	,	PUNCT
arestyrurj-165	210	10	d.	d.	PROPN
arestyrurj-165	210	11	,	,	PUNCT
arestyrurj-165	210	12	zhou	zhou	PROPN
arestyrurj-165	210	13	,	,	PUNCT
arestyrurj-165	210	14	h.	h.	PROPN
arestyrurj-165	210	15	,	,	PUNCT
arestyrurj-165	210	16	&	&	CCONJ
arestyrurj-165	210	17	li	li	PROPN
arestyrurj-165	210	18	,	,	PUNCT
arestyrurj-165	210	19	l.	l.	PROPN
arestyrurj-165	210	20	(	(	PUNCT
arestyrurj-165	210	21	2018	2018	NUM
arestyrurj-165	210	22	)	)	PUNCT
arestyrurj-165	210	23	.	.	PUNCT
arestyrurj-165	211	1	tucker	tucker	PROPN
arestyrurj-165	211	2	tensor	tensor	NOUN
arestyrurj-165	211	3	regression	regression	NOUN
arestyrurj-165	211	4	and	and	CCONJ
arestyrurj-165	211	5	neuroimaging	neuroimage	VERB
arestyrurj-165	211	6	analysis	analysis	NOUN
arestyrurj-165	211	7	.	.	PUNCT
arestyrurj-165	212	1	statistics	statistic	NOUN
arestyrurj-165	212	2	in	in	ADP
arestyrurj-165	212	3	biosciences	bioscience	NOUN
arestyrurj-165	212	4	,	,	PUNCT
arestyrurj-165	212	5	10(3	10(3	NUM
arestyrurj-165	212	6	)	)	PUNCT
arestyrurj-165	212	7	,	,	PUNCT
arestyrurj-165	212	8	520–545	520–545	NUM
arestyrurj-165	212	9	.	.	PUNCT
arestyrurj-165	213	1	[	[	X
arestyrurj-165	213	2	11	11	NUM
arestyrurj-165	213	3	]	]	SYM
arestyrurj-165	213	4	li	li	PROPN
arestyrurj-165	213	5	,	,	PUNCT
arestyrurj-165	213	6	y.	y.	PROPN
arestyrurj-165	213	7	,	,	PUNCT
arestyrurj-165	213	8	zhu	zhu	PROPN
arestyrurj-165	213	9	,	,	PUNCT
arestyrurj-165	213	10	h.	h.	PROPN
arestyrurj-165	213	11	,	,	PUNCT
arestyrurj-165	213	12	shen	shen	PROPN
arestyrurj-165	213	13	,	,	PUNCT
arestyrurj-165	213	14	d.	d.	PROPN
arestyrurj-165	213	15	,	,	PUNCT
arestyrurj-165	213	16	lin	lin	PROPN
arestyrurj-165	213	17	,	,	PUNCT
arestyrurj-165	213	18	w.	w.	PROPN
arestyrurj-165	213	19	,	,	PUNCT
arestyrurj-165	213	20	gilmore	gilmore	PROPN
arestyrurj-165	213	21	,	,	PUNCT
arestyrurj-165	213	22	j.	j.	PROPN
arestyrurj-165	213	23	h.	h.	PROPN
arestyrurj-165	213	24	,	,	PUNCT
arestyrurj-165	213	25	&	&	CCONJ
arestyrurj-165	213	26	ibrahim	ibrahim	PROPN
arestyrurj-165	213	27	,	,	PUNCT
arestyrurj-165	213	28	j.	j.	PROPN
arestyrurj-165	213	29	g.	g.	PROPN
arestyrurj-165	213	30	(	(	PUNCT
arestyrurj-165	213	31	2011	2011	NUM
arestyrurj-165	213	32	)	)	PUNCT
arestyrurj-165	213	33	.	.	PUNCT
arestyrurj-165	214	1	multiscale	multiscale	ADJ
arestyrurj-165	214	2	adaptive	adaptive	ADJ
arestyrurj-165	214	3	regression	regression	NOUN
arestyrurj-165	214	4	models	model	NOUN
arestyrurj-165	214	5	for	for	ADP
arestyrurj-165	214	6	neuroimaging	neuroimaging	ADJ
arestyrurj-165	214	7	data	datum	NOUN
arestyrurj-165	214	8	:	:	PUNCT
arestyrurj-165	214	9	multiscale	multiscale	ADJ
arestyrurj-165	214	10	adaptive	adaptive	ADJ
arestyrurj-165	214	11	regression	regression	NOUN
arestyrurj-165	214	12	models	model	NOUN
arestyrurj-165	214	13	.	.	PUNCT
arestyrurj-165	215	1	journal	journal	NOUN
arestyrurj-165	215	2	of	of	ADP
arestyrurj-165	215	3	the	the	DET
arestyrurj-165	215	4	royal	royal	ADJ
arestyrurj-165	215	5	statistical	statistical	ADJ
arestyrurj-165	215	6	society	society	NOUN
arestyrurj-165	215	7	.	.	PUNCT
arestyrurj-165	216	1	series	series	PROPN
arestyrurj-165	216	2	b	b	PROPN
arestyrurj-165	216	3	,	,	PUNCT
arestyrurj-165	216	4	statistical	statistical	ADJ
arestyrurj-165	216	5	methodology	methodology	NOUN
arestyrurj-165	216	6	,	,	PUNCT
arestyrurj-165	216	7	73(4	73(4	NOUN
arestyrurj-165	216	8	)	)	PUNCT
arestyrurj-165	216	9	,	,	PUNCT
arestyrurj-165	216	10	559–578	559–578	NUM
arestyrurj-165	216	11	.	.	PUNCT
arestyrurj-165	217	1	[	[	X
arestyrurj-165	217	2	12	12	NUM
arestyrurj-165	217	3	]	]	X
arestyrurj-165	217	4	nguyen	nguyen	NOUN
arestyrurj-165	217	5	,	,	PUNCT
arestyrurj-165	217	6	h.	h.	PROPN
arestyrurj-165	217	7	v.	v.	PROPN
arestyrurj-165	217	8	,	,	PUNCT
arestyrurj-165	217	9	&	&	CCONJ
arestyrurj-165	217	10	bai	bai	PROPN
arestyrurj-165	217	11	,	,	PUNCT
arestyrurj-165	217	12	l.	l.	PROPN
arestyrurj-165	217	13	(	(	PUNCT
arestyrurj-165	217	14	2011	2011	NUM
arestyrurj-165	217	15	)	)	PUNCT
arestyrurj-165	217	16	.	.	PUNCT
arestyrurj-165	218	1	cosine	cosine	NOUN
arestyrurj-165	218	2	similarity	similarity	PROPN
arestyrurj-165	218	3	metric	metric	ADJ
arestyrurj-165	218	4	learning	learning	NOUN
arestyrurj-165	218	5	for	for	ADP
arestyrurj-165	218	6	face	face	NOUN
arestyrurj-165	218	7	verification	verification	NOUN
arestyrurj-165	218	8	.	.	PUNCT
arestyrurj-165	219	1	in	in	ADP
arestyrurj-165	219	2	computer	computer	NOUN
arestyrurj-165	219	3	vision	vision	NOUN
arestyrurj-165	219	4	–	–	PUNCT
arestyrurj-165	219	5	accv	accv	NOUN
arestyrurj-165	219	6	2010	2010	NUM
arestyrurj-165	219	7	(	(	PUNCT
arestyrurj-165	219	8	vol	vol	NOUN
arestyrurj-165	219	9	.	.	PUNCT
arestyrurj-165	219	10	6493	6493	NUM
arestyrurj-165	219	11	,	,	PUNCT
arestyrurj-165	219	12	issue	issue	NOUN
arestyrurj-165	219	13	2	2	NUM
arestyrurj-165	219	14	,	,	PUNCT
arestyrurj-165	219	15	pp	pp	ADJ
arestyrurj-165	219	16	.	.	PUNCT
arestyrurj-165	220	1	709–720	709–720	NUM
arestyrurj-165	220	2	)	)	PUNCT
arestyrurj-165	220	3	.	.	PUNCT
arestyrurj-165	221	1	springer	springer	PROPN
arestyrurj-165	221	2	berlin	berlin	PROPN
arestyrurj-165	221	3	heidelberg	heidelberg	PROPN
arestyrurj-165	221	4	.	.	PUNCT
arestyrurj-165	222	1	[	[	X
arestyrurj-165	222	2	13	13	NUM
arestyrurj-165	222	3	]	]	SYM
arestyrurj-165	222	4	o’donnell	o’donnell	PROPN
arestyrurj-165	222	5	,	,	PUNCT
arestyrurj-165	222	6	l.	l.	PROPN
arestyrurj-165	222	7	j.	j.	PROPN
arestyrurj-165	222	8	,	,	PUNCT
arestyrurj-165	222	9	&	&	CCONJ
arestyrurj-165	222	10	westin	westin	PROPN
arestyrurj-165	222	11	,	,	PUNCT
arestyrurj-165	222	12	c.-f	c.-f	NOUN
arestyrurj-165	222	13	.	.	PUNCT
arestyrurj-165	223	1	(	(	PUNCT
arestyrurj-165	223	2	2011	2011	NUM
arestyrurj-165	223	3	)	)	PUNCT
arestyrurj-165	223	4	.	.	PUNCT
arestyrurj-165	224	1	an	an	DET
arestyrurj-165	224	2	introduction	introduction	NOUN
arestyrurj-165	224	3	to	to	ADP
arestyrurj-165	224	4	diffusion	diffusion	NOUN
arestyrurj-165	224	5	tensor	tensor	NOUN
arestyrurj-165	224	6	image	image	NOUN
arestyrurj-165	224	7	analysis	analysis	NOUN
arestyrurj-165	224	8	.	.	PUNCT
arestyrurj-165	225	1	neurosurgery	neurosurgery	ADJ
arestyrurj-165	225	2	clinics	clinic	NOUN
arestyrurj-165	225	3	of	of	ADP
arestyrurj-165	225	4	north	north	PROPN
arestyrurj-165	225	5	america	america	PROPN
arestyrurj-165	225	6	,	,	PUNCT
arestyrurj-165	225	7	22(2	22(2	NUM
arestyrurj-165	225	8	)	)	PUNCT
arestyrurj-165	225	9	,	,	PUNCT
arestyrurj-165	225	10	185–196	185–196	NUM
arestyrurj-165	225	11	.	.	PUNCT
arestyrurj-165	226	1	[	[	X
arestyrurj-165	226	2	14	14	NUM
arestyrurj-165	226	3	]	]	SYM
arestyrurj-165	226	4	rabanser	rabanser	NOUN
arestyrurj-165	226	5	,	,	PUNCT
arestyrurj-165	226	6	s.	s.	PROPN
arestyrurj-165	226	7	,	,	PUNCT
arestyrurj-165	226	8	shchur	shchur	ADJ
arestyrurj-165	226	9	,	,	PUNCT
arestyrurj-165	226	10	o.	o.	PROPN
arestyrurj-165	226	11	,	,	PUNCT
arestyrurj-165	226	12	&	&	CCONJ
arestyrurj-165	226	13	günnemann	günnemann	PROPN
arestyrurj-165	226	14	,	,	PUNCT
arestyrurj-165	226	15	s.	s.	PROPN
arestyrurj-165	226	16	(	(	PUNCT
arestyrurj-165	226	17	2017	2017	NUM
arestyrurj-165	226	18	)	)	PUNCT
arestyrurj-165	226	19	.	.	PUNCT
arestyrurj-165	227	1	introduction	introduction	NOUN
arestyrurj-165	227	2	to	to	ADP
arestyrurj-165	227	3	tensor	tensor	NOUN
arestyrurj-165	227	4	decompositions	decomposition	NOUN
arestyrurj-165	227	5	and	and	CCONJ
arestyrurj-165	227	6	their	their	PRON
arestyrurj-165	227	7	applications	application	NOUN
arestyrurj-165	227	8	in	in	ADP
arestyrurj-165	227	9	machine	machine	NOUN
arestyrurj-165	227	10	learning	learning	NOUN
arestyrurj-165	227	11	.	.	PUNCT
arestyrurj-165	228	1	[	[	X
arestyrurj-165	228	2	15	15	NUM
arestyrurj-165	228	3	]	]	X
arestyrurj-165	228	4	tan	tan	PROPN
arestyrurj-165	228	5	,	,	PUNCT
arestyrurj-165	228	6	x.	x.	PROPN
arestyrurj-165	228	7	,	,	PUNCT
arestyrurj-165	228	8	zhang	zhang	PROPN
arestyrurj-165	228	9	,	,	PUNCT
arestyrurj-165	228	10	y.	y.	PROPN
arestyrurj-165	228	11	,	,	PUNCT
arestyrurj-165	228	12	tang	tang	PROPN
arestyrurj-165	228	13	,	,	PUNCT
arestyrurj-165	228	14	s.	s.	PROPN
arestyrurj-165	228	15	,	,	PUNCT
arestyrurj-165	228	16	shao	shao	PROPN
arestyrurj-165	228	17	,	,	PUNCT
arestyrurj-165	228	18	j.	j.	PROPN
arestyrurj-165	228	19	,	,	PUNCT
arestyrurj-165	228	20	wu	wu	PROPN
arestyrurj-165	228	21	,	,	PUNCT
arestyrurj-165	228	22	f.	f.	PROPN
arestyrurj-165	228	23	,	,	PUNCT
arestyrurj-165	228	24	&	&	CCONJ
arestyrurj-165	228	25	zhuang	zhuang	PROPN
arestyrurj-165	228	26	,	,	PUNCT
arestyrurj-165	228	27	y.	y.	PROPN
arestyrurj-165	228	28	(	(	PUNCT
arestyrurj-165	228	29	2013	2013	NUM
arestyrurj-165	228	30	)	)	PUNCT
arestyrurj-165	228	31	.	.	PUNCT
arestyrurj-165	229	1	logistic	logistic	ADJ
arestyrurj-165	229	2	tensor	tensor	NOUN
arestyrurj-165	229	3	regression	regression	NOUN
arestyrurj-165	229	4	for	for	ADP
arestyrurj-165	229	5	classification	classification	NOUN
arestyrurj-165	229	6	.	.	PUNCT
arestyrurj-165	230	1	in	in	ADP
arestyrurj-165	230	2	intelligent	intelligent	ADJ
arestyrurj-165	230	3	science	science	NOUN
arestyrurj-165	230	4	and	and	CCONJ
arestyrurj-165	230	5	intelligent	intelligent	ADJ
arestyrurj-165	230	6	data	datum	NOUN
arestyrurj-165	230	7	engineering	engineering	NOUN
arestyrurj-165	230	8	(	(	PUNCT
arestyrurj-165	230	9	vol	vol	NOUN
arestyrurj-165	230	10	.	.	PROPN
arestyrurj-165	230	11	7751	7751	NUM
arestyrurj-165	230	12	,	,	PUNCT
arestyrurj-165	230	13	pp	pp	ADV
arestyrurj-165	230	14	.	.	PUNCT
arestyrurj-165	231	1	573–581	573–581	NUM
arestyrurj-165	231	2	)	)	PUNCT
arestyrurj-165	231	3	.	.	PUNCT
arestyrurj-165	232	1	springer	springer	PROPN
arestyrurj-165	232	2	berlin	berlin	PROPN
arestyrurj-165	232	3	heidelberg	heidelberg	PROPN
arestyrurj-165	232	4	.	.	PUNCT
arestyrurj-165	233	1	[	[	X
arestyrurj-165	233	2	16	16	NUM
arestyrurj-165	233	3	]	]	PUNCT
arestyrurj-165	233	4	tomioka	tomioka	NOUN
arestyrurj-165	233	5	,	,	PUNCT
arestyrurj-165	233	6	r.	r.	PROPN
arestyrurj-165	233	7	,	,	PUNCT
arestyrurj-165	233	8	&	&	CCONJ
arestyrurj-165	233	9	suzuki	suzuki	PROPN
arestyrurj-165	233	10	,	,	PUNCT
arestyrurj-165	233	11	t.	t.	PROPN
arestyrurj-165	233	12	(	(	PUNCT
arestyrurj-165	233	13	2013	2013	NUM
arestyrurj-165	233	14	)	)	PUNCT
arestyrurj-165	233	15	.	.	PUNCT
arestyrurj-165	234	1	convex	convex	PROPN
arestyrurj-165	234	2	tensor	tensor	NOUN
arestyrurj-165	234	3	decomposition	decomposition	NOUN
arestyrurj-165	234	4	via	via	ADP
arestyrurj-165	234	5	structured	structure	VERB
arestyrurj-165	234	6	schatten	schatten	ADJ
arestyrurj-165	234	7	norm	norm	NOUN
arestyrurj-165	234	8	regularization	regularization	NOUN
arestyrurj-165	234	9	.	.	PUNCT
arestyrurj-165	235	1	[	[	X
arestyrurj-165	235	2	17	17	NUM
arestyrurj-165	235	3	]	]	X
arestyrurj-165	235	4	virtanen	virtanen	NOUN
arestyrurj-165	235	5	,	,	PUNCT
arestyrurj-165	235	6	p.	p.	NOUN
arestyrurj-165	235	7	,	,	PUNCT
arestyrurj-165	235	8	gommers	gommer	NOUN
arestyrurj-165	235	9	,	,	PUNCT
arestyrurj-165	235	10	r.	r.	PROPN
arestyrurj-165	235	11	,	,	PUNCT
arestyrurj-165	235	12	oliphant	oliphant	PROPN
arestyrurj-165	235	13	,	,	PUNCT
arestyrurj-165	235	14	t.	t.	PROPN
arestyrurj-165	235	15	e.	e.	PROPN
arestyrurj-165	235	16	,	,	PUNCT
arestyrurj-165	235	17	haberland	haberland	PROPN
arestyrurj-165	235	18	,	,	PUNCT
arestyrurj-165	235	19	m.	m.	NOUN
arestyrurj-165	235	20	,	,	PUNCT
arestyrurj-165	235	21	reddy	reddy	PROPN
arestyrurj-165	235	22	,	,	PUNCT
arestyrurj-165	235	23	t.	t.	PROPN
arestyrurj-165	235	24	,	,	PUNCT
arestyrurj-165	235	25	cournapeau	cournapeau	PROPN
arestyrurj-165	235	26	,	,	PUNCT
arestyrurj-165	235	27	d.	d.	PROPN
arestyrurj-165	235	28	,	,	PUNCT
arestyrurj-165	235	29	burovski	burovski	PROPN
arestyrurj-165	235	30	,	,	PUNCT
arestyrurj-165	235	31	e.	e.	PROPN
arestyrurj-165	235	32	,	,	PUNCT
arestyrurj-165	235	33	peterson	peterson	PROPN
arestyrurj-165	235	34	,	,	PUNCT
arestyrurj-165	235	35	p.	p.	PROPN
arestyrurj-165	235	36	,	,	PUNCT
arestyrurj-165	235	37	weckesser	weckesser	PROPN
arestyrurj-165	235	38	,	,	PUNCT
arestyrurj-165	235	39	w.	w.	PROPN
arestyrurj-165	235	40	,	,	PUNCT
arestyrurj-165	235	41	bright	bright	ADJ
arestyrurj-165	235	42	,	,	PUNCT
arestyrurj-165	235	43	j.	j.	PROPN
arestyrurj-165	235	44	,	,	PUNCT
arestyrurj-165	235	45	van	van	PROPN
arestyrurj-165	235	46	der	der	PROPN
arestyrurj-165	235	47	walt	walt	PROPN
arestyrurj-165	235	48	,	,	PUNCT
arestyrurj-165	235	49	s.	s.	PROPN
arestyrurj-165	235	50	j.	j.	PROPN
arestyrurj-165	235	51	,	,	PUNCT
arestyrurj-165	235	52	brett	brett	PROPN
arestyrurj-165	235	53	,	,	PUNCT
arestyrurj-165	235	54	m.	m.	NOUN
arestyrurj-165	235	55	,	,	PUNCT
arestyrurj-165	235	56	wilson	wilson	PROPN
arestyrurj-165	235	57	,	,	PUNCT
arestyrurj-165	235	58	j.	j.	PROPN
arestyrurj-165	235	59	,	,	PUNCT
arestyrurj-165	235	60	millman	millman	PROPN
arestyrurj-165	235	61	,	,	PUNCT
arestyrurj-165	235	62	k.	k.	PROPN
arestyrurj-165	235	63	j.	j.	PROPN
arestyrurj-165	235	64	,	,	PUNCT
arestyrurj-165	235	65	mayorov	mayorov	PROPN
arestyrurj-165	235	66	,	,	PUNCT
arestyrurj-165	235	67	n.	n.	NOUN
arestyrurj-165	235	68	,	,	PUNCT
arestyrurj-165	235	69	nelson	nelson	PROPN
arestyrurj-165	235	70	,	,	PUNCT
arestyrurj-165	235	71	a.	a.	PROPN
arestyrurj-165	235	72	r.	r.	PROPN
arestyrurj-165	235	73	j.	j.	PROPN
arestyrurj-165	235	74	,	,	PUNCT
arestyrurj-165	235	75	jones	jones	PROPN
arestyrurj-165	235	76	,	,	PUNCT
arestyrurj-165	235	77	e.	e.	PROPN
arestyrurj-165	235	78	,	,	PUNCT
arestyrurj-165	235	79	kern	kern	PROPN
arestyrurj-165	235	80	,	,	PUNCT
arestyrurj-165	235	81	r.	r.	PROPN
arestyrurj-165	235	82	,	,	PUNCT
arestyrurj-165	235	83	larson	larson	PROPN
arestyrurj-165	235	84	,	,	PUNCT
arestyrurj-165	235	85	e.	e.	PROPN
arestyrurj-165	235	86	,	,	PUNCT
arestyrurj-165	235	87	…	…	PUNCT
arestyrurj-165	235	88	moore	moore	PROPN
arestyrurj-165	235	89	,	,	PUNCT
arestyrurj-165	235	90	e.	e.	PROPN
arestyrurj-165	235	91	w.	w.	PROPN
arestyrurj-165	235	92	(	(	PUNCT
arestyrurj-165	235	93	2020	2020	NUM
arestyrurj-165	235	94	)	)	PUNCT
arestyrurj-165	235	95	.	.	PUNCT
arestyrurj-165	236	1	scipy	scipy	PROPN
arestyrurj-165	236	2	1.0	1.0	NUM
arestyrurj-165	236	3	:	:	PUNCT
arestyrurj-165	236	4	fundamental	fundamental	ADJ
arestyrurj-165	236	5	algorithms	algorithm	NOUN
arestyrurj-165	236	6	for	for	ADP
arestyrurj-165	236	7	scientific	scientific	ADJ
arestyrurj-165	236	8	computing	computing	NOUN
arestyrurj-165	236	9	in	in	ADP
arestyrurj-165	236	10	python	python	PROPN
arestyrurj-165	236	11	.	.	PUNCT
arestyrurj-165	237	1	nature	nature	NOUN
arestyrurj-165	237	2	methods	method	NOUN
arestyrurj-165	237	3	,	,	PUNCT
arestyrurj-165	237	4	17(3	17(3	NUM
arestyrurj-165	237	5	)	)	PUNCT
arestyrurj-165	237	6	,	,	PUNCT
arestyrurj-165	237	7	261–272	261–272	NUM
arestyrurj-165	237	8	.	.	PUNCT
arestyrurj-165	238	1	[	[	X
arestyrurj-165	238	2	18	18	NUM
arestyrurj-165	238	3	]	]	X
arestyrurj-165	238	4	weiwei	weiwei	PROPN
arestyrurj-165	238	5	guo	guo	PROPN
arestyrurj-165	238	6	,	,	PUNCT
arestyrurj-165	238	7	kotsia	kotsia	PROPN
arestyrurj-165	238	8	,	,	PUNCT
arestyrurj-165	238	9	i.	i.	PROPN
arestyrurj-165	238	10	,	,	PUNCT
arestyrurj-165	238	11	&	&	CCONJ
arestyrurj-165	238	12	patras	patras	PROPN
arestyrurj-165	238	13	,	,	PUNCT
arestyrurj-165	238	14	i.	i.	PROPN
arestyrurj-165	238	15	(	(	PUNCT
arestyrurj-165	238	16	2012	2012	NUM
arestyrurj-165	238	17	)	)	PUNCT
arestyrurj-165	238	18	.	.	PUNCT
arestyrurj-165	239	1	tensor	tensor	NOUN
arestyrurj-165	239	2	learning	learn	VERB
arestyrurj-165	239	3	for	for	ADP
arestyrurj-165	239	4	regression	regression	NOUN
arestyrurj-165	239	5	.	.	PUNCT
arestyrurj-165	240	1	ieee	ieee	NOUN
arestyrurj-165	240	2	transactions	transaction	NOUN
arestyrurj-165	240	3	on	on	ADP
arestyrurj-165	240	4	image	image	NOUN
arestyrurj-165	240	5	processing	processing	NOUN
arestyrurj-165	240	6	,	,	PUNCT
arestyrurj-165	240	7	21(2	21(2	NUM
arestyrurj-165	240	8	)	)	PUNCT
arestyrurj-165	240	9	,	,	PUNCT
arestyrurj-165	240	10	816–827	816–827	NUM
arestyrurj-165	240	11	.	.	PUNCT
arestyrurj-165	241	1	[	[	X
arestyrurj-165	241	2	19	19	NUM
arestyrurj-165	241	3	]	]	X
arestyrurj-165	241	4	wimalawarne	wimalawarne	NOUN
arestyrurj-165	241	5	,	,	PUNCT
arestyrurj-165	241	6	k.	k.	PROPN
arestyrurj-165	241	7	,	,	PUNCT
arestyrurj-165	241	8	tomioka	tomioka	NOUN
arestyrurj-165	241	9	,	,	PUNCT
arestyrurj-165	241	10	r.	r.	PROPN
arestyrurj-165	241	11	,	,	PUNCT
arestyrurj-165	241	12	&	&	CCONJ
arestyrurj-165	241	13	sugiyama	sugiyama	NOUN
arestyrurj-165	241	14	,	,	PUNCT
arestyrurj-165	241	15	m.	m.	NOUN
arestyrurj-165	241	16	(	(	PUNCT
arestyrurj-165	241	17	2016	2016	NUM
arestyrurj-165	241	18	)	)	PUNCT
arestyrurj-165	241	19	.	.	PUNCT
arestyrurj-165	242	1	theoretical	theoretical	ADJ
arestyrurj-165	242	2	and	and	CCONJ
arestyrurj-165	242	3	experimental	experimental	ADJ
arestyrurj-165	242	4	analyses	analysis	NOUN
arestyrurj-165	242	5	of	of	ADP
arestyrurj-165	242	6	tensor	tensor	NOUN
arestyrurj-165	242	7	-	-	PUNCT
arestyrurj-165	242	8	based	base	VERB
arestyrurj-165	242	9	regression	regression	NOUN
arestyrurj-165	242	10	and	and	CCONJ
arestyrurj-165	242	11	classification	classification	NOUN
arestyrurj-165	242	12	.	.	PUNCT
arestyrurj-165	243	1	neural	neural	ADJ
arestyrurj-165	243	2	computation	computation	NOUN
arestyrurj-165	243	3	,	,	PUNCT
arestyrurj-165	243	4	28(4	28(4	NUM
arestyrurj-165	243	5	)	)	PUNCT
arestyrurj-165	243	6	,	,	PUNCT
arestyrurj-165	243	7	686–715	686–715	NUM
arestyrurj-165	243	8	.	.	PUNCT
arestyrurj-165	244	1	[	[	X
arestyrurj-165	244	2	20	20	NUM
arestyrurj-165	244	3	]	]	X
arestyrurj-165	244	4	wright	wright	PROPN
arestyrurj-165	244	5	,	,	PUNCT
arestyrurj-165	244	6	s.	s.	PROPN
arestyrurj-165	244	7	j.	j.	PROPN
arestyrurj-165	244	8	(	(	PUNCT
arestyrurj-165	244	9	2015	2015	NUM
arestyrurj-165	244	10	)	)	PUNCT
arestyrurj-165	244	11	.	.	PUNCT
arestyrurj-165	245	1	coordinate	coordinate	VERB
arestyrurj-165	245	2	descent	descent	NOUN
arestyrurj-165	245	3	algorithms	algorithm	NOUN
arestyrurj-165	245	4	.	.	PUNCT
arestyrurj-165	246	1	mathematical	mathematical	ADJ
arestyrurj-165	246	2	programming	programming	NOUN
arestyrurj-165	246	3	,	,	PUNCT
arestyrurj-165	246	4	151(1	151(1	NUM
arestyrurj-165	246	5	)	)	PUNCT
arestyrurj-165	246	6	,	,	PUNCT
arestyrurj-165	246	7	3–34	3–34	PROPN
arestyrurj-165	246	8	.	.	PUNCT
arestyrurj-165	247	1	[	[	X
arestyrurj-165	247	2	21	21	NUM
arestyrurj-165	247	3	]	]	X
arestyrurj-165	247	4	zhou	zhou	PROPN
arestyrurj-165	247	5	,	,	PUNCT
arestyrurj-165	247	6	h.	h.	PROPN
arestyrurj-165	247	7	,	,	PUNCT
arestyrurj-165	247	8	li	li	PROPN
arestyrurj-165	247	9	,	,	PUNCT
arestyrurj-165	247	10	l.	l.	PROPN
arestyrurj-165	247	11	,	,	PUNCT
arestyrurj-165	247	12	&	&	CCONJ
arestyrurj-165	247	13	zhu	zhu	PROPN
arestyrurj-165	247	14	,	,	PUNCT
arestyrurj-165	247	15	h.	h.	PROPN
arestyrurj-165	247	16	(	(	PUNCT
arestyrurj-165	247	17	2013	2013	NUM
arestyrurj-165	247	18	)	)	PUNCT
arestyrurj-165	247	19	.	.	PUNCT
arestyrurj-165	248	1	tensor	tensor	NOUN
arestyrurj-165	248	2	regression	regression	NOUN
arestyrurj-165	248	3	with	with	ADP
arestyrurj-165	248	4	applications	application	NOUN
arestyrurj-165	248	5	in	in	ADP
arestyrurj-165	248	6	neuroimaging	neuroimage	VERB
arestyrurj-165	248	7	data	datum	NOUN
arestyrurj-165	248	8	analysis	analysis	NOUN
arestyrurj-165	248	9	.	.	PUNCT
arestyrurj-165	249	1	journal	journal	NOUN
arestyrurj-165	249	2	of	of	ADP
arestyrurj-165	249	3	the	the	DET
arestyrurj-165	249	4	american	american	PROPN
arestyrurj-165	249	5	statistical	statistical	PROPN
arestyrurj-165	249	6	association	association	PROPN
arestyrurj-165	249	7	,	,	PUNCT
arestyrurj-165	249	8	108(502	108(502	NUM
arestyrurj-165	249	9	)	)	PUNCT
arestyrurj-165	249	10	,	,	PUNCT
arestyrurj-165	249	11	540–552	540–552	NUM
arestyrurj-165	249	12	.	.	PUNCT
arestyrurj-165	250	1	soo	soo	PROPN
arestyrurj-165	250	2	min	min	PROPN
arestyrurj-165	250	3	kwon	kwon	PROPN
arestyrurj-165	250	4	is	be	AUX
arestyrurj-165	250	5	currently	currently	ADV
arestyrurj-165	250	6	pursuing	pursue	VERB
arestyrurj-165	250	7	a	a	DET
arestyrurj-165	250	8	m.s	m.s	PROPN
arestyrurj-165	250	9	.	.	PROPN
arestyrurj-165	250	10	degree	degree	NOUN
arestyrurj-165	250	11	in	in	ADP
arestyrurj-165	250	12	the	the	DET
arestyrurj-165	250	13	department	department	NOUN
arestyrurj-165	250	14	of	of	ADP
arestyrurj-165	250	15	electrical	electrical	ADJ
arestyrurj-165	250	16	and	and	CCONJ
arestyrurj-165	250	17	computer	computer	NOUN
arestyrurj-165	250	18	engineering	engineering	NOUN
arestyrurj-165	250	19	at	at	ADP
arestyrurj-165	250	20	rutgers	rutger	NOUN
arestyrurj-165	250	21	,	,	PUNCT
arestyrurj-165	250	22	the	the	DET
arestyrurj-165	250	23	state	state	PROPN
arestyrurj-165	250	24	university	university	PROPN
arestyrurj-165	250	25	of	of	ADP
arestyrurj-165	250	26	new	new	PROPN
arestyrurj-165	250	27	jersey	jersey	PROPN
arestyrurj-165	250	28	.	.	PUNCT
arestyrurj-165	251	1	his	his	PRON
arestyrurj-165	251	2	research	research	NOUN
arestyrurj-165	251	3	interests	interest	NOUN
arestyrurj-165	251	4	broadly	broadly	ADV
arestyrurj-165	251	5	lie	lie	VERB
arestyrurj-165	251	6	in	in	ADP
arestyrurj-165	251	7	optimization	optimization	NOUN
arestyrurj-165	251	8	,	,	PUNCT
arestyrurj-165	251	9	multidimensional	multidimensional	ADJ
arestyrurj-165	251	10	(	(	PUNCT
arestyrurj-165	251	11	tensor	tensor	NOUN
arestyrurj-165	251	12	)	)	PUNCT
arestyrurj-165	251	13	data	datum	NOUN
arestyrurj-165	251	14	analysis	analysis	NOUN
arestyrurj-165	251	15	,	,	PUNCT
arestyrurj-165	251	16	differential	differential	NOUN
arestyrurj-165	251	17	privacy	privacy	NOUN
arestyrurj-165	251	18	,	,	PUNCT
arestyrurj-165	251	19	and	and	CCONJ
arestyrurj-165	251	20	distributed	distributed	ADJ
arestyrurj-165	251	21	learning	learning	NOUN
arestyrurj-165	251	22	.	.	PUNCT
arestyrurj-165	252	1	he	he	PRON
arestyrurj-165	252	2	earned	earn	VERB
arestyrurj-165	252	3	his	his	PRON
arestyrurj-165	252	4	b.s	b.s	PROPN
arestyrurj-165	252	5	.	.	PROPN
arestyrurj-165	252	6	degree	degree	NOUN
arestyrurj-165	252	7	in	in	ADP
arestyrurj-165	252	8	electrical	electrical	ADJ
arestyrurj-165	252	9	and	and	CCONJ
arestyrurj-165	252	10	computing	compute	VERB
arestyrurj-165	252	11	engineering	engineering	NOUN
arestyrurj-165	252	12	from	from	ADP
arestyrurj-165	252	13	rutgers	rutgers	PROPN
arestyrurj-165	252	14	university	university	PROPN
arestyrurj-165	252	15	in	in	ADP
arestyrurj-165	252	16	2020	2020	NUM
arestyrurj-165	252	17	.	.	PUNCT
arestyrurj-165	253	1	he	he	PRON
arestyrurj-165	253	2	completed	complete	VERB
arestyrurj-165	253	3	his	his	PRON
arestyrurj-165	253	4	undergraduate	undergraduate	ADJ
arestyrurj-165	253	5	thesis	thesis	NOUN
arestyrurj-165	253	6	under	under	ADP
arestyrurj-165	253	7	supervision	supervision	NOUN
arestyrurj-165	253	8	of	of	ADP
arestyrurj-165	253	9	prof	prof	PROPN
arestyrurj-165	253	10	.	.	PROPN
arestyrurj-165	254	1	anand	anand	PROPN
arestyrurj-165	254	2	d.	d.	PROPN
arestyrurj-165	254	3	sarwate	sarwate	VERB
arestyrurj-165	254	4	on	on	ADP
arestyrurj-165	254	5	tensor	tensor	NOUN
arestyrurj-165	254	6	-	-	PUNCT
arestyrurj-165	254	7	based	base	VERB
arestyrurj-165	254	8	machine	machine	NOUN
arestyrurj-165	254	9	learning	learning	NOUN
arestyrurj-165	254	10	algorithms	algorithm	NOUN
arestyrurj-165	254	11	.	.	PUNCT
arestyrurj-165	255	1	soo	soo	PROPN
arestyrurj-165	255	2	min	min	PROPN
arestyrurj-165	255	3	hopes	hope	VERB
arestyrurj-165	255	4	to	to	PART
arestyrurj-165	255	5	pursue	pursue	VERB
arestyrurj-165	255	6	a	a	DET
arestyrurj-165	255	7	phd	phd	NOUN
arestyrurj-165	255	8	degree	degree	NOUN
arestyrurj-165	255	9	upon	upon	SCONJ
arestyrurj-165	255	10	completion	completion	NOUN
arestyrurj-165	255	11	of	of	ADP
arestyrurj-165	255	12	his	his	PRON
arestyrurj-165	255	13	m.s	m.s	PROPN
arestyrurj-165	255	14	.	.	PROPN
arestyrurj-165	255	15	degree	degree	NOUN
arestyrurj-165	255	16	.	.	PUNCT