id	sid	tid	token	lemma	pos
cana-4230	1	1	communications	communication	NOUN
cana-4230	1	2	on	on	ADP
cana-4230	1	3	applied	apply	VERB
cana-4230	1	4	nonlinear	nonlinear	ADJ
cana-4230	1	5	analysis	analysis	NOUN
cana-4230	1	6	issn	issn	NOUN
cana-4230	1	7	:	:	PUNCT
cana-4230	1	8	1074	1074	NUM
cana-4230	1	9	-	-	PUNCT
cana-4230	1	10	133x	133x	NUM
cana-4230	1	11	vol	vol	NOUN
cana-4230	1	12	32	32	NUM
cana-4230	1	13	no	no	NOUN
cana-4230	1	14	.	.	PUNCT
cana-4230	2	1	8s	8s	PROPN
cana-4230	2	2	(	(	PUNCT
cana-4230	2	3	2025	2025	NUM
cana-4230	2	4	)	)	PUNCT
cana-4230	2	5	893	893	NUM
cana-4230	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	2	7	nonlinear	nonlinear	ADJ
cana-4230	2	8	algebraic	algebraic	ADJ
cana-4230	2	9	topology	topology	NOUN
cana-4230	2	10	:	:	PUNCT
cana-4230	2	11	a	a	DET
cana-4230	2	12	framework	framework	NOUN
cana-4230	2	13	for	for	ADP
cana-4230	2	14	high	high	ADJ
cana-4230	2	15	-	-	PUNCT
cana-4230	2	16	dimensional	dimensional	ADJ
cana-4230	2	17	data	datum	NOUN
cana-4230	2	18	analysis	analysis	NOUN
cana-4230	2	19	dr	dr	PROPN
cana-4230	2	20	.	.	PROPN
cana-4230	2	21	snigdha	snigdha	PROPN
cana-4230	2	22	madhab	madhab	PROPN
cana-4230	2	23	ghosh1	ghosh1	PROPN
cana-4230	2	24	*	*	PUNCT
cana-4230	2	25	,	,	PUNCT
cana-4230	2	26	sarrthak	sarrthak	ADJ
cana-4230	2	27	tripathi2	tripathi2	NOUN
cana-4230	2	28	,	,	PUNCT
cana-4230	2	29	sanjay	sanjay	PROPN
cana-4230	2	30	madaan3	madaan3	PROPN
cana-4230	2	31	,	,	PUNCT
cana-4230	2	32	dr	dr	PROPN
cana-4230	2	33	.	.	PROPN
cana-4230	2	34	sheeja	sheeja	PROPN
cana-4230	2	35	sudheer4	sudheer4	PROPN
cana-4230	2	36	,	,	PUNCT
cana-4230	2	37	gunendra	gunendra	PROPN
cana-4230	2	38	chandra	chandra	PROPN
cana-4230	2	39	das5	das5	PROPN
cana-4230	2	40	,	,	PUNCT
cana-4230	2	41	agin	agin	PROPN
cana-4230	2	42	kumari6	kumari6	PROPN
cana-4230	2	43	,	,	PUNCT
cana-4230	2	44	ritu	ritu	PROPN
cana-4230	2	45	goyal7	goyal7	NOUN
cana-4230	2	46	1*assistant	1*assistant	ADJ
cana-4230	2	47	professor	professor	NOUN
cana-4230	2	48	,	,	PUNCT
cana-4230	2	49	department	department	PROPN
cana-4230	2	50	of	of	ADP
cana-4230	2	51	cse	cse	PROPN
cana-4230	2	52	-	-	PUNCT
cana-4230	2	53	ai	ai	PROPN
cana-4230	2	54	,	,	PUNCT
cana-4230	2	55	brainware	brainware	NOUN
cana-4230	2	56	university	university	NOUN
cana-4230	2	57	,	,	PUNCT
cana-4230	2	58	barasat	barasat	VERB
cana-4230	2	59	,	,	PUNCT
cana-4230	2	60	kolkata	kolkata	PROPN
cana-4230	2	61	,	,	PUNCT
cana-4230	2	62	west	west	ADJ
cana-4230	2	63	bengal	bengal	ADJ
cana-4230	2	64	https://orcid.org/0000-0003-2999-9594	https://orcid.org/0000-0003-2999-9594	NOUN
cana-4230	2	65	.	.	PUNCT
cana-4230	2	66	sm.ghosh.kgp@gmail.com	sm.ghosh.kgp@gmail.com	X
cana-4230	3	1	2senior	2senior	NUM
cana-4230	3	2	software	software	NOUN
cana-4230	3	3	engineer	engineer	NOUN
cana-4230	3	4	,	,	PUNCT
cana-4230	3	5	optum	optum	PROPN
cana-4230	3	6	healthcare	healthcare	PROPN
cana-4230	3	7	,	,	PUNCT
cana-4230	3	8	sarthak.trip99@gmail.com	sarthak.trip99@gmail.com	PROPN
cana-4230	3	9	3department	3department	NUM
cana-4230	3	10	of	of	ADP
cana-4230	3	11	computer	computer	NOUN
cana-4230	3	12	engineering	engineering	NOUN
cana-4230	3	13	and	and	CCONJ
cana-4230	3	14	applications	application	NOUN
cana-4230	3	15	,	,	PUNCT
cana-4230	3	16	gla	gla	PROPN
cana-4230	3	17	university	university	PROPN
cana-4230	3	18	,	,	PUNCT
cana-4230	3	19	mathura	mathura	NOUN
cana-4230	3	20	,	,	PUNCT
cana-4230	3	21	uttar	uttar	PROPN
cana-4230	3	22	pradesh	pradesh	PROPN
cana-4230	3	23	,	,	PUNCT
cana-4230	3	24	india	india	PROPN
cana-4230	3	25	,	,	PUNCT
cana-4230	3	26	sanjaymadaan87@gmail.com	sanjaymadaan87@gmail.com	PROPN
cana-4230	3	27	,	,	PUNCT
cana-4230	3	28	sanjay.madaan@gla.ac.in	sanjay.madaan@gla.ac.in	NOUN
cana-4230	3	29	,	,	PUNCT
cana-4230	3	30	https://orcid.org/0000-0002-3583-0552	https://orcid.org/0000-0002-3583-0552	VERB
cana-4230	3	31	4assistant	4assistant	NUM
cana-4230	3	32	professor	professor	NOUN
cana-4230	3	33	,	,	PUNCT
cana-4230	3	34	department	department	NOUN
cana-4230	3	35	of	of	ADP
cana-4230	3	36	master	master	PROPN
cana-4230	3	37	of	of	ADP
cana-4230	3	38	computer	computer	NOUN
cana-4230	3	39	applications	application	NOUN
cana-4230	3	40	,	,	PUNCT
cana-4230	3	41	easwari	easwari	PROPN
cana-4230	3	42	engineering	engineering	NOUN
cana-4230	3	43	college	college	PROPN
cana-4230	3	44	,	,	PUNCT
cana-4230	3	45	chennai	chennai	PROPN
cana-4230	3	46	,	,	PUNCT
cana-4230	3	47	india	india	PROPN
cana-4230	3	48	,	,	PUNCT
cana-4230	3	49	sheesudheer@gmail.com	sheesudheer@gmail.com	PROPN
cana-4230	4	1	5associate	5associate	PROPN
cana-4230	4	2	professor	professor	NOUN
cana-4230	4	3	,	,	PUNCT
cana-4230	4	4	faculty	faculty	NOUN
cana-4230	4	5	of	of	ADP
cana-4230	4	6	science	science	NOUN
cana-4230	4	7	,	,	PUNCT
cana-4230	4	8	assam	assam	PROPN
cana-4230	4	9	down	down	ADP
cana-4230	4	10	town	town	PROPN
cana-4230	4	11	university	university	PROPN
cana-4230	4	12	,	,	PUNCT
cana-4230	4	13	panikhaiti	panikhaiti	NOUN
cana-4230	4	14	,	,	PUNCT
cana-4230	4	15	guwahati781026	guwahati781026	PROPN
cana-4230	4	16	,	,	PUNCT
cana-4230	4	17	assam	assam	PROPN
cana-4230	4	18	,	,	PUNCT
cana-4230	4	19	india	india	PROPN
cana-4230	4	20	,	,	PUNCT
cana-4230	4	21	gicidas@gmail.com	gicidas@gmail.com	X
cana-4230	4	22	6department	6department	NUM
cana-4230	4	23	of	of	ADP
cana-4230	4	24	mathematics	mathematic	NOUN
cana-4230	4	25	,	,	PUNCT
cana-4230	4	26	chaudhary	chaudhary	PROPN
cana-4230	4	27	bansi	bansi	PROPN
cana-4230	4	28	lal	lal	PROPN
cana-4230	4	29	university	university	PROPN
cana-4230	4	30	,	,	PUNCT
cana-4230	4	31	bhiwani-127021	bhiwani-127021	NOUN
cana-4230	4	32	,	,	PUNCT
cana-4230	4	33	india	india	PROPN
cana-4230	4	34	,	,	PUNCT
cana-4230	4	35	agincblu@gmail.com	agincblu@gmail.com	X
cana-4230	5	1	7department	7department	NUM
cana-4230	5	2	of	of	ADP
cana-4230	5	3	mathematics	mathematic	NOUN
cana-4230	5	4	,	,	PUNCT
cana-4230	5	5	chaudhary	chaudhary	PROPN
cana-4230	5	6	bansi	bansi	PROPN
cana-4230	5	7	lal	lal	PROPN
cana-4230	5	8	university	university	PROPN
cana-4230	5	9	,	,	PUNCT
cana-4230	5	10	bhiwani-127021	bhiwani-127021	NOUN
cana-4230	5	11	,	,	PUNCT
cana-4230	5	12	india	india	PROPN
cana-4230	5	13	,	,	PUNCT
cana-4230	5	14	mona7692@gmail.com	mona7692@gmail.com	NOUN
cana-4230	6	1	article	article	NOUN
cana-4230	6	2	history	history	NOUN
cana-4230	6	3	:	:	PUNCT
cana-4230	6	4	received	receive	VERB
cana-4230	6	5	:	:	PUNCT
cana-4230	6	6	12	12	NUM
cana-4230	6	7	-	-	SYM
cana-4230	6	8	11	11	NUM
cana-4230	6	9	-	-	PUNCT
cana-4230	6	10	2024	2024	NUM
cana-4230	6	11	revised	revise	VERB
cana-4230	6	12	:	:	PUNCT
cana-4230	6	13	15	15	NUM
cana-4230	6	14	-	-	SYM
cana-4230	6	15	12	12	NUM
cana-4230	6	16	-	-	PUNCT
cana-4230	6	17	2024	2024	NUM
cana-4230	6	18	accepted	accept	VERB
cana-4230	6	19	:	:	PUNCT
cana-4230	6	20	11	11	NUM
cana-4230	6	21	-	-	SYM
cana-4230	6	22	01	01	NUM
cana-4230	6	23	-	-	PUNCT
cana-4230	6	24	2025	2025	NUM
cana-4230	6	25	abstract	abstract	NOUN
cana-4230	6	26	:	:	PUNCT
cana-4230	6	27	high	high	ADJ
cana-4230	6	28	-	-	PUNCT
cana-4230	6	29	dimensional	dimensional	ADJ
cana-4230	6	30	data	datum	NOUN
cana-4230	6	31	analysis	analysis	NOUN
cana-4230	6	32	using	use	VERB
cana-4230	6	33	nlat	nlat	NOUN
cana-4230	6	34	shows	show	VERB
cana-4230	6	35	a	a	DET
cana-4230	6	36	new	new	ADJ
cana-4230	6	37	impulse	impulse	NOUN
cana-4230	6	38	in	in	ADP
cana-4230	6	39	the	the	DET
cana-4230	6	40	methods	method	NOUN
cana-4230	6	41	of	of	ADP
cana-4230	6	42	algebraic	algebraic	ADJ
cana-4230	6	43	topology	topology	NOUN
cana-4230	6	44	which	which	PRON
cana-4230	6	45	reveal	reveal	VERB
cana-4230	6	46	specific	specific	ADJ
cana-4230	6	47	features	feature	NOUN
cana-4230	6	48	of	of	ADP
cana-4230	6	49	topological	topological	ADJ
cana-4230	6	50	structures	structure	NOUN
cana-4230	6	51	connected	connect	VERB
cana-4230	6	52	with	with	ADP
cana-4230	6	53	connected	connected	ADJ
cana-4230	6	54	components	component	NOUN
cana-4230	6	55	,	,	PUNCT
cana-4230	6	56	holes	hole	NOUN
cana-4230	6	57	,	,	PUNCT
cana-4230	6	58	and	and	CCONJ
cana-4230	6	59	voids	voids	NOUN
cana-4230	6	60	.	.	PUNCT
cana-4230	7	1	this	this	DET
cana-4230	7	2	work	work	NOUN
cana-4230	7	3	aims	aim	VERB
cana-4230	7	4	to	to	PART
cana-4230	7	5	explore	explore	VERB
cana-4230	7	6	tda	tda	NOUN
cana-4230	7	7	methodologies	methodology	NOUN
cana-4230	7	8	,	,	PUNCT
cana-4230	7	9	with	with	ADP
cana-4230	7	10	focus	focus	NOUN
cana-4230	7	11	on	on	ADP
cana-4230	7	12	persistent	persistent	ADJ
cana-4230	7	13	homology	homology	NOUN
cana-4230	7	14	,	,	PUNCT
cana-4230	7	15	for	for	ADP
cana-4230	7	16	solving	solve	VERB
cana-4230	7	17	a	a	DET
cana-4230	7	18	number	number	NOUN
cana-4230	7	19	of	of	ADP
cana-4230	7	20	issues	issue	NOUN
cana-4230	7	21	arising	arise	VERB
cana-4230	7	22	in	in	ADP
cana-4230	7	23	the	the	DET
cana-4230	7	24	course	course	NOUN
cana-4230	7	25	of	of	ADP
cana-4230	7	26	working	work	VERB
cana-4230	7	27	with	with	ADP
cana-4230	7	28	large	large	ADJ
cana-4230	7	29	,	,	PUNCT
cana-4230	7	30	high	high	ADJ
cana-4230	7	31	-	-	PUNCT
cana-4230	7	32	dimensional	dimensional	ADJ
cana-4230	7	33	data	datum	NOUN
cana-4230	7	34	across	across	ADP
cana-4230	7	35	various	various	ADJ
cana-4230	7	36	disciplines	discipline	NOUN
cana-4230	7	37	including	include	VERB
cana-4230	7	38	biology	biology	NOUN
cana-4230	7	39	,	,	PUNCT
cana-4230	7	40	neuroscience	neuroscience	NOUN
cana-4230	7	41	,	,	PUNCT
cana-4230	7	42	and	and	CCONJ
cana-4230	7	43	machine	machine	NOUN
cana-4230	7	44	learning	learning	NOUN
cana-4230	7	45	.	.	PUNCT
cana-4230	8	1	while	while	SCONJ
cana-4230	8	2	compared	compare	VERB
cana-4230	8	3	with	with	ADP
cana-4230	8	4	the	the	DET
cana-4230	8	5	traditional	traditional	ADJ
cana-4230	8	6	linear	linear	ADJ
cana-4230	8	7	methods	method	NOUN
cana-4230	8	8	of	of	ADP
cana-4230	8	9	dimensionality	dimensionality	NOUN
cana-4230	8	10	reduction	reduction	NOUN
cana-4230	8	11	,	,	PUNCT
cana-4230	8	12	which	which	PRON
cana-4230	8	13	generally	generally	ADV
cana-4230	8	14	leads	lead	VERB
cana-4230	8	15	to	to	ADP
cana-4230	8	16	the	the	DET
cana-4230	8	17	loss	loss	NOUN
cana-4230	8	18	of	of	ADP
cana-4230	8	19	structural	structural	ADJ
cana-4230	8	20	information	information	NOUN
cana-4230	8	21	,	,	PUNCT
cana-4230	8	22	the	the	DET
cana-4230	8	23	al	al	PROPN
cana-4230	8	24	employs	employ	VERB
cana-4230	8	25	algebraic	algebraic	ADJ
cana-4230	8	26	topology	topology	NOUN
cana-4230	8	27	for	for	ADP
cana-4230	8	28	nonlinear	nonlinear	ADJ
cana-4230	8	29	structure	structure	NOUN
cana-4230	8	30	-	-	PUNCT
cana-4230	8	31	preserving	preserve	VERB
cana-4230	8	32	,	,	PUNCT
cana-4230	8	33	making	make	VERB
cana-4230	8	34	it	it	PRON
cana-4230	8	35	feasible	feasible	ADJ
cana-4230	8	36	for	for	ADP
cana-4230	8	37	multi	multi	ADJ
cana-4230	8	38	-	-	ADJ
cana-4230	8	39	scale	scale	ADJ
cana-4230	8	40	and	and	CCONJ
cana-4230	8	41	multi	multi	ADJ
cana-4230	8	42	-	-	ADJ
cana-4230	8	43	dimensional	dimensional	ADJ
cana-4230	8	44	pattern	pattern	NOUN
cana-4230	8	45	analysis	analysis	NOUN
cana-4230	8	46	.	.	PUNCT
cana-4230	9	1	in	in	ADP
cana-4230	9	2	this	this	DET
cana-4230	9	3	paper	paper	NOUN
cana-4230	9	4	,	,	PUNCT
cana-4230	9	5	we	we	PRON
cana-4230	9	6	provide	provide	VERB
cana-4230	9	7	a	a	DET
cana-4230	9	8	detailed	detailed	ADJ
cana-4230	9	9	description	description	NOUN
cana-4230	9	10	of	of	ADP
cana-4230	9	11	how	how	SCONJ
cana-4230	9	12	to	to	PART
cana-4230	9	13	perform	perform	VERB
cana-4230	9	14	tda	tda	NOUN
cana-4230	9	15	for	for	ADP
cana-4230	9	16	highdimensional	highdimensional	ADJ
cana-4230	9	17	data	datum	NOUN
cana-4230	9	18	and	and	CCONJ
cana-4230	9	19	describe	describe	VERB
cana-4230	9	20	computational	computational	ADJ
cana-4230	9	21	packages	package	NOUN
cana-4230	9	22	such	such	ADJ
cana-4230	9	23	as	as	ADP
cana-4230	9	24	ripser	ripser	NOUN
cana-4230	9	25	and	and	CCONJ
cana-4230	9	26	dipha	dipha	PROPN
cana-4230	9	27	,	,	PUNCT
cana-4230	9	28	which	which	PRON
cana-4230	9	29	are	be	AUX
cana-4230	9	30	built	build	VERB
cana-4230	9	31	for	for	ADP
cana-4230	9	32	high	high	ADJ
cana-4230	9	33	-	-	PUNCT
cana-4230	9	34	dimensional	dimensional	ADJ
cana-4230	9	35	data	datum	NOUN
cana-4230	9	36	.	.	PUNCT
cana-4230	10	1	furthermore	furthermore	ADV
cana-4230	10	2	,	,	PUNCT
cana-4230	10	3	we	we	PRON
cana-4230	10	4	analyze	analyze	VERB
cana-4230	10	5	the	the	DET
cana-4230	10	6	opportunity	opportunity	NOUN
cana-4230	10	7	for	for	ADP
cana-4230	10	8	combining	combine	VERB
cana-4230	10	9	tda	tda	NOUN
cana-4230	10	10	with	with	ADP
cana-4230	10	11	machine	machine	NOUN
cana-4230	10	12	learning	learning	NOUN
cana-4230	10	13	models	model	NOUN
cana-4230	10	14	for	for	ADP
cana-4230	10	15	the	the	DET
cana-4230	10	16	improvement	improvement	NOUN
cana-4230	10	17	of	of	ADP
cana-4230	10	18	classification	classification	NOUN
cana-4230	10	19	,	,	PUNCT
cana-4230	10	20	clustering	clustering	NOUN
cana-4230	10	21	,	,	PUNCT
cana-4230	10	22	and	and	CCONJ
cana-4230	10	23	anomaly	anomaly	NOUN
cana-4230	10	24	detection	detection	NOUN
cana-4230	10	25	.	.	PUNCT
cana-4230	11	1	these	these	DET
cana-4230	11	2	techniques	technique	NOUN
cana-4230	11	3	are	be	AUX
cana-4230	11	4	illustrated	illustrate	VERB
cana-4230	11	5	by	by	ADP
cana-4230	11	6	genomics	genomic	NOUN
cana-4230	11	7	and	and	CCONJ
cana-4230	11	8	neuroscience	neuroscience	NOUN
cana-4230	11	9	instances	instance	NOUN
cana-4230	11	10	,	,	PUNCT
cana-4230	11	11	but	but	CCONJ
cana-4230	11	12	talks	talk	NOUN
cana-4230	11	13	raise	raise	VERB
cana-4230	11	14	issues	issue	NOUN
cana-4230	11	15	of	of	ADP
cana-4230	11	16	future	future	ADJ
cana-4230	11	17	computation	computation	NOUN
cana-4230	11	18	,	,	PUNCT
cana-4230	11	19	especially	especially	ADV
cana-4230	11	20	scalability	scalability	NOUN
cana-4230	11	21	and	and	CCONJ
cana-4230	11	22	real	real	ADJ
cana-4230	11	23	-	-	PUNCT
cana-4230	11	24	time	time	NOUN
cana-4230	11	25	.	.	PUNCT
cana-4230	12	1	possible	possible	ADJ
cana-4230	12	2	avenues	avenue	NOUN
cana-4230	12	3	for	for	ADP
cana-4230	12	4	future	future	ADJ
cana-4230	12	5	work	work	NOUN
cana-4230	12	6	include	include	VERB
cana-4230	12	7	creating	create	VERB
cana-4230	12	8	interfaces	interface	NOUN
cana-4230	12	9	to	to	ADP
cana-4230	12	10	tda	tda	NOUN
cana-4230	12	11	tools	tool	NOUN
cana-4230	12	12	that	that	PRON
cana-4230	12	13	are	be	AUX
cana-4230	12	14	even	even	ADV
cana-4230	12	15	easier	easy	ADJ
cana-4230	12	16	to	to	PART
cana-4230	12	17	use	use	VERB
cana-4230	12	18	,	,	PUNCT
cana-4230	12	19	integrating	integrate	VERB
cana-4230	12	20	tda	tda	NOUN
cana-4230	12	21	technology	technology	NOUN
cana-4230	12	22	into	into	ADP
cana-4230	12	23	more	more	ADJ
cana-4230	12	24	common	common	ADJ
cana-4230	12	25	data	datum	NOUN
cana-4230	12	26	analytics	analytic	NOUN
cana-4230	12	27	software	software	NOUN
cana-4230	12	28	,	,	PUNCT
cana-4230	12	29	and	and	CCONJ
cana-4230	12	30	exploring	explore	VERB
cana-4230	12	31	new	new	ADJ
cana-4230	12	32	areas	area	NOUN
cana-4230	12	33	of	of	ADP
cana-4230	12	34	science	science	NOUN
cana-4230	12	35	and	and	CCONJ
cana-4230	12	36	engineering	engineering	NOUN
cana-4230	12	37	such	such	ADJ
cana-4230	12	38	as	as	ADP
cana-4230	12	39	quantum	quantum	NOUN
cana-4230	12	40	computing	computing	NOUN
cana-4230	12	41	and	and	CCONJ
cana-4230	12	42	cryptography	cryptography	NOUN
cana-4230	12	43	.	.	PUNCT
cana-4230	13	1	this	this	DET
cana-4230	13	2	work	work	NOUN
cana-4230	13	3	demonstrates	demonstrate	VERB
cana-4230	13	4	that	that	SCONJ
cana-4230	13	5	nonlinear	nonlinear	ADJ
cana-4230	13	6	algebraic	algebraic	ADJ
cana-4230	13	7	topology	topology	NOUN
cana-4230	13	8	is	be	AUX
cana-4230	13	9	now	now	ADV
cana-4230	13	10	moving	move	VERB
cana-4230	13	11	as	as	ADP
cana-4230	13	12	a	a	DET
cana-4230	13	13	powerful	powerful	ADJ
cana-4230	13	14	approach	approach	NOUN
cana-4230	13	15	for	for	ADP
cana-4230	13	16	high	high	ADJ
cana-4230	13	17	-	-	PUNCT
cana-4230	13	18	dimensional	dimensional	ADJ
cana-4230	13	19	data	datum	NOUN
cana-4230	13	20	analysis	analysis	NOUN
cana-4230	13	21	and	and	CCONJ
cana-4230	13	22	displaying	display	VERB
cana-4230	13	23	that	that	SCONJ
cana-4230	13	24	it	it	PRON
cana-4230	13	25	is	be	AUX
cana-4230	13	26	an	an	DET
cana-4230	13	27	essential	essential	ADJ
cana-4230	13	28	instrument	instrument	NOUN
cana-4230	13	29	for	for	ADP
cana-4230	13	30	scientists	scientist	NOUN
cana-4230	13	31	and	and	CCONJ
cana-4230	13	32	engineers	engineer	NOUN
cana-4230	13	33	who	who	PRON
cana-4230	13	34	searching	search	VERB
cana-4230	13	35	for	for	ADP
cana-4230	13	36	hidden	hidden	ADJ
cana-4230	13	37	structures	structure	NOUN
cana-4230	13	38	of	of	ADP
cana-4230	13	39	a	a	DET
cana-4230	13	40	large	large	ADJ
cana-4230	13	41	number	number	NOUN
cana-4230	13	42	of	of	ADP
cana-4230	13	43	data	datum	NOUN
cana-4230	13	44	in	in	ADP
cana-4230	13	45	a	a	DET
cana-4230	13	46	variety	variety	NOUN
cana-4230	13	47	of	of	ADP
cana-4230	13	48	scientific	scientific	ADJ
cana-4230	13	49	and	and	CCONJ
cana-4230	13	50	engineering	engineering	NOUN
cana-4230	13	51	fields	field	NOUN
cana-4230	13	52	.	.	PUNCT
cana-4230	14	1	mailto:sarthak.trip99@gmail.com	mailto:sarthak.trip99@gmail.com	X
cana-4230	14	2	mailto:sheesudheer@gmail.com	mailto:sheesudheer@gmail.com	X
cana-4230	15	1	mailto:gicidas@gmail.com	mailto:gicidas@gmail.com	X
cana-4230	15	2	mailto:agincblu@gmail.com	mailto:agincblu@gmail.com	X
cana-4230	16	1	mailto:mona7692@gmail.com	mailto:mona7692@gmail.com	X
cana-4230	16	2	communications	communication	NOUN
cana-4230	16	3	on	on	ADP
cana-4230	16	4	applied	apply	VERB
cana-4230	16	5	nonlinear	nonlinear	ADJ
cana-4230	16	6	analysis	analysis	NOUN
cana-4230	16	7	issn	issn	NOUN
cana-4230	16	8	:	:	PUNCT
cana-4230	16	9	1074	1074	NUM
cana-4230	16	10	-	-	PUNCT
cana-4230	16	11	133x	133x	NUM
cana-4230	16	12	vol	vol	NOUN
cana-4230	16	13	32	32	NUM
cana-4230	16	14	no	no	NOUN
cana-4230	16	15	.	.	PUNCT
cana-4230	17	1	8s	8s	PROPN
cana-4230	17	2	(	(	PUNCT
cana-4230	17	3	2025	2025	NUM
cana-4230	17	4	)	)	PUNCT
cana-4230	17	5	894	894	NUM
cana-4230	17	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	17	7	keywords	keyword	NOUN
cana-4230	17	8	:	:	PUNCT
cana-4230	17	9	nonlinear	nonlinear	ADJ
cana-4230	17	10	algebraic	algebraic	PROPN
cana-4230	17	11	topology	topology	NOUN
cana-4230	17	12	,	,	PUNCT
cana-4230	17	13	topological	topological	ADJ
cana-4230	17	14	data	datum	NOUN
cana-4230	17	15	analysis	analysis	NOUN
cana-4230	17	16	(	(	PUNCT
cana-4230	17	17	tda	tda	NOUN
cana-4230	17	18	)	)	PUNCT
cana-4230	17	19	,	,	PUNCT
cana-4230	17	20	highdimensional	highdimensional	ADJ
cana-4230	17	21	data	datum	NOUN
cana-4230	17	22	analysis	analysis	NOUN
cana-4230	17	23	,	,	PUNCT
cana-4230	17	24	persistent	persistent	ADJ
cana-4230	17	25	homology	homology	NOUN
cana-4230	17	26	,	,	PUNCT
cana-4230	17	27	simplicial	simplicial	ADJ
cana-4230	17	28	complexes	complex	NOUN
cana-4230	17	29	,	,	PUNCT
cana-4230	17	30	machine	machine	NOUN
cana-4230	17	31	learning	learn	VERB
cana-4230	17	32	1	1	NUM
cana-4230	17	33	.	.	PUNCT
cana-4230	17	34	introduction	introduction	NOUN
cana-4230	17	35	over	over	ADP
cana-4230	17	36	the	the	DET
cana-4230	17	37	last	last	ADJ
cana-4230	17	38	decade	decade	NOUN
cana-4230	17	39	,	,	PUNCT
cana-4230	17	40	increased	increase	VERB
cana-4230	17	41	availability	availability	NOUN
cana-4230	17	42	and	and	CCONJ
cana-4230	17	43	extension	extension	NOUN
cana-4230	17	44	of	of	ADP
cana-4230	17	45	high	high	ADJ
cana-4230	17	46	-	-	PUNCT
cana-4230	17	47	dimensional	dimensional	ADJ
cana-4230	17	48	data	datum	NOUN
cana-4230	17	49	in	in	ADP
cana-4230	17	50	various	various	ADJ
cana-4230	17	51	areas	area	NOUN
cana-4230	17	52	,	,	PUNCT
cana-4230	17	53	including	include	VERB
cana-4230	17	54	biology	biology	NOUN
cana-4230	17	55	,	,	PUNCT
cana-4230	17	56	physics	physics	NOUN
cana-4230	17	57	,	,	PUNCT
cana-4230	17	58	social	social	ADJ
cana-4230	17	59	sciences	science	NOUN
cana-4230	17	60	,	,	PUNCT
cana-4230	17	61	etc	etc	X
cana-4230	17	62	.	.	X
cana-4230	17	63	,	,	PUNCT
cana-4230	17	64	has	have	AUX
cana-4230	17	65	raised	raise	VERB
cana-4230	17	66	the	the	DET
cana-4230	17	67	need	need	NOUN
cana-4230	17	68	for	for	ADP
cana-4230	17	69	search	search	NOUN
cana-4230	17	70	for	for	ADP
cana-4230	17	71	enhanced	enhanced	ADJ
cana-4230	17	72	models	model	NOUN
cana-4230	17	73	of	of	ADP
cana-4230	17	74	data	datum	NOUN
cana-4230	17	75	analysis	analysis	NOUN
cana-4230	17	76	.	.	PUNCT
cana-4230	18	1	above	above	ADP
cana-4230	18	2	mentioned	mention	VERB
cana-4230	18	3	datasets	dataset	NOUN
cana-4230	18	4	pose	pose	VERB
cana-4230	18	5	certain	certain	ADJ
cana-4230	18	6	difficulties	difficulty	NOUN
cana-4230	18	7	due	due	ADP
cana-4230	18	8	to	to	ADP
cana-4230	18	9	the	the	DET
cana-4230	18	10	‘	'	PUNCT
cana-4230	18	11	curse	curse	NOUN
cana-4230	18	12	of	of	ADP
cana-4230	18	13	dimensionality	dimensionality	NOUN
cana-4230	18	14	,	,	PUNCT
cana-4230	18	15	’	'	PUNCT
cana-4230	18	16	meaning	meaning	NOUN
cana-4230	18	17	,	,	PUNCT
cana-4230	18	18	high	high	ADJ
cana-4230	18	19	-	-	PUNCT
cana-4230	18	20	dimensionality	dimensionality	NOUN
cana-4230	18	21	data	datum	NOUN
cana-4230	18	22	is	be	AUX
cana-4230	18	23	more	more	ADV
cana-4230	18	24	difficult	difficult	ADJ
cana-4230	18	25	to	to	PART
cana-4230	18	26	analyze	analyze	VERB
cana-4230	18	27	and	and	CCONJ
cana-4230	18	28	visualize	visualize	VERB
cana-4230	18	29	.	.	PUNCT
cana-4230	19	1	however	however	ADV
cana-4230	19	2	,	,	PUNCT
cana-4230	19	3	approaches	approach	NOUN
cana-4230	19	4	like	like	ADP
cana-4230	19	5	principal	principal	ADJ
cana-4230	19	6	component	component	NOUN
cana-4230	19	7	analysis	analysis	NOUN
cana-4230	19	8	(	(	PUNCT
cana-4230	19	9	pca	pca	NOUN
cana-4230	19	10	)	)	PUNCT
cana-4230	19	11	and	and	CCONJ
cana-4230	19	12	linear	linear	ADJ
cana-4230	19	13	discriminant	discriminant	ADJ
cana-4230	19	14	analysis	analysis	NOUN
cana-4230	19	15	(	(	PUNCT
cana-4230	19	16	lda	lda	PROPN
cana-4230	19	17	)	)	PUNCT
cana-4230	19	18	,	,	PUNCT
cana-4230	19	19	which	which	PRON
cana-4230	19	20	are	be	AUX
cana-4230	19	21	based	base	VERB
cana-4230	19	22	on	on	ADP
cana-4230	19	23	the	the	DET
cana-4230	19	24	linear	linear	PROPN
cana-4230	19	25	model	model	NOUN
cana-4230	19	26	,	,	PUNCT
cana-4230	19	27	may	may	AUX
cana-4230	19	28	not	not	PART
cana-4230	19	29	capture	capture	VERB
cana-4230	19	30	all	all	DET
cana-4230	19	31	the	the	DET
cana-4230	19	32	scenarios	scenario	NOUN
cana-4230	19	33	that	that	PRON
cana-4230	19	34	may	may	AUX
cana-4230	19	35	exists	exist	VERB
cana-4230	19	36	in	in	ADP
cana-4230	19	37	high	high	ADJ
cana-4230	19	38	-	-	PUNCT
cana-4230	19	39	dimensional	dimensional	ADJ
cana-4230	19	40	data	datum	NOUN
cana-4230	19	41	spaces	space	NOUN
cana-4230	19	42	.	.	PUNCT
cana-4230	20	1	to	to	PART
cana-4230	20	2	tackle	tackle	VERB
cana-4230	20	3	these	these	DET
cana-4230	20	4	challenges	challenge	NOUN
cana-4230	20	5	,	,	PUNCT
cana-4230	20	6	algebraic	algebraic	ADJ
cana-4230	20	7	topology	topology	NOUN
cana-4230	20	8	has	have	AUX
cana-4230	20	9	latterly	latterly	ADV
cana-4230	20	10	become	become	VERB
cana-4230	20	11	an	an	DET
cana-4230	20	12	effective	effective	ADJ
cana-4230	20	13	way	way	NOUN
cana-4230	20	14	of	of	ADP
cana-4230	20	15	mining	mining	NOUN
cana-4230	20	16	patterns	pattern	NOUN
cana-4230	20	17	from	from	ADP
cana-4230	20	18	high	high	ADJ
cana-4230	20	19	-	-	PUNCT
cana-4230	20	20	dimensional	dimensional	ADJ
cana-4230	20	21	databases	database	NOUN
cana-4230	20	22	.	.	PUNCT
cana-4230	21	1	algebraic	algebraic	ADJ
cana-4230	21	2	topology	topology	NOUN
cana-4230	21	3	can	can	AUX
cana-4230	21	4	be	be	AUX
cana-4230	21	5	used	use	VERB
cana-4230	21	6	to	to	PART
cana-4230	21	7	perform	perform	VERB
cana-4230	21	8	geometry	geometry	NOUN
cana-4230	21	9	on	on	ADP
cana-4230	21	10	data	datum	NOUN
cana-4230	21	11	–	–	PUNCT
cana-4230	21	12	to	to	PART
cana-4230	21	13	extract	extract	VERB
cana-4230	21	14	the	the	DET
cana-4230	21	15	shape	shape	NOUN
cana-4230	21	16	,	,	PUNCT
cana-4230	21	17	or	or	CCONJ
cana-4230	21	18	“	"	PUNCT
cana-4230	21	19	topology	topology	NOUN
cana-4230	21	20	”	"	PUNCT
cana-4230	21	21	of	of	ADP
cana-4230	21	22	the	the	DET
cana-4230	21	23	data	datum	NOUN
cana-4230	21	24	while	while	SCONJ
cana-4230	21	25	bypassing	bypass	VERB
cana-4230	21	26	what	what	PRON
cana-4230	21	27	is	be	AUX
cana-4230	21	28	uninformative	uninformative	ADJ
cana-4230	21	29	,	,	PUNCT
cana-4230	21	30	or	or	CCONJ
cana-4230	21	31	“	"	PUNCT
cana-4230	21	32	noise	noise	NOUN
cana-4230	21	33	.	.	PUNCT
cana-4230	21	34	”	"	PUNCT
cana-4230	22	1	more	more	ADV
cana-4230	22	2	precisely	precisely	ADV
cana-4230	22	3	,	,	PUNCT
cana-4230	22	4	tda	tda	NOUN
cana-4230	22	5	,	,	PUNCT
cana-4230	22	6	which	which	PRON
cana-4230	22	7	belongs	belong	VERB
cana-4230	22	8	to	to	ADP
cana-4230	22	9	the	the	DET
cana-4230	22	10	framework	framework	NOUN
cana-4230	22	11	of	of	ADP
cana-4230	22	12	applied	apply	VERB
cana-4230	22	13	algebraic	algebraic	ADJ
cana-4230	22	14	topology	topology	NOUN
cana-4230	22	15	,	,	PUNCT
cana-4230	22	16	has	have	AUX
cana-4230	22	17	been	be	AUX
cana-4230	22	18	shown	show	VERB
cana-4230	22	19	useful	useful	ADJ
cana-4230	22	20	for	for	ADP
cana-4230	22	21	extracting	extract	VERB
cana-4230	22	22	features	feature	NOUN
cana-4230	22	23	,	,	PUNCT
cana-4230	22	24	such	such	ADJ
cana-4230	22	25	as	as	ADP
cana-4230	22	26	connected	connected	ADJ
cana-4230	22	27	components	component	NOUN
cana-4230	22	28	,	,	PUNCT
cana-4230	22	29	loops	loop	NOUN
cana-4230	22	30	,	,	PUNCT
cana-4230	22	31	or	or	CCONJ
cana-4230	22	32	voids	void	NOUN
cana-4230	22	33	that	that	PRON
cana-4230	22	34	persist	persist	VERB
cana-4230	22	35	at	at	ADP
cana-4230	22	36	all	all	DET
cana-4230	22	37	scales	scale	NOUN
cana-4230	22	38	within	within	ADP
cana-4230	22	39	the	the	DET
cana-4230	22	40	input	input	NOUN
cana-4230	22	41	data	datum	NOUN
cana-4230	22	42	set	set	VERB
cana-4230	22	43	(	(	PUNCT
cana-4230	22	44	edelsbrunner	edelsbrunner	NOUN
cana-4230	22	45	&	&	CCONJ
cana-4230	22	46	harer	harer	NOUN
cana-4230	22	47	,	,	PUNCT
cana-4230	22	48	2010	2010	NUM
cana-4230	22	49	)	)	PUNCT
cana-4230	22	50	.	.	PUNCT
cana-4230	23	1	these	these	DET
cana-4230	23	2	features	feature	NOUN
cana-4230	23	3	can	can	AUX
cana-4230	23	4	help	help	VERB
cana-4230	23	5	to	to	PART
cana-4230	23	6	discover	discover	VERB
cana-4230	23	7	important	important	ADJ
cana-4230	23	8	properties	property	NOUN
cana-4230	23	9	of	of	ADP
cana-4230	23	10	the	the	DET
cana-4230	23	11	data	data	NOUN
cana-4230	23	12	’s	’s	PART
cana-4230	23	13	structure	structure	NOUN
cana-4230	23	14	in	in	ADP
cana-4230	23	15	situations	situation	NOUN
cana-4230	23	16	where	where	SCONJ
cana-4230	23	17	geometric	geometric	ADJ
cana-4230	23	18	sense	sense	NOUN
cana-4230	23	19	can	can	AUX
cana-4230	23	20	be	be	AUX
cana-4230	23	21	misleading	misleading	ADJ
cana-4230	23	22	.	.	PUNCT
cana-4230	24	1	since	since	SCONJ
cana-4230	24	2	the	the	DET
cana-4230	24	3	origins	origin	NOUN
cana-4230	24	4	of	of	ADP
cana-4230	24	5	algebraic	algebraic	ADJ
cana-4230	24	6	topology	topology	NOUN
cana-4230	24	7	,	,	PUNCT
cana-4230	24	8	many	many	ADJ
cana-4230	24	9	works	work	NOUN
cana-4230	24	10	have	have	AUX
cana-4230	24	11	narrowed	narrow	VERB
cana-4230	24	12	down	down	ADP
cana-4230	24	13	geometries	geometry	NOUN
cana-4230	24	14	to	to	ADP
cana-4230	24	15	linear	linear	ADJ
cana-4230	24	16	spaces	space	NOUN
cana-4230	24	17	and	and	CCONJ
cana-4230	24	18	simplicial	simplicial	ADJ
cana-4230	24	19	complexes	complex	NOUN
cana-4230	24	20	;	;	PUNCT
cana-4230	24	21	recent	recent	ADJ
cana-4230	24	22	breakthroughs	breakthrough	NOUN
cana-4230	24	23	began	begin	VERB
cana-4230	24	24	to	to	PART
cana-4230	24	25	involve	involve	VERB
cana-4230	24	26	more	more	ADJ
cana-4230	24	27	general	general	ADJ
cana-4230	24	28	geometries	geometry	NOUN
cana-4230	24	29	more	more	ADV
cana-4230	24	30	suitable	suitable	ADJ
cana-4230	24	31	to	to	ADP
cana-4230	24	32	high	high	ADJ
cana-4230	24	33	-	-	PUNCT
cana-4230	24	34	dimensional	dimensional	ADJ
cana-4230	24	35	data	datum	NOUN
cana-4230	24	36	.	.	PUNCT
cana-4230	25	1	nonlinear	nonlinear	ADJ
cana-4230	25	2	algebraic	algebraic	PROPN
cana-4230	25	3	topology	topology	NOUN
cana-4230	25	4	generalizes	generalize	VERB
cana-4230	25	5	tda	tda	NOUN
cana-4230	25	6	by	by	ADP
cana-4230	25	7	admitting	admit	VERB
cana-4230	25	8	more	more	ADV
cana-4230	25	9	flexible	flexible	ADJ
cana-4230	25	10	mathematics	mathematic	NOUN
cana-4230	25	11	and	and	CCONJ
cana-4230	25	12	computations	computation	NOUN
cana-4230	25	13	that	that	PRON
cana-4230	25	14	can	can	AUX
cana-4230	25	15	accommodate	accommodate	VERB
cana-4230	25	16	the	the	DET
cana-4230	25	17	inherent	inherent	ADJ
cana-4230	25	18	,	,	PUNCT
cana-4230	25	19	often	often	ADV
cana-4230	25	20	non	non	ADJ
cana-4230	25	21	-	-	ADJ
cana-4230	25	22	linear	linear	ADJ
cana-4230	25	23	,	,	PUNCT
cana-4230	25	24	geometry	geometry	NOUN
cana-4230	25	25	of	of	ADP
cana-4230	25	26	contemporaneous	contemporaneous	ADJ
cana-4230	25	27	large	large	ADJ
cana-4230	25	28	data	data	NOUN
cana-4230	25	29	sets	set	NOUN
cana-4230	25	30	(	(	PUNCT
cana-4230	25	31	carlsson	carlsson	PROPN
cana-4230	25	32	,	,	PUNCT
cana-4230	25	33	2009	2009	NUM
cana-4230	25	34	)	)	PUNCT
cana-4230	25	35	.	.	PUNCT
cana-4230	26	1	this	this	DET
cana-4230	26	2	lines	line	NOUN
cana-4230	26	3	up	up	ADP
cana-4230	26	4	nonlinear	nonlinear	ADJ
cana-4230	26	5	perspective	perspective	NOUN
cana-4230	26	6	allows	allow	VERB
cana-4230	26	7	for	for	ADP
cana-4230	26	8	stronger	strong	ADJ
cana-4230	26	9	analysis	analysis	NOUN
cana-4230	26	10	and	and	CCONJ
cana-4230	26	11	presents	present	VERB
cana-4230	26	12	a	a	DET
cana-4230	26	13	new	new	ADJ
cana-4230	26	14	way	way	NOUN
cana-4230	26	15	of	of	ADP
cana-4230	26	16	approaching	approach	VERB
cana-4230	26	17	problems	problem	NOUN
cana-4230	26	18	associated	associate	VERB
cana-4230	26	19	with	with	ADP
cana-4230	26	20	high	high	ADJ
cana-4230	26	21	dimensionality	dimensionality	NOUN
cana-4230	26	22	of	of	ADP
cana-4230	26	23	data	datum	NOUN
cana-4230	26	24	.	.	PUNCT
cana-4230	27	1	in	in	ADP
cana-4230	27	2	this	this	DET
cana-4230	27	3	paper	paper	NOUN
cana-4230	27	4	,	,	PUNCT
cana-4230	27	5	we	we	PRON
cana-4230	27	6	develop	develop	VERB
cana-4230	27	7	a	a	DET
cana-4230	27	8	new	new	ADJ
cana-4230	27	9	apparatus	apparatus	NOUN
cana-4230	27	10	based	base	VERB
cana-4230	27	11	on	on	ADP
cana-4230	27	12	nonlinear	nonlinear	ADJ
cana-4230	27	13	algebraic	algebraic	ADJ
cana-4230	27	14	topology	topology	NOUN
cana-4230	27	15	applicable	applicable	ADJ
cana-4230	27	16	to	to	ADP
cana-4230	27	17	the	the	DET
cana-4230	27	18	analysis	analysis	NOUN
cana-4230	27	19	of	of	ADP
cana-4230	27	20	higher	high	ADJ
cana-4230	27	21	dimensional	dimensional	ADJ
cana-4230	27	22	data	datum	NOUN
cana-4230	27	23	.	.	PUNCT
cana-4230	28	1	our	our	PRON
cana-4230	28	2	approach	approach	NOUN
cana-4230	28	3	utilizes	utilize	VERB
cana-4230	28	4	complex	complex	ADJ
cana-4230	28	5	topological	topological	ADJ
cana-4230	28	6	features	feature	NOUN
cana-4230	28	7	,	,	PUNCT
cana-4230	28	8	including	include	VERB
cana-4230	28	9	persistent	persistent	ADJ
cana-4230	28	10	homology	homology	NOUN
cana-4230	28	11	and	and	CCONJ
cana-4230	28	12	simplices	simplice	NOUN
cana-4230	28	13	,	,	PUNCT
cana-4230	28	14	to	to	PART
cana-4230	28	15	extract	extract	VERB
cana-4230	28	16	the	the	DET
cana-4230	28	17	underlying	underlie	VERB
cana-4230	28	18	geometric	geometric	ADJ
cana-4230	28	19	features	feature	NOUN
cana-4230	28	20	in	in	ADP
cana-4230	28	21	complex	complex	ADJ
cana-4230	28	22	datasets	dataset	NOUN
cana-4230	28	23	of	of	ADP
cana-4230	28	24	a	a	DET
cana-4230	28	25	multivariate	multivariate	NOUN
cana-4230	28	26	nature	nature	NOUN
cana-4230	28	27	.	.	PUNCT
cana-4230	29	1	as	as	ADP
cana-4230	29	2	such	such	ADJ
cana-4230	29	3	,	,	PUNCT
cana-4230	29	4	using	use	VERB
cana-4230	29	5	these	these	DET
cana-4230	29	6	tools	tool	NOUN
cana-4230	29	7	,	,	PUNCT
cana-4230	29	8	we	we	PRON
cana-4230	29	9	propose	propose	VERB
cana-4230	29	10	a	a	DET
cana-4230	29	11	general	general	ADJ
cana-4230	29	12	method	method	NOUN
cana-4230	29	13	for	for	ADP
cana-4230	29	14	analyzing	analyze	VERB
cana-4230	29	15	highdimensional	highdimensional	ADJ
cana-4230	29	16	data	datum	NOUN
cana-4230	29	17	that	that	PRON
cana-4230	29	18	eliminates	eliminate	VERB
cana-4230	29	19	certain	certain	ADJ
cana-4230	29	20	kinds	kind	NOUN
cana-4230	29	21	of	of	ADP
cana-4230	29	22	weaknesses	weakness	NOUN
cana-4230	29	23	.	.	PUNCT
cana-4230	30	1	this	this	DET
cana-4230	30	2	study	study	NOUN
cana-4230	30	3	is	be	AUX
cana-4230	30	4	organized	organize	VERB
cana-4230	30	5	as	as	SCONJ
cana-4230	30	6	follows	follow	VERB
cana-4230	30	7	:	:	PUNCT
cana-4230	30	8	section	section	NOUN
cana-4230	30	9	2	2	NUM
cana-4230	30	10	probabilistic	probabilistic	ADJ
cana-4230	30	11	backgrounds	background	NOUN
cana-4230	30	12	of	of	ADP
cana-4230	30	13	nonlinear	nonlinear	ADJ
cana-4230	30	14	algebraic	algebraic	ADJ
cana-4230	30	15	topology	topology	NOUN
cana-4230	30	16	is	be	AUX
cana-4230	30	17	summarized	summarize	VERB
cana-4230	30	18	,	,	PUNCT
cana-4230	30	19	in	in	ADP
cana-4230	30	20	section	section	NOUN
cana-4230	30	21	3	3	NUM
cana-4230	30	22	,	,	PUNCT
cana-4230	30	23	it	it	PRON
cana-4230	30	24	presents	present	VERB
cana-4230	30	25	the	the	DET
cana-4230	30	26	proposed	propose	VERB
cana-4230	30	27	framework	framework	NOUN
cana-4230	30	28	for	for	ADP
cana-4230	30	29	high	high	ADJ
cana-4230	30	30	-	-	PUNCT
cana-4230	30	31	dimensional	dimensional	ADJ
cana-4230	30	32	data	datum	NOUN
cana-4230	30	33	analysis	analysis	NOUN
cana-4230	30	34	.	.	PUNCT
cana-4230	31	1	section	section	NOUN
cana-4230	31	2	4	4	NUM
cana-4230	31	3	extends	extend	VERB
cana-4230	31	4	to	to	ADP
cana-4230	31	5	precise	precise	ADJ
cana-4230	31	6	utilization	utilization	NOUN
cana-4230	31	7	of	of	ADP
cana-4230	31	8	the	the	DET
cana-4230	31	9	nonlinear	nonlinear	ADJ
cana-4230	31	10	techniques	technique	NOUN
cana-4230	31	11	in	in	ADP
cana-4230	31	12	the	the	DET
cana-4230	31	13	framework	framework	NOUN
cana-4230	31	14	in	in	ADP
cana-4230	31	15	section	section	NOUN
cana-4230	31	16	5	5	NUM
cana-4230	31	17	,	,	PUNCT
cana-4230	31	18	various	various	ADJ
cana-4230	31	19	application	application	NOUN
cana-4230	31	20	is	be	AUX
cana-4230	31	21	illustrated	illustrate	VERB
cana-4230	31	22	through	through	ADP
cana-4230	31	23	case	case	NOUN
cana-4230	31	24	studies	study	NOUN
cana-4230	31	25	.	.	PUNCT
cana-4230	32	1	section	section	NOUN
cana-4230	32	2	6	6	NUM
cana-4230	32	3	describes	describe	VERB
cana-4230	32	4	the	the	DET
cana-4230	32	5	computational	computational	ADJ
cana-4230	32	6	tools	tool	NOUN
cana-4230	32	7	and	and	CCONJ
cana-4230	32	8	algorithms	algorithm	NOUN
cana-4230	32	9	used	use	VERB
cana-4230	32	10	for	for	ADP
cana-4230	32	11	the	the	DET
cana-4230	32	12	framework	framework	NOUN
cana-4230	32	13	,	,	PUNCT
cana-4230	32	14	and	and	CCONJ
cana-4230	32	15	section	section	NOUN
cana-4230	32	16	7	7	NUM
cana-4230	32	17	gives	give	VERB
cana-4230	32	18	a	a	DET
cana-4230	32	19	brief	brief	ADJ
cana-4230	32	20	note	note	NOUN
cana-4230	32	21	on	on	ADP
cana-4230	32	22	the	the	DET
cana-4230	32	23	merits	merit	NOUN
cana-4230	32	24	,	,	PUNCT
cana-4230	32	25	demerits	demerit	NOUN
cana-4230	32	26	,	,	PUNCT
cana-4230	32	27	and	and	CCONJ
cana-4230	32	28	potential	potential	ADJ
cana-4230	32	29	trends	trend	NOUN
cana-4230	32	30	of	of	ADP
cana-4230	32	31	nonlinear	nonlinear	ADJ
cana-4230	32	32	algebraic	algebraic	ADJ
cana-4230	32	33	topology	topology	NOUN
cana-4230	32	34	in	in	ADP
cana-4230	32	35	the	the	DET
cana-4230	32	36	field	field	NOUN
cana-4230	32	37	of	of	ADP
cana-4230	32	38	data	datum	NOUN
cana-4230	32	39	analysis	analysis	NOUN
cana-4230	32	40	.	.	PUNCT
cana-4230	33	1	communications	communication	NOUN
cana-4230	33	2	on	on	ADP
cana-4230	33	3	applied	apply	VERB
cana-4230	33	4	nonlinear	nonlinear	ADJ
cana-4230	33	5	analysis	analysis	NOUN
cana-4230	33	6	issn	issn	NOUN
cana-4230	33	7	:	:	PUNCT
cana-4230	33	8	1074	1074	NUM
cana-4230	33	9	-	-	PUNCT
cana-4230	33	10	133x	133x	NUM
cana-4230	33	11	vol	vol	NOUN
cana-4230	33	12	32	32	NUM
cana-4230	33	13	no	no	NOUN
cana-4230	33	14	.	.	PUNCT
cana-4230	34	1	8s	8s	PROPN
cana-4230	34	2	(	(	PUNCT
cana-4230	34	3	2025	2025	NUM
cana-4230	34	4	)	)	PUNCT
cana-4230	34	5	895	895	NUM
cana-4230	34	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	34	7	2	2	NUM
cana-4230	34	8	.	.	PUNCT
cana-4230	34	9	theoretical	theoretical	ADJ
cana-4230	34	10	foundations	foundation	NOUN
cana-4230	34	11	of	of	ADP
cana-4230	34	12	nonlinear	nonlinear	ADJ
cana-4230	34	13	algebraic	algebraic	PROPN
cana-4230	34	14	topology	topology	PROPN
cana-4230	34	15	nonlinear	nonlinear	ADJ
cana-4230	34	16	algebraic	algebraic	ADJ
cana-4230	34	17	topology	topology	NOUN
cana-4230	34	18	can	can	AUX
cana-4230	34	19	be	be	AUX
cana-4230	34	20	stated	state	VERB
cana-4230	34	21	as	as	ADP
cana-4230	34	22	an	an	DET
cana-4230	34	23	analysis	analysis	NOUN
cana-4230	34	24	of	of	ADP
cana-4230	34	25	data	datum	NOUN
cana-4230	34	26	that	that	PRON
cana-4230	34	27	are	be	AUX
cana-4230	34	28	situated	situate	VERB
cana-4230	34	29	in	in	ADP
cana-4230	34	30	spaces	space	NOUN
cana-4230	34	31	other	other	ADJ
cana-4230	34	32	than	than	ADP
cana-4230	34	33	euclidean	euclidean	ADJ
cana-4230	34	34	.	.	PUNCT
cana-4230	35	1	this	this	DET
cana-4230	35	2	approach	approach	NOUN
cana-4230	35	3	is	be	AUX
cana-4230	35	4	an	an	DET
cana-4230	35	5	extension	extension	NOUN
cana-4230	35	6	of	of	ADP
cana-4230	35	7	concepts	concept	NOUN
cana-4230	35	8	from	from	ADP
cana-4230	35	9	classical	classical	ADJ
cana-4230	35	10	algebraic	algebraic	ADJ
cana-4230	35	11	topology	topology	NOUN
cana-4230	35	12	,	,	PUNCT
cana-4230	35	13	which	which	PRON
cana-4230	35	14	aims	aim	VERB
cana-4230	35	15	at	at	ADP
cana-4230	35	16	studying	study	VERB
cana-4230	35	17	properties	property	NOUN
cana-4230	35	18	of	of	ADP
cana-4230	35	19	shapes	shape	NOUN
cana-4230	35	20	by	by	ADP
cana-4230	35	21	investigating	investigate	VERB
cana-4230	35	22	properties	property	NOUN
cana-4230	35	23	of	of	ADP
cana-4230	35	24	topological	topological	ADJ
cana-4230	35	25	spaces	space	NOUN
cana-4230	35	26	,	,	PUNCT
cana-4230	35	27	continuous	continuous	ADJ
cana-4230	35	28	transformations	transformation	NOUN
cana-4230	35	29	,	,	PUNCT
cana-4230	35	30	and	and	CCONJ
cana-4230	35	31	such	such	ADJ
cana-4230	35	32	invariants	invariant	NOUN
cana-4230	35	33	as	as	ADP
cana-4230	35	34	homology	homology	NOUN
cana-4230	35	35	or	or	CCONJ
cana-4230	35	36	cohomology	cohomology	NOUN
cana-4230	35	37	(	(	PUNCT
cana-4230	35	38	hatcher	hatcher	PROPN
cana-4230	35	39	2002	2002	NUM
cana-4230	35	40	)	)	PUNCT
cana-4230	35	41	.	.	PUNCT
cana-4230	36	1	when	when	SCONJ
cana-4230	36	2	applied	apply	VERB
cana-4230	36	3	to	to	ADP
cana-4230	36	4	nonlinear	nonlinear	ADJ
cana-4230	36	5	environments	environment	NOUN
cana-4230	36	6	,	,	PUNCT
cana-4230	36	7	they	they	PRON
cana-4230	36	8	are	be	AUX
cana-4230	36	9	truly	truly	ADV
cana-4230	36	10	invaluable	invaluable	ADJ
cana-4230	36	11	for	for	ADP
cana-4230	36	12	the	the	DET
cana-4230	36	13	study	study	NOUN
cana-4230	36	14	of	of	ADP
cana-4230	36	15	the	the	DET
cana-4230	36	16	complex	complex	ADJ
cana-4230	36	17	structures	structure	NOUN
cana-4230	36	18	of	of	ADP
cana-4230	36	19	largedimensional	largedimensional	ADJ
cana-4230	36	20	data	datum	NOUN
cana-4230	36	21	collections	collection	NOUN
cana-4230	36	22	,	,	PUNCT
cana-4230	36	23	where	where	SCONJ
cana-4230	36	24	traditional	traditional	ADJ
cana-4230	36	25	approaches	approach	NOUN
cana-4230	36	26	prove	prove	VERB
cana-4230	36	27	inefficient	inefficient	ADJ
cana-4230	36	28	.	.	PUNCT
cana-4230	37	1	figure	figure	VERB
cana-4230	37	2	1	1	NUM
cana-4230	37	3	:	:	PUNCT
cana-4230	37	4	theoretical	theoretical	ADJ
cana-4230	37	5	foundations	foundation	NOUN
cana-4230	37	6	of	of	ADP
cana-4230	37	7	nonlinear	nonlinear	ADJ
cana-4230	37	8	algebraic	algebraic	ADJ
cana-4230	37	9	topology	topology	NOUN
cana-4230	37	10	2.1	2.1	NUM
cana-4230	37	11	overview	overview	NOUN
cana-4230	37	12	of	of	ADP
cana-4230	37	13	algebraic	algebraic	ADJ
cana-4230	37	14	topology	topology	NOUN
cana-4230	37	15	classical	classical	ADJ
cana-4230	37	16	algebraic	algebraic	ADJ
cana-4230	37	17	topology	topology	NOUN
cana-4230	37	18	as	as	ADP
cana-4230	37	19	a	a	DET
cana-4230	37	20	branch	branch	NOUN
cana-4230	37	21	of	of	ADP
cana-4230	37	22	mathematics	mathematic	NOUN
cana-4230	37	23	is	be	AUX
cana-4230	37	24	focused	focus	VERB
cana-4230	37	25	on	on	ADP
cana-4230	37	26	the	the	DET
cana-4230	37	27	investigation	investigation	NOUN
cana-4230	37	28	of	of	ADP
cana-4230	37	29	what	what	PRON
cana-4230	37	30	are	be	AUX
cana-4230	37	31	called	call	VERB
cana-4230	37	32	topological	topological	ADJ
cana-4230	37	33	spaces	space	NOUN
cana-4230	37	34	by	by	ADP
cana-4230	37	35	attaching	attach	VERB
cana-4230	37	36	more	more	ADJ
cana-4230	37	37	elementary	elementary	ADJ
cana-4230	37	38	algebraic	algebraic	ADJ
cana-4230	37	39	structures	structure	NOUN
cana-4230	37	40	,	,	PUNCT
cana-4230	37	41	like	like	ADP
cana-4230	37	42	groups	group	NOUN
cana-4230	37	43	or	or	CCONJ
cana-4230	37	44	rings	ring	NOUN
cana-4230	37	45	,	,	PUNCT
cana-4230	37	46	to	to	ADP
cana-4230	37	47	them	they	PRON
cana-4230	37	48	.	.	PUNCT
cana-4230	38	1	this	this	PRON
cana-4230	38	2	makes	make	VERB
cana-4230	38	3	it	it	PRON
cana-4230	38	4	possible	possible	ADJ
cana-4230	38	5	to	to	PART
cana-4230	38	6	put	put	VERB
cana-4230	38	7	spaces	space	NOUN
cana-4230	38	8	into	into	ADP
cana-4230	38	9	equivalence	equivalence	NOUN
cana-4230	38	10	classes	class	NOUN
cana-4230	38	11	that	that	PRON
cana-4230	38	12	possess	possess	VERB
cana-4230	38	13	characteristics	characteristic	NOUN
cana-4230	38	14	that	that	PRON
cana-4230	38	15	do	do	AUX
cana-4230	38	16	not	not	PART
cana-4230	38	17	change	change	VERB
cana-4230	38	18	when	when	SCONJ
cana-4230	38	19	the	the	DET
cana-4230	38	20	volumes	volume	NOUN
cana-4230	38	21	are	be	AUX
cana-4230	38	22	deformed	deform	VERB
cana-4230	38	23	,	,	PUNCT
cana-4230	38	24	for	for	ADP
cana-4230	38	25	example	example	NOUN
cana-4230	38	26	,	,	PUNCT
cana-4230	38	27	stretched	stretch	VERB
cana-4230	38	28	or	or	CCONJ
cana-4230	38	29	bent	bent	ADJ
cana-4230	38	30	,	,	PUNCT
cana-4230	38	31	but	but	CCONJ
cana-4230	38	32	not	not	PART
cana-4230	38	33	twisted	twist	VERB
cana-4230	38	34	or	or	CCONJ
cana-4230	38	35	joined	join	VERB
cana-4230	38	36	together	together	ADV
cana-4230	38	37	or	or	CCONJ
cana-4230	38	38	ripped	rip	VERB
cana-4230	38	39	apart	apart	ADV
cana-4230	38	40	(	(	PUNCT
cana-4230	38	41	munkres	munkre	NOUN
cana-4230	38	42	,	,	PUNCT
cana-4230	38	43	2000	2000	NUM
cana-4230	38	44	)	)	PUNCT
cana-4230	38	45	.	.	PUNCT
cana-4230	39	1	objects	object	NOUN
cana-4230	39	2	of	of	ADP
cana-4230	39	3	interest	interest	NOUN
cana-4230	39	4	in	in	ADP
cana-4230	39	5	algebraic	algebraic	ADJ
cana-4230	39	6	topology	topology	NOUN
cana-4230	39	7	are	be	AUX
cana-4230	39	8	homologies	homology	NOUN
cana-4230	39	9	and	and	CCONJ
cana-4230	39	10	cohomologies	cohomologie	NOUN
cana-4230	39	11	collectively	collectively	ADV
cana-4230	39	12	giving	give	VERB
cana-4230	39	13	information	information	NOUN
cana-4230	39	14	on	on	ADP
cana-4230	39	15	how	how	SCONJ
cana-4230	39	16	many	many	ADJ
cana-4230	39	17	connected	connected	ADJ
cana-4230	39	18	pieces	piece	NOUN
cana-4230	39	19	,	,	PUNCT
cana-4230	39	20	holes	hole	NOUN
cana-4230	39	21	,	,	PUNCT
cana-4230	39	22	and	and	CCONJ
cana-4230	39	23	voids	voids	NOUN
cana-4230	39	24	of	of	ADP
cana-4230	39	25	higher	high	ADJ
cana-4230	39	26	dimensions	dimension	NOUN
cana-4230	39	27	the	the	DET
cana-4230	39	28	topological	topological	ADJ
cana-4230	39	29	space	space	NOUN
cana-4230	39	30	has	have	AUX
cana-4230	39	31	.	.	PUNCT
cana-4230	40	1	these	these	DET
cana-4230	40	2	invariants	invariant	NOUN
cana-4230	40	3	are	be	AUX
cana-4230	40	4	calculated	calculate	VERB
cana-4230	40	5	with	with	ADP
cana-4230	40	6	the	the	DET
cana-4230	40	7	help	help	NOUN
cana-4230	40	8	of	of	ADP
cana-4230	40	9	some	some	DET
cana-4230	40	10	constructs	construct	NOUN
cana-4230	40	11	such	such	ADJ
cana-4230	40	12	as	as	ADP
cana-4230	40	13	simplicial	simplicial	ADJ
cana-4230	40	14	complexes	complex	NOUN
cana-4230	40	15	,	,	PUNCT
cana-4230	40	16	which	which	PRON
cana-4230	40	17	enable	enable	VERB
cana-4230	40	18	to	to	PART
cana-4230	40	19	approximation	approximation	NOUN
cana-4230	40	20	of	of	ADP
cana-4230	40	21	topological	topological	ADJ
cana-4230	40	22	spaces	space	NOUN
cana-4230	40	23	with	with	ADP
cana-4230	40	24	a	a	DET
cana-4230	40	25	combinatorial	combinatorial	ADJ
cana-4230	40	26	technique	technique	NOUN
cana-4230	40	27	.	.	PUNCT
cana-4230	41	1	algebraic	algebraic	ADJ
cana-4230	41	2	topology	topology	NOUN
cana-4230	41	3	as	as	ADP
cana-4230	41	4	a	a	DET
cana-4230	41	5	method	method	NOUN
cana-4230	41	6	of	of	ADP
cana-4230	41	7	data	datum	NOUN
cana-4230	41	8	analysis	analysis	NOUN
cana-4230	41	9	is	be	AUX
cana-4230	41	10	closely	closely	ADV
cana-4230	41	11	connected	connect	VERB
cana-4230	41	12	with	with	ADP
cana-4230	41	13	the	the	DET
cana-4230	41	14	concept	concept	NOUN
cana-4230	41	15	of	of	ADP
cana-4230	41	16	persistent	persistent	ADJ
cana-4230	41	17	homology	homology	NOUN
cana-4230	41	18	,	,	PUNCT
cana-4230	41	19	which	which	PRON
cana-4230	41	20	is	be	AUX
cana-4230	41	21	an	an	DET
cana-4230	41	22	augmentation	augmentation	NOUN
cana-4230	41	23	of	of	ADP
cana-4230	41	24	classical	classical	ADJ
cana-4230	41	25	homology	homology	NOUN
cana-4230	41	26	.	.	PUNCT
cana-4230	42	1	developed	develop	VERB
cana-4230	42	2	by	by	ADP
cana-4230	42	3	edelsbrunner	edelsbrunner	NOUN
cana-4230	42	4	,	,	PUNCT
cana-4230	42	5	letscher	letscher	NOUN
cana-4230	42	6	,	,	PUNCT
cana-4230	42	7	and	and	CCONJ
cana-4230	42	8	zomorodian	zomorodian	ADJ
cana-4230	42	9	(	(	PUNCT
cana-4230	42	10	2002	2002	NUM
cana-4230	42	11	)	)	PUNCT
cana-4230	42	12	,	,	PUNCT
cana-4230	42	13	persistent	persistent	ADJ
cana-4230	42	14	homology	homology	NOUN
cana-4230	42	15	extends	extend	VERB
cana-4230	42	16	topology	topology	NOUN
cana-4230	42	17	captured	capture	VERB
cana-4230	42	18	at	at	ADP
cana-4230	42	19	different	different	ADJ
cana-4230	42	20	scale	scale	NOUN
cana-4230	42	21	levels	level	NOUN
cana-4230	42	22	of	of	ADP
cana-4230	42	23	a	a	DET
cana-4230	42	24	dataset	dataset	NOUN
cana-4230	42	25	to	to	PART
cana-4230	42	26	track	track	VERB
cana-4230	42	27	the	the	DET
cana-4230	42	28	creation	creation	NOUN
cana-4230	42	29	and	and	CCONJ
cana-4230	42	30	annihilation	annihilation	NOUN
cana-4230	42	31	of	of	ADP
cana-4230	42	32	a	a	DET
cana-4230	42	33	feature	feature	NOUN
cana-4230	42	34	,	,	PUNCT
cana-4230	42	35	including	include	VERB
cana-4230	42	36	connected	connect	VERB
cana-4230	42	37	components	component	NOUN
cana-4230	42	38	and	and	CCONJ
cana-4230	42	39	loops	loop	NOUN
cana-4230	42	40	.	.	PUNCT
cana-4230	43	1	this	this	DET
cana-4230	43	2	multi	multi	ADJ
cana-4230	43	3	-	-	ADJ
cana-4230	43	4	scale	scale	ADJ
cana-4230	43	5	approach	approach	NOUN
cana-4230	43	6	makes	make	VERB
cana-4230	43	7	sense	sense	NOUN
cana-4230	43	8	for	for	ADP
cana-4230	43	9	explaining	explain	VERB
cana-4230	43	10	why	why	SCONJ
cana-4230	43	11	and	and	CCONJ
cana-4230	43	12	how	how	SCONJ
cana-4230	43	13	some	some	DET
cana-4230	43	14	features	feature	NOUN
cana-4230	43	15	are	be	AUX
cana-4230	43	16	retained	retain	VERB
cana-4230	43	17	in	in	ADP
cana-4230	43	18	noisy	noisy	ADJ
cana-4230	43	19	or	or	CCONJ
cana-4230	43	20	high	high	ADV
cana-4230	43	21	-	-	PUNCT
cana-4230	43	22	dimensional	dimensional	ADJ
cana-4230	43	23	environments	environment	NOUN
cana-4230	43	24	.	.	PUNCT
cana-4230	44	1	communications	communication	NOUN
cana-4230	44	2	on	on	ADP
cana-4230	44	3	applied	apply	VERB
cana-4230	44	4	nonlinear	nonlinear	ADJ
cana-4230	44	5	analysis	analysis	NOUN
cana-4230	44	6	issn	issn	NOUN
cana-4230	44	7	:	:	PUNCT
cana-4230	44	8	1074	1074	NUM
cana-4230	44	9	-	-	PUNCT
cana-4230	44	10	133x	133x	NUM
cana-4230	44	11	vol	vol	NOUN
cana-4230	44	12	32	32	NUM
cana-4230	44	13	no	no	NOUN
cana-4230	44	14	.	.	PUNCT
cana-4230	45	1	8s	8s	PROPN
cana-4230	45	2	(	(	PUNCT
cana-4230	45	3	2025	2025	NUM
cana-4230	45	4	)	)	PUNCT
cana-4230	45	5	896	896	NUM
cana-4230	45	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	45	7	2.2	2.2	NUM
cana-4230	45	8	nonlinear	nonlinear	ADJ
cana-4230	45	9	approaches	approach	NOUN
cana-4230	45	10	to	to	ADP
cana-4230	45	11	topological	topological	ADJ
cana-4230	45	12	data	datum	NOUN
cana-4230	45	13	analysis	analysis	NOUN
cana-4230	45	14	the	the	DET
cana-4230	45	15	linearity	linearity	NOUN
cana-4230	45	16	assumption	assumption	NOUN
cana-4230	45	17	that	that	PRON
cana-4230	45	18	is	be	AUX
cana-4230	45	19	core	core	NOUN
cana-4230	45	20	to	to	ADP
cana-4230	45	21	majority	majority	NOUN
cana-4230	45	22	tda	tda	NOUN
cana-4230	45	23	methods	method	NOUN
cana-4230	45	24	compromises	compromise	VERB
cana-4230	45	25	its	its	PRON
cana-4230	45	26	applicability	applicability	NOUN
cana-4230	45	27	in	in	ADP
cana-4230	45	28	the	the	DET
cana-4230	45	29	analysis	analysis	NOUN
cana-4230	45	30	of	of	ADP
cana-4230	45	31	more	more	ADV
cana-4230	45	32	complex	complex	ADJ
cana-4230	45	33	nonlinear	nonlinear	ADJ
cana-4230	45	34	data	data	NOUN
cana-4230	45	35	sets	set	NOUN
cana-4230	45	36	.	.	PUNCT
cana-4230	46	1	nonlinear	nonlinear	ADJ
cana-4230	46	2	algebraic	algebraic	PROPN
cana-4230	46	3	topology	topology	NOUN
cana-4230	46	4	consolidates	consolidate	VERB
cana-4230	46	5	these	these	DET
cana-4230	46	6	notions	notion	NOUN
cana-4230	46	7	by	by	ADP
cana-4230	46	8	penetrating	penetrate	VERB
cana-4230	46	9	deeper	deeply	ADV
cana-4230	46	10	into	into	ADP
cana-4230	46	11	geometric	geometric	ADJ
cana-4230	46	12	structures	structure	NOUN
cana-4230	46	13	and	and	CCONJ
cana-4230	46	14	provides	provide	VERB
cana-4230	46	15	a	a	DET
cana-4230	46	16	tool	tool	NOUN
cana-4230	46	17	for	for	ADP
cana-4230	46	18	studying	study	VERB
cana-4230	46	19	spaces	space	NOUN
cana-4230	46	20	that	that	PRON
cana-4230	46	21	can	can	AUX
cana-4230	46	22	not	not	PART
cana-4230	46	23	be	be	AUX
cana-4230	46	24	viewed	view	VERB
cana-4230	46	25	as	as	ADP
cana-4230	46	26	linear	linear	ADJ
cana-4230	46	27	transformations	transformation	NOUN
cana-4230	46	28	only	only	ADV
cana-4230	46	29	.	.	PUNCT
cana-4230	47	1	this	this	PRON
cana-4230	47	2	is	be	AUX
cana-4230	47	3	especially	especially	ADV
cana-4230	47	4	true	true	ADJ
cana-4230	47	5	for	for	ADP
cana-4230	47	6	cases	case	NOUN
cana-4230	47	7	of	of	ADP
cana-4230	47	8	high	high	ADJ
cana-4230	47	9	generality	generality	NOUN
cana-4230	47	10	in	in	ADP
cana-4230	47	11	which	which	PRON
cana-4230	47	12	the	the	DET
cana-4230	47	13	intrinsic	intrinsic	ADJ
cana-4230	47	14	relations	relation	NOUN
cana-4230	47	15	between	between	ADP
cana-4230	47	16	these	these	DET
cana-4230	47	17	points	point	NOUN
cana-4230	47	18	may	may	AUX
cana-4230	47	19	not	not	PART
cana-4230	47	20	always	always	ADV
cana-4230	47	21	strictly	strictly	ADV
cana-4230	47	22	linear	linear	ADJ
cana-4230	47	23	,	,	PUNCT
cana-4230	47	24	as	as	SCONJ
cana-4230	47	25	is	be	AUX
cana-4230	47	26	the	the	DET
cana-4230	47	27	case	case	NOUN
cana-4230	47	28	with	with	ADP
cana-4230	47	29	manifold	manifold	ADJ
cana-4230	47	30	learning	learning	NOUN
cana-4230	47	31	or	or	CCONJ
cana-4230	47	32	clustering	clustering	NOUN
cana-4230	47	33	of	of	ADP
cana-4230	47	34	a	a	DET
cana-4230	47	35	complex	complex	ADJ
cana-4230	47	36	network	network	NOUN
cana-4230	47	37	(	(	PUNCT
cana-4230	47	38	carlsson	carlsson	PROPN
cana-4230	47	39	,	,	PUNCT
cana-4230	47	40	2009	2009	NUM
cana-4230	47	41	)	)	PUNCT
cana-4230	47	42	.	.	PUNCT
cana-4230	48	1	another	another	DET
cana-4230	48	2	unique	unique	ADJ
cana-4230	48	3	feature	feature	NOUN
cana-4230	48	4	of	of	ADP
cana-4230	48	5	nonlinear	nonlinear	ADJ
cana-4230	48	6	algebraic	algebraic	ADJ
cana-4230	48	7	topology	topology	NOUN
cana-4230	48	8	is	be	AUX
cana-4230	48	9	data	datum	NOUN
cana-4230	48	10	images	image	NOUN
cana-4230	48	11	,	,	PUNCT
cana-4230	48	12	which	which	PRON
cana-4230	48	13	allows	allow	VERB
cana-4230	48	14	a	a	DET
cana-4230	48	15	choice	choice	NOUN
cana-4230	48	16	of	of	ADP
cana-4230	48	17	representation	representation	NOUN
cana-4230	48	18	depending	depend	VERB
cana-4230	48	19	on	on	ADP
cana-4230	48	20	the	the	DET
cana-4230	48	21	case	case	NOUN
cana-4230	48	22	.	.	PUNCT
cana-4230	49	1	for	for	ADP
cana-4230	49	2	instance	instance	NOUN
cana-4230	49	3	,	,	PUNCT
cana-4230	49	4	while	while	SCONJ
cana-4230	49	5	standard	standard	ADJ
cana-4230	49	6	geometrical	geometrical	ADJ
cana-4230	49	7	structures	structure	NOUN
cana-4230	49	8	,	,	PUNCT
cana-4230	49	9	known	know	VERB
cana-4230	49	10	as	as	ADP
cana-4230	49	11	simplicial	simplicial	ADJ
cana-4230	49	12	complexes	complex	NOUN
cana-4230	49	13	,	,	PUNCT
cana-4230	49	14	can	can	AUX
cana-4230	49	15	be	be	AUX
cana-4230	49	16	applied	apply	VERB
cana-4230	49	17	to	to	PART
cana-4230	49	18	describe	describe	VERB
cana-4230	49	19	point	point	NOUN
cana-4230	49	20	clouds	cloud	NOUN
cana-4230	49	21	,	,	PUNCT
cana-4230	49	22	other	other	ADJ
cana-4230	49	23	formations	formation	NOUN
cana-4230	49	24	such	such	ADJ
cana-4230	49	25	as	as	ADP
cana-4230	49	26	čech	čech	NOUN
cana-4230	49	27	or	or	CCONJ
cana-4230	49	28	vietoris	vietoris	ADJ
cana-4230	49	29	–	–	PUNCT
cana-4230	49	30	rips	rip	NOUN
cana-4230	49	31	formations	formation	NOUN
cana-4230	49	32	may	may	AUX
cana-4230	49	33	be	be	AUX
cana-4230	49	34	used	use	VERB
cana-4230	49	35	to	to	PART
cana-4230	49	36	capture	capture	VERB
cana-4230	49	37	interactions	interaction	NOUN
cana-4230	49	38	between	between	ADP
cana-4230	49	39	data	datum	NOUN
cana-4230	49	40	entities	entity	NOUN
cana-4230	49	41	(	(	PUNCT
cana-4230	49	42	zomorodian	zomorodian	ADJ
cana-4230	49	43	,	,	PUNCT
cana-4230	49	44	2012	2012	NUM
cana-4230	49	45	)	)	PUNCT
cana-4230	49	46	.	.	PUNCT
cana-4230	50	1	these	these	DET
cana-4230	50	2	complexes	complex	NOUN
cana-4230	50	3	enhance	enhance	VERB
cana-4230	50	4	the	the	DET
cana-4230	50	5	efficient	efficient	ADJ
cana-4230	50	6	calculation	calculation	NOUN
cana-4230	50	7	of	of	ADP
cana-4230	50	8	topological	topological	ADJ
cana-4230	50	9	invariants	invariant	NOUN
cana-4230	50	10	especially	especially	ADV
cana-4230	50	11	when	when	SCONJ
cana-4230	50	12	working	work	VERB
cana-4230	50	13	with	with	ADP
cana-4230	50	14	data	datum	NOUN
cana-4230	50	15	that	that	PRON
cana-4230	50	16	has	have	VERB
cana-4230	50	17	complex	complex	ADJ
cana-4230	50	18	geometric	geometric	ADJ
cana-4230	50	19	features	feature	NOUN
cana-4230	50	20	with	with	ADP
cana-4230	50	21	high	high	ADJ
cana-4230	50	22	levels	level	NOUN
cana-4230	50	23	of	of	ADP
cana-4230	50	24	curvature	curvature	NOUN
cana-4230	50	25	.	.	PUNCT
cana-4230	51	1	however	however	ADV
cana-4230	51	2	,	,	PUNCT
cana-4230	51	3	the	the	DET
cana-4230	51	4	advancements	advancement	NOUN
cana-4230	51	5	in	in	ADP
cana-4230	51	6	recent	recent	ADJ
cana-4230	51	7	years	year	NOUN
cana-4230	51	8	have	have	AUX
cana-4230	51	9	pointed	point	VERB
cana-4230	51	10	out	out	ADP
cana-4230	51	11	new	new	ADJ
cana-4230	51	12	techniques	technique	NOUN
cana-4230	51	13	to	to	PART
cana-4230	51	14	generalize	generalize	VERB
cana-4230	51	15	the	the	DET
cana-4230	51	16	idea	idea	NOUN
cana-4230	51	17	of	of	ADP
cana-4230	51	18	persistence	persistence	NOUN
cana-4230	51	19	to	to	ADP
cana-4230	51	20	more	more	ADV
cana-4230	51	21	complicated	complicated	ADJ
cana-4230	51	22	contexts	contexts	NOUN
cana-4230	51	23	in	in	ADP
cana-4230	51	24	tda	tda	PROPN
cana-4230	51	25	.	.	PUNCT
cana-4230	52	1	for	for	ADP
cana-4230	52	2	instance	instance	NOUN
cana-4230	52	3	,	,	PUNCT
cana-4230	52	4	multidimensional	multidimensional	ADJ
cana-4230	52	5	persistence	persistence	NOUN
cana-4230	52	6	which	which	PRON
cana-4230	52	7	is	be	AUX
cana-4230	52	8	an	an	DET
cana-4230	52	9	expansion	expansion	NOUN
cana-4230	52	10	of	of	ADP
cana-4230	52	11	persistent	persistent	ADJ
cana-4230	52	12	homology	homology	NOUN
cana-4230	52	13	for	for	ADP
cana-4230	52	14	simultaneous	simultaneous	ADJ
cana-4230	52	15	analysis	analysis	NOUN
cana-4230	52	16	of	of	ADP
cana-4230	52	17	data	datum	NOUN
cana-4230	52	18	with	with	ADP
cana-4230	52	19	respect	respect	NOUN
cana-4230	52	20	to	to	ADP
cana-4230	52	21	multiple	multiple	ADJ
cana-4230	52	22	parameters	parameter	NOUN
cana-4230	52	23	is	be	AUX
cana-4230	52	24	capable	capable	ADJ
cana-4230	52	25	of	of	ADP
cana-4230	52	26	yielding	yield	VERB
cana-4230	52	27	a	a	DET
cana-4230	52	28	more	more	ADV
cana-4230	52	29	detailed	detailed	ADJ
cana-4230	52	30	examination	examination	NOUN
cana-4230	52	31	of	of	ADP
cana-4230	52	32	datasets	dataset	NOUN
cana-4230	52	33	characterized	characterize	VERB
cana-4230	52	34	by	by	ADP
cana-4230	52	35	a	a	DET
cana-4230	52	36	multiplicity	multiplicity	NOUN
cana-4230	52	37	of	of	ADP
cana-4230	52	38	scales	scale	NOUN
cana-4230	52	39	or	or	CCONJ
cana-4230	52	40	features	feature	NOUN
cana-4230	52	41	(	(	PUNCT
cana-4230	52	42	cerri	cerri	PROPN
cana-4230	52	43	et	et	PROPN
cana-4230	52	44	al	al	PROPN
cana-4230	52	45	.	.	PROPN
cana-4230	52	46	,	,	PUNCT
cana-4230	52	47	2013	2013	NUM
cana-4230	52	48	)	)	PUNCT
cana-4230	52	49	.	.	PUNCT
cana-4230	53	1	it	it	PRON
cana-4230	53	2	is	be	AUX
cana-4230	53	3	very	very	ADV
cana-4230	53	4	important	important	ADJ
cana-4230	53	5	in	in	ADP
cana-4230	53	6	numerous	numerous	ADJ
cana-4230	53	7	high	high	ADJ
cana-4230	53	8	-	-	PUNCT
cana-4230	53	9	dimensional	dimensional	ADJ
cana-4230	53	10	problems	problem	NOUN
cana-4230	53	11	because	because	SCONJ
cana-4230	53	12	the	the	DET
cana-4230	53	13	relationships	relationship	NOUN
cana-4230	53	14	between	between	ADP
cana-4230	53	15	features	feature	NOUN
cana-4230	53	16	may	may	AUX
cana-4230	53	17	be	be	AUX
cana-4230	53	18	quite	quite	ADV
cana-4230	53	19	complex	complex	ADJ
cana-4230	53	20	and	and	CCONJ
cana-4230	53	21	require	require	VERB
cana-4230	53	22	multidimensional	multidimensional	ADJ
cana-4230	53	23	mappings	mapping	NOUN
cana-4230	53	24	.	.	PUNCT
cana-4230	54	1	2.3	2.3	NUM
cana-4230	54	2	key	key	ADJ
cana-4230	54	3	mathematical	mathematical	ADJ
cana-4230	54	4	concepts	concept	NOUN
cana-4230	54	5	in	in	ADP
cana-4230	54	6	high	high	ADJ
cana-4230	54	7	-	-	PUNCT
cana-4230	54	8	dimensional	dimensional	ADJ
cana-4230	54	9	data	datum	NOUN
cana-4230	54	10	mathematical	mathematical	ADJ
cana-4230	54	11	properties	property	NOUN
cana-4230	54	12	of	of	ADP
cana-4230	54	13	high	high	ADJ
cana-4230	54	14	-	-	PUNCT
cana-4230	54	15	dimensional	dimensional	ADJ
cana-4230	54	16	data	datum	NOUN
cana-4230	54	17	which	which	PRON
cana-4230	54	18	serves	serve	VERB
cana-4230	54	19	as	as	ADP
cana-4230	54	20	the	the	DET
cana-4230	54	21	basis	basis	NOUN
cana-4230	54	22	for	for	ADP
cana-4230	54	23	nonlinear	nonlinear	ADJ
cana-4230	54	24	algebraic	algebraic	ADJ
cana-4230	54	25	topology	topology	NOUN
cana-4230	54	26	include	include	VERB
cana-4230	54	27	the	the	DET
cana-4230	54	28	following	following	NOUN
cana-4230	54	29	.	.	PUNCT
cana-4230	55	1	one	one	NUM
cana-4230	55	2	of	of	ADP
cana-4230	55	3	them	they	PRON
cana-4230	55	4	is	be	AUX
cana-4230	55	5	the	the	DET
cana-4230	55	6	concept	concept	NOUN
cana-4230	55	7	of	of	ADP
cana-4230	55	8	simplicial	simplicial	ADJ
cana-4230	55	9	complexes	complex	NOUN
cana-4230	55	10	that	that	PRON
cana-4230	55	11	offer	offer	VERB
cana-4230	55	12	a	a	DET
cana-4230	55	13	combinatorial	combinatorial	ADJ
cana-4230	55	14	view	view	NOUN
cana-4230	55	15	of	of	ADP
cana-4230	55	16	data	datum	NOUN
cana-4230	55	17	based	base	VERB
cana-4230	55	18	on	on	ADP
cana-4230	55	19	its	its	PRON
cana-4230	55	20	decomposition	decomposition	NOUN
cana-4230	55	21	into	into	ADP
cana-4230	55	22	vertices	vertex	NOUN
cana-4230	55	23	;	;	PUNCT
cana-4230	55	24	edges	edge	NOUN
cana-4230	55	25	and	and	CCONJ
cana-4230	55	26	higher	high	ADJ
cana-4230	55	27	dimensional	dimensional	ADJ
cana-4230	55	28	simplices	simplice	NOUN
cana-4230	55	29	(	(	PUNCT
cana-4230	55	30	edelsbrunner	edelsbrunner	NOUN
cana-4230	55	31	&	&	CCONJ
cana-4230	55	32	harer	harer	NOUN
cana-4230	55	33	,	,	PUNCT
cana-4230	55	34	2010	2010	NUM
cana-4230	55	35	)	)	PUNCT
cana-4230	55	36	.	.	PUNCT
cana-4230	56	1	simplicial	simplicial	ADJ
cana-4230	56	2	complexes	complex	NOUN
cana-4230	56	3	are	be	AUX
cana-4230	56	4	the	the	DET
cana-4230	56	5	combinatorial	combinatorial	ADJ
cana-4230	56	6	geometric	geometric	ADJ
cana-4230	56	7	representation	representation	NOUN
cana-4230	56	8	where	where	SCONJ
cana-4230	56	9	the	the	DET
cana-4230	56	10	connectivity	connectivity	NOUN
cana-4230	56	11	and	and	CCONJ
cana-4230	56	12	relations	relation	NOUN
cana-4230	56	13	of	of	ADP
cana-4230	56	14	the	the	DET
cana-4230	56	15	points	point	NOUN
cana-4230	56	16	of	of	ADP
cana-4230	56	17	the	the	DET
cana-4230	56	18	data	datum	NOUN
cana-4230	56	19	set	set	VERB
cana-4230	56	20	are	be	AUX
cana-4230	56	21	encoded	encode	VERB
cana-4230	56	22	;	;	PUNCT
cana-4230	56	23	computation	computation	NOUN
cana-4230	56	24	of	of	ADP
cana-4230	56	25	topological	topological	ADJ
cana-4230	56	26	invariants	invariant	NOUN
cana-4230	56	27	that	that	PRON
cana-4230	56	28	are	be	AUX
cana-4230	56	29	crucial	crucial	ADJ
cana-4230	56	30	for	for	ADP
cana-4230	56	31	indicating	indicate	VERB
cana-4230	56	32	features	feature	NOUN
cana-4230	56	33	of	of	ADP
cana-4230	56	34	the	the	DET
cana-4230	56	35	data	datum	NOUN
cana-4230	56	36	set	set	VERB
cana-4230	56	37	can	can	AUX
cana-4230	56	38	then	then	ADV
cana-4230	56	39	be	be	AUX
cana-4230	56	40	undertaken	undertake	VERB
cana-4230	56	41	.	.	PUNCT
cana-4230	57	1	another	another	DET
cana-4230	57	2	very	very	ADV
cana-4230	57	3	relevant	relevant	ADJ
cana-4230	57	4	concept	concept	NOUN
cana-4230	57	5	is	be	AUX
cana-4230	57	6	persistent	persistent	ADJ
cana-4230	57	7	homology	homology	NOUN
cana-4230	57	8	which	which	PRON
cana-4230	57	9	studies	study	NOUN
cana-4230	57	10	changes	change	VERB
cana-4230	57	11	in	in	ADP
cana-4230	57	12	topology	topology	NOUN
cana-4230	57	13	features	feature	NOUN
cana-4230	57	14	corresponding	correspond	VERB
cana-4230	57	15	to	to	ADP
cana-4230	57	16	some	some	DET
cana-4230	57	17	parameter	parameter	NOUN
cana-4230	57	18	,	,	PUNCT
cana-4230	57	19	often	often	ADV
cana-4230	57	20	a	a	DET
cana-4230	57	21	scale	scale	NOUN
cana-4230	57	22	or	or	CCONJ
cana-4230	57	23	a	a	DET
cana-4230	57	24	distance	distance	NOUN
cana-4230	57	25	,	,	PUNCT
cana-4230	57	26	as	as	SCONJ
cana-4230	57	27	this	this	DET
cana-4230	57	28	parameter	parameter	NOUN
cana-4230	57	29	increases	increase	VERB
cana-4230	57	30	(	(	PUNCT
cana-4230	57	31	zomorodian	zomorodian	ADJ
cana-4230	57	32	,	,	PUNCT
cana-4230	57	33	2005	2005	NUM
cana-4230	57	34	)	)	PUNCT
cana-4230	57	35	.	.	PUNCT
cana-4230	58	1	such	such	ADJ
cana-4230	58	2	stabilities	stability	NOUN
cana-4230	58	3	,	,	PUNCT
cana-4230	58	4	constant	constant	ADJ
cana-4230	58	5	across	across	ADP
cana-4230	58	6	different	different	ADJ
cana-4230	58	7	scales	scale	NOUN
cana-4230	58	8	,	,	PUNCT
cana-4230	58	9	reveal	reveal	VERB
cana-4230	58	10	their	their	PRON
cana-4230	58	11	importance	importance	NOUN
cana-4230	58	12	in	in	ADP
cana-4230	58	13	the	the	DET
cana-4230	58	14	data	datum	NOUN
cana-4230	58	15	,	,	PUNCT
cana-4230	58	16	separating	separate	VERB
cana-4230	58	17	signal	signal	NOUN
cana-4230	58	18	from	from	ADP
cana-4230	58	19	noise	noise	NOUN
cana-4230	58	20	.	.	PUNCT
cana-4230	59	1	the	the	DET
cana-4230	59	2	result	result	NOUN
cana-4230	59	3	can	can	AUX
cana-4230	59	4	then	then	ADV
cana-4230	59	5	be	be	AUX
cana-4230	59	6	plotted	plot	VERB
cana-4230	59	7	as	as	ADP
cana-4230	59	8	a	a	DET
cana-4230	59	9	persistence	persistence	NOUN
cana-4230	59	10	diagram	diagram	NOUN
cana-4230	59	11	or	or	CCONJ
cana-4230	59	12	barcode	barcode	NOUN
cana-4230	59	13	where	where	SCONJ
cana-4230	59	14	the	the	DET
cana-4230	59	15	birth	birth	NOUN
cana-4230	59	16	and	and	CCONJ
cana-4230	59	17	death	death	NOUN
cana-4230	59	18	of	of	ADP
cana-4230	59	19	the	the	DET
cana-4230	59	20	topological	topological	ADJ
cana-4230	59	21	features	feature	NOUN
cana-4230	59	22	are	be	AUX
cana-4230	59	23	illustrated	illustrate	VERB
cana-4230	59	24	and	and	CCONJ
cana-4230	59	25	easily	easily	ADV
cana-4230	59	26	compared	compare	VERB
cana-4230	59	27	against	against	ADP
cana-4230	59	28	other	other	ADJ
cana-4230	59	29	datasets	dataset	NOUN
cana-4230	59	30	.	.	PUNCT
cana-4230	60	1	another	another	DET
cana-4230	60	2	important	important	ADJ
cana-4230	60	3	role	role	NOUN
cana-4230	60	4	in	in	ADP
cana-4230	60	5	connection	connection	NOUN
cana-4230	60	6	with	with	ADP
cana-4230	60	7	nonlinear	nonlinear	ADJ
cana-4230	60	8	algebraic	algebraic	ADJ
cana-4230	60	9	topology	topology	NOUN
cana-4230	60	10	is	be	AUX
cana-4230	60	11	played	play	VERB
cana-4230	60	12	by	by	ADP
cana-4230	60	13	manifolds	manifold	NOUN
cana-4230	60	14	,	,	PUNCT
cana-4230	60	15	especially	especially	ADV
cana-4230	60	16	when	when	SCONJ
cana-4230	60	17	the	the	DET
cana-4230	60	18	high	high	ADV
cana-4230	60	19	-	-	PUNCT
cana-4230	60	20	dimensional	dimensional	ADJ
cana-4230	60	21	data	datum	NOUN
cana-4230	60	22	can	can	AUX
cana-4230	60	23	be	be	AUX
cana-4230	60	24	placed	place	VERB
cana-4230	60	25	on	on	ADP
cana-4230	60	26	the	the	DET
cana-4230	60	27	surface	surface	NOUN
cana-4230	60	28	of	of	ADP
cana-4230	60	29	a	a	DET
cana-4230	60	30	much	much	ADV
cana-4230	60	31	lower	low	ADJ
cana-4230	60	32	dimension	dimension	NOUN
cana-4230	60	33	,	,	PUNCT
cana-4230	60	34	curved	curve	VERB
cana-4230	60	35	.	.	PUNCT
cana-4230	61	1	the	the	DET
cana-4230	61	2	idea	idea	NOUN
cana-4230	61	3	of	of	ADP
cana-4230	61	4	manifold	manifold	ADJ
cana-4230	61	5	learning	learning	NOUN
cana-4230	61	6	is	be	AUX
cana-4230	61	7	to	to	PART
cana-4230	61	8	preserve	preserve	VERB
cana-4230	61	9	the	the	DET
cana-4230	61	10	nonlinear	nonlinear	ADJ
cana-4230	61	11	structure	structure	NOUN
cana-4230	61	12	of	of	ADP
cana-4230	61	13	the	the	DET
cana-4230	61	14	data	datum	NOUN
cana-4230	61	15	,	,	PUNCT
cana-4230	61	16	and	and	CCONJ
cana-4230	61	17	much	much	ADJ
cana-4230	61	18	attention	attention	NOUN
cana-4230	61	19	has	have	AUX
cana-4230	61	20	recently	recently	ADV
cana-4230	61	21	been	be	AUX
cana-4230	61	22	paid	pay	VERB
cana-4230	61	23	to	to	ADP
cana-4230	61	24	the	the	DET
cana-4230	61	25	topological	topological	ADJ
cana-4230	61	26	approach	approach	NOUN
cana-4230	61	27	to	to	PART
cana-4230	61	28	detect	detect	VERB
cana-4230	61	29	and	and	CCONJ
cana-4230	61	30	estimate	estimate	VERB
cana-4230	61	31	the	the	DET
cana-4230	61	32	manifold	manifold	ADJ
cana-4230	61	33	features	feature	NOUN
cana-4230	61	34	.	.	PUNCT
cana-4230	62	1	communications	communication	NOUN
cana-4230	62	2	on	on	ADP
cana-4230	62	3	applied	apply	VERB
cana-4230	62	4	nonlinear	nonlinear	ADJ
cana-4230	62	5	analysis	analysis	NOUN
cana-4230	62	6	issn	issn	NOUN
cana-4230	62	7	:	:	PUNCT
cana-4230	62	8	1074	1074	NUM
cana-4230	62	9	-	-	PUNCT
cana-4230	62	10	133x	133x	NUM
cana-4230	62	11	vol	vol	NOUN
cana-4230	62	12	32	32	NUM
cana-4230	62	13	no	no	NOUN
cana-4230	62	14	.	.	PUNCT
cana-4230	63	1	8s	8s	PROPN
cana-4230	63	2	(	(	PUNCT
cana-4230	63	3	2025	2025	NUM
cana-4230	63	4	)	)	PUNCT
cana-4230	63	5	897	897	NUM
cana-4230	63	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	63	7	given	give	VERB
cana-4230	63	8	the	the	DET
cana-4230	63	9	increasingly	increasingly	ADV
cana-4230	63	10	frequent	frequent	ADJ
cana-4230	63	11	application	application	NOUN
cana-4230	63	12	of	of	ADP
cana-4230	63	13	high	high	ADJ
cana-4230	63	14	-	-	PUNCT
cana-4230	63	15	dimensional	dimensional	ADJ
cana-4230	63	16	nonlinear	nonlinear	ADJ
cana-4230	63	17	data	datum	NOUN
cana-4230	63	18	analysis	analysis	NOUN
cana-4230	63	19	,	,	PUNCT
cana-4230	63	20	the	the	DET
cana-4230	63	21	synergy	synergy	NOUN
cana-4230	63	22	between	between	ADP
cana-4230	63	23	algebraic	algebraic	ADJ
cana-4230	63	24	topology	topology	NOUN
cana-4230	63	25	and	and	CCONJ
cana-4230	63	26	nonlinear	nonlinear	ADJ
cana-4230	63	27	analysis	analysis	NOUN
cana-4230	63	28	is	be	AUX
cana-4230	63	29	a	a	DET
cana-4230	63	30	powerful	powerful	ADJ
cana-4230	63	31	approach	approach	NOUN
cana-4230	63	32	for	for	ADP
cana-4230	63	33	gaining	gain	VERB
cana-4230	63	34	insights	insight	NOUN
cana-4230	63	35	from	from	ADP
cana-4230	63	36	the	the	DET
cana-4230	63	37	results	result	NOUN
cana-4230	63	38	.	.	PUNCT
cana-4230	64	1	with	with	SCONJ
cana-4230	64	2	this	this	DET
cana-4230	64	3	theoretical	theoretical	ADJ
cana-4230	64	4	basis	basis	NOUN
cana-4230	64	5	developed	develop	VERB
cana-4230	64	6	,	,	PUNCT
cana-4230	64	7	this	this	DET
cana-4230	64	8	work	work	NOUN
cana-4230	64	9	proceeds	proceed	VERB
cana-4230	64	10	to	to	ADP
cana-4230	64	11	the	the	DET
cana-4230	64	12	application	application	NOUN
cana-4230	64	13	of	of	ADP
cana-4230	64	14	nonlinear	nonlinear	ADJ
cana-4230	64	15	algebraic	algebraic	ADJ
cana-4230	64	16	topology	topology	NOUN
cana-4230	64	17	to	to	ADP
cana-4230	64	18	high	high	ADV
cana-4230	64	19	-	-	PUNCT
cana-4230	64	20	dimensional	dimensional	ADJ
cana-4230	64	21	data	datum	NOUN
cana-4230	64	22	analysis	analysis	NOUN
cana-4230	64	23	described	describe	VERB
cana-4230	64	24	in	in	ADP
cana-4230	64	25	the	the	DET
cana-4230	64	26	next	next	ADJ
cana-4230	64	27	sections	section	NOUN
cana-4230	64	28	.	.	PUNCT
cana-4230	65	1	3	3	X
cana-4230	65	2	.	.	X
cana-4230	65	3	framework	framework	NOUN
cana-4230	65	4	for	for	ADP
cana-4230	65	5	high	high	ADJ
cana-4230	65	6	-	-	PUNCT
cana-4230	65	7	dimensional	dimensional	ADJ
cana-4230	65	8	data	datum	NOUN
cana-4230	65	9	analysis	analysis	NOUN
cana-4230	65	10	the	the	DET
cana-4230	65	11	framework	framework	NOUN
cana-4230	65	12	for	for	ADP
cana-4230	65	13	high	high	ADJ
cana-4230	65	14	-	-	PUNCT
cana-4230	65	15	dimensional	dimensional	ADJ
cana-4230	65	16	data	datum	NOUN
cana-4230	65	17	analysis	analysis	NOUN
cana-4230	65	18	proposed	propose	VERB
cana-4230	65	19	in	in	ADP
cana-4230	65	20	this	this	DET
cana-4230	65	21	work	work	NOUN
cana-4230	65	22	is	be	AUX
cana-4230	65	23	aimed	aim	VERB
cana-4230	65	24	at	at	ADP
cana-4230	65	25	covering	cover	VERB
cana-4230	65	26	the	the	DET
cana-4230	65	27	deficiencies	deficiency	NOUN
cana-4230	65	28	related	relate	VERB
cana-4230	65	29	to	to	ADP
cana-4230	65	30	complicated	complicated	ADJ
cana-4230	65	31	nonlinear	nonlinear	ADJ
cana-4230	65	32	dependencies	dependency	NOUN
cana-4230	65	33	in	in	ADP
cana-4230	65	34	present	present	ADJ
cana-4230	65	35	-	-	PUNCT
cana-4230	65	36	day	day	NOUN
cana-4230	65	37	sets	set	NOUN
cana-4230	65	38	.	.	PUNCT
cana-4230	66	1	this	this	DET
cana-4230	66	2	framework	framework	NOUN
cana-4230	66	3	combines	combine	VERB
cana-4230	66	4	nonlinear	nonlinear	ADJ
cana-4230	66	5	algebraic	algebraic	ADJ
cana-4230	66	6	topology	topology	NOUN
cana-4230	66	7	and	and	CCONJ
cana-4230	66	8	high	high	ADJ
cana-4230	66	9	-	-	PUNCT
cana-4230	66	10	level	level	NOUN
cana-4230	66	11	computational	computational	ADJ
cana-4230	66	12	methods	method	NOUN
cana-4230	66	13	to	to	PART
cana-4230	66	14	achieve	achieve	VERB
cana-4230	66	15	a	a	DET
cana-4230	66	16	scalable	scalable	ADJ
cana-4230	66	17	and	and	CCONJ
cana-4230	66	18	exact	exact	ADJ
cana-4230	66	19	approach	approach	NOUN
cana-4230	66	20	toward	toward	ADP
cana-4230	66	21	discovering	discover	VERB
cana-4230	66	22	rich	rich	ADJ
cana-4230	66	23	structural	structural	ADJ
cana-4230	66	24	features	feature	NOUN
cana-4230	66	25	from	from	ADP
cana-4230	66	26	high	high	ADJ
cana-4230	66	27	-	-	PUNCT
cana-4230	66	28	dimensional	dimensional	ADJ
cana-4230	66	29	data	datum	NOUN
cana-4230	66	30	.	.	PUNCT
cana-4230	67	1	the	the	DET
cana-4230	67	2	most	most	ADV
cana-4230	67	3	important	important	ADJ
cana-4230	67	4	modules	module	NOUN
cana-4230	67	5	in	in	ADP
cana-4230	67	6	the	the	DET
cana-4230	67	7	framework	framework	NOUN
cana-4230	67	8	are	be	AUX
cana-4230	67	9	data	datum	NOUN
cana-4230	67	10	preprocessing	preprocesse	VERB
cana-4230	67	11	and	and	CCONJ
cana-4230	67	12	topological	topological	ADJ
cana-4230	67	13	feature	feature	NOUN
cana-4230	67	14	extraction	extraction	NOUN
cana-4230	67	15	and	and	CCONJ
cana-4230	67	16	analysis	analysis	NOUN
cana-4230	67	17	,	,	PUNCT
cana-4230	67	18	which	which	PRON
cana-4230	67	19	are	be	AUX
cana-4230	67	20	organized	organize	VERB
cana-4230	67	21	to	to	PART
cana-4230	67	22	use	use	VERB
cana-4230	67	23	persistent	persistent	ADJ
cana-4230	67	24	homology	homology	NOUN
cana-4230	67	25	and	and	CCONJ
cana-4230	67	26	simplicial	simplicial	ADJ
cana-4230	67	27	complexes	complex	NOUN
cana-4230	67	28	for	for	ADP
cana-4230	67	29	more	more	ADV
cana-4230	67	30	effective	effective	ADJ
cana-4230	67	31	data	datum	NOUN
cana-4230	67	32	structural	structural	ADJ
cana-4230	67	33	analysis	analysis	NOUN
cana-4230	67	34	.	.	PUNCT
cana-4230	68	1	3.1	3.1	NUM
cana-4230	68	2	challenges	challenge	NOUN
cana-4230	68	3	in	in	ADP
cana-4230	68	4	high	high	ADJ
cana-4230	68	5	-	-	PUNCT
cana-4230	68	6	dimensional	dimensional	ADJ
cana-4230	68	7	data	datum	NOUN
cana-4230	68	8	spaces	space	NOUN
cana-4230	68	9	working	work	VERB
cana-4230	68	10	with	with	ADP
cana-4230	68	11	high	high	ADJ
cana-4230	68	12	-	-	PUNCT
cana-4230	68	13	dimensional	dimensional	ADJ
cana-4230	68	14	data	datum	NOUN
cana-4230	68	15	means	mean	VERB
cana-4230	68	16	facing	face	VERB
cana-4230	68	17	seven	seven	NUM
cana-4230	68	18	main	main	ADJ
cana-4230	68	19	challenges	challenge	NOUN
cana-4230	68	20	,	,	PUNCT
cana-4230	68	21	namely	namely	ADV
cana-4230	68	22	the	the	DET
cana-4230	68	23	curse	curse	NOUN
cana-4230	68	24	of	of	ADP
cana-4230	68	25	dimensionality	dimensionality	NOUN
cana-4230	68	26	,	,	PUNCT
cana-4230	68	27	over	over	ADV
cana-4230	68	28	-	-	PUNCT
cana-4230	68	29	fitting	fitting	ADJ
cana-4230	68	30	,	,	PUNCT
cana-4230	68	31	and	and	CCONJ
cana-4230	68	32	problems	problem	NOUN
cana-4230	68	33	with	with	ADP
cana-4230	68	34	understanding	understand	VERB
cana-4230	68	35	how	how	SCONJ
cana-4230	68	36	objects	object	NOUN
cana-4230	68	37	in	in	ADP
cana-4230	68	38	high	high	ADJ
cana-4230	68	39	-	-	PUNCT
cana-4230	68	40	dimensional	dimensional	ADJ
cana-4230	68	41	space	space	NOUN
cana-4230	68	42	are	be	AUX
cana-4230	68	43	positioned	position	VERB
cana-4230	68	44	relative	relative	ADJ
cana-4230	68	45	to	to	ADP
cana-4230	68	46	each	each	DET
cana-4230	68	47	other	other	ADJ
cana-4230	68	48	.	.	PUNCT
cana-4230	69	1	these	these	DET
cana-4230	69	2	challenges	challenge	NOUN
cana-4230	69	3	often	often	ADV
cana-4230	69	4	reduce	reduce	VERB
cana-4230	69	5	the	the	DET
cana-4230	69	6	efficacy	efficacy	NOUN
cana-4230	69	7	of	of	ADP
cana-4230	69	8	regular	regular	ADJ
cana-4230	69	9	approaches	approach	NOUN
cana-4230	69	10	to	to	ADP
cana-4230	69	11	both	both	DET
cana-4230	69	12	machine	machine	NOUN
cana-4230	69	13	learning	learning	NOUN
cana-4230	69	14	,	,	PUNCT
cana-4230	69	15	and	and	CCONJ
cana-4230	69	16	statistical	statistical	ADJ
cana-4230	69	17	analysis	analysis	NOUN
cana-4230	69	18	(	(	PUNCT
cana-4230	69	19	bellman	bellman	NOUN
cana-4230	69	20	,	,	PUNCT
cana-4230	69	21	1961	1961	NUM
cana-4230	69	22	)	)	PUNCT
cana-4230	69	23	.	.	PUNCT
cana-4230	70	1	the	the	DET
cana-4230	70	2	term	term	NOUN
cana-4230	70	3	curse	curse	NOUN
cana-4230	70	4	of	of	ADP
cana-4230	70	5	dimensionality	dimensionality	NOUN
cana-4230	70	6	bears	bear	VERB
cana-4230	70	7	testimony	testimony	NOUN
cana-4230	70	8	to	to	ADP
cana-4230	70	9	the	the	DET
cana-4230	70	10	rapid	rapid	ADJ
cana-4230	70	11	growth	growth	NOUN
cana-4230	70	12	in	in	ADP
cana-4230	70	13	the	the	DET
cana-4230	70	14	volume	volume	NOUN
cana-4230	70	15	as	as	SCONJ
cana-4230	70	16	the	the	DET
cana-4230	70	17	dimensions	dimension	NOUN
cana-4230	70	18	arise	arise	VERB
cana-4230	70	19	and	and	CCONJ
cana-4230	70	20	this	this	PRON
cana-4230	70	21	makes	make	VERB
cana-4230	70	22	it	it	PRON
cana-4230	70	23	almost	almost	ADV
cana-4230	70	24	impossible	impossible	ADJ
cana-4230	70	25	for	for	ADP
cana-4230	70	26	any	any	DET
cana-4230	70	27	method	method	NOUN
cana-4230	70	28	or	or	CCONJ
cana-4230	70	29	algorithm	algorithm	NOUN
cana-4230	70	30	to	to	PART
cana-4230	70	31	seek	seek	VERB
cana-4230	70	32	solutions	solution	NOUN
cana-4230	70	33	without	without	ADP
cana-4230	70	34	getting	getting	AUX
cana-4230	70	35	imbedded	imbed	VERB
cana-4230	70	36	in	in	ADP
cana-4230	70	37	noise	noise	NOUN
cana-4230	70	38	(	(	PUNCT
cana-4230	70	39	donoho	donoho	NOUN
cana-4230	70	40	,	,	PUNCT
cana-4230	70	41	2000	2000	NUM
cana-4230	70	42	)	)	PUNCT
cana-4230	70	43	.	.	PUNCT
cana-4230	71	1	in	in	ADP
cana-4230	71	2	addition	addition	NOUN
cana-4230	71	3	,	,	PUNCT
cana-4230	71	4	the	the	DET
cana-4230	71	5	high	high	ADJ
cana-4230	71	6	dimensionality	dimensionality	NOUN
cana-4230	71	7	of	of	ADP
cana-4230	71	8	the	the	DET
cana-4230	71	9	space	space	NOUN
cana-4230	71	10	does	do	AUX
cana-4230	71	11	not	not	PART
cana-4230	71	12	allow	allow	VERB
cana-4230	71	13	for	for	ADP
cana-4230	71	14	simple	simple	ADJ
cana-4230	71	15	visualization	visualization	NOUN
cana-4230	71	16	of	of	ADP
cana-4230	71	17	data	datum	NOUN
cana-4230	71	18	structures	structure	NOUN
cana-4230	71	19	,	,	PUNCT
cana-4230	71	20	and	and	CCONJ
cana-4230	71	21	their	their	PRON
cana-4230	71	22	analysis	analysis	NOUN
cana-4230	71	23	needs	need	VERB
cana-4230	71	24	more	more	ADV
cana-4230	71	25	powerful	powerful	ADJ
cana-4230	71	26	techniques	technique	NOUN
cana-4230	71	27	that	that	PRON
cana-4230	71	28	can	can	AUX
cana-4230	71	29	function	function	VERB
cana-4230	71	30	effectively	effectively	ADV
cana-4230	71	31	in	in	ADP
cana-4230	71	32	such	such	ADJ
cana-4230	71	33	environments	environment	NOUN
cana-4230	71	34	.	.	PUNCT
cana-4230	72	1	3.2	3.2	NUM
cana-4230	72	2	structure	structure	NOUN
cana-4230	72	3	of	of	ADP
cana-4230	72	4	the	the	DET
cana-4230	72	5	proposed	propose	VERB
cana-4230	72	6	framework	framework	NOUN
cana-4230	72	7	the	the	DET
cana-4230	72	8	proposed	propose	VERB
cana-4230	72	9	framework	framework	NOUN
cana-4230	72	10	consists	consist	VERB
cana-4230	72	11	of	of	ADP
cana-4230	72	12	three	three	NUM
cana-4230	72	13	main	main	ADJ
cana-4230	72	14	stages	stage	NOUN
cana-4230	72	15	:	:	PUNCT
cana-4230	72	16	raw	raw	ADJ
cana-4230	72	17	data	datum	NOUN
cana-4230	72	18	preparation	preparation	NOUN
cana-4230	72	19	,	,	PUNCT
cana-4230	72	20	topological	topological	ADJ
cana-4230	72	21	feature	feature	NOUN
cana-4230	72	22	extraction	extraction	NOUN
cana-4230	72	23	,	,	PUNCT
cana-4230	72	24	and	and	CCONJ
cana-4230	72	25	evaluation	evaluation	NOUN
cana-4230	72	26	.	.	PUNCT
cana-4230	73	1	all	all	DET
cana-4230	73	2	these	these	DET
cana-4230	73	3	phases	phase	NOUN
cana-4230	73	4	are	be	AUX
cana-4230	73	5	important	important	ADJ
cana-4230	73	6	for	for	ADP
cana-4230	73	7	the	the	DET
cana-4230	73	8	accurate	accurate	ADJ
cana-4230	73	9	application	application	NOUN
cana-4230	73	10	of	of	ADP
cana-4230	73	11	nonlinear	nonlinear	ADJ
cana-4230	73	12	algebraic	algebraic	ADJ
cana-4230	73	13	topology	topology	NOUN
cana-4230	73	14	on	on	ADP
cana-4230	73	15	high	high	ADJ
cana-4230	73	16	-	-	PUNCT
cana-4230	73	17	dimensional	dimensional	ADJ
cana-4230	73	18	data	datum	NOUN
cana-4230	73	19	.	.	PUNCT
cana-4230	74	1	table	table	NOUN
cana-4230	74	2	1	1	NUM
cana-4230	74	3	outlines	outline	VERB
cana-4230	74	4	the	the	DET
cana-4230	74	5	steps	step	NOUN
cana-4230	74	6	in	in	ADP
cana-4230	74	7	the	the	DET
cana-4230	74	8	framework	framework	NOUN
cana-4230	74	9	,	,	PUNCT
cana-4230	74	10	detailing	detail	VERB
cana-4230	74	11	the	the	DET
cana-4230	74	12	processes	process	NOUN
cana-4230	74	13	involved	involve	VERB
cana-4230	74	14	at	at	ADP
cana-4230	74	15	each	each	DET
cana-4230	74	16	stage	stage	NOUN
cana-4230	74	17	.	.	PUNCT
cana-4230	75	1	stage	stage	NOUN
cana-4230	75	2	description	description	NOUN
cana-4230	75	3	methods	method	NOUN
cana-4230	75	4	1	1	NUM
cana-4230	75	5	.	.	PUNCT
cana-4230	75	6	data	datum	NOUN
cana-4230	75	7	preprocessing	preprocesse	VERB
cana-4230	75	8	prepare	prepare	VERB
cana-4230	75	9	high	high	ADV
cana-4230	75	10	-	-	PUNCT
cana-4230	75	11	dimensional	dimensional	ADJ
cana-4230	75	12	data	datum	NOUN
cana-4230	75	13	for	for	ADP
cana-4230	75	14	analysis	analysis	NOUN
cana-4230	75	15	by	by	ADP
cana-4230	75	16	reducing	reduce	VERB
cana-4230	75	17	noise	noise	NOUN
cana-4230	75	18	and	and	CCONJ
cana-4230	75	19	normalizing	normalize	VERB
cana-4230	75	20	features	feature	NOUN
cana-4230	75	21	dimensionality	dimensionality	NOUN
cana-4230	75	22	reduction	reduction	NOUN
cana-4230	75	23	(	(	PUNCT
cana-4230	75	24	pca	pca	PROPN
cana-4230	75	25	,	,	PUNCT
cana-4230	75	26	t	t	PROPN
cana-4230	75	27	-	-	PUNCT
cana-4230	75	28	sne	sne	NOUN
cana-4230	75	29	)	)	PUNCT
cana-4230	75	30	,	,	PUNCT
cana-4230	75	31	data	datum	NOUN
cana-4230	75	32	normalization	normalization	NOUN
cana-4230	75	33	2	2	NUM
cana-4230	75	34	.	.	PUNCT
cana-4230	76	1	topological	topological	ADJ
cana-4230	76	2	feature	feature	NOUN
cana-4230	76	3	extraction	extraction	NOUN
cana-4230	76	4	identify	identify	VERB
cana-4230	76	5	topological	topological	ADJ
cana-4230	76	6	structures	structure	NOUN
cana-4230	76	7	in	in	ADP
cana-4230	76	8	the	the	DET
cana-4230	76	9	data	datum	NOUN
cana-4230	76	10	,	,	PUNCT
cana-4230	76	11	such	such	ADJ
cana-4230	76	12	as	as	ADP
cana-4230	76	13	loops	loop	NOUN
cana-4230	76	14	,	,	PUNCT
cana-4230	76	15	connected	connected	ADJ
cana-4230	76	16	components	component	NOUN
cana-4230	76	17	,	,	PUNCT
cana-4230	76	18	and	and	CCONJ
cana-4230	76	19	voids	void	NOUN
cana-4230	76	20	persistent	persistent	ADJ
cana-4230	76	21	homology	homology	NOUN
cana-4230	76	22	,	,	PUNCT
cana-4230	76	23	simplicial	simplicial	ADJ
cana-4230	76	24	complexes	complex	NOUN
cana-4230	76	25	3	3	NUM
cana-4230	76	26	.	.	X
cana-4230	77	1	analysis	analysis	NOUN
cana-4230	77	2	interpret	interpret	VERB
cana-4230	77	3	the	the	DET
cana-4230	77	4	extracted	extract	VERB
cana-4230	77	5	topological	topological	ADJ
cana-4230	77	6	features	feature	NOUN
cana-4230	77	7	for	for	ADP
cana-4230	77	8	insights	insight	NOUN
cana-4230	77	9	into	into	ADP
cana-4230	77	10	the	the	DET
cana-4230	77	11	data	data	NOUN
cana-4230	77	12	structure	structure	NOUN
cana-4230	77	13	persistence	persistence	NOUN
cana-4230	77	14	diagrams	diagram	NOUN
cana-4230	77	15	,	,	PUNCT
cana-4230	77	16	barcodes	barcode	NOUN
cana-4230	77	17	,	,	PUNCT
cana-4230	77	18	feature	feature	NOUN
cana-4230	77	19	significance	significance	NOUN
cana-4230	77	20	analysis	analysis	NOUN
cana-4230	77	21	communications	communication	NOUN
cana-4230	77	22	on	on	ADP
cana-4230	77	23	applied	apply	VERB
cana-4230	77	24	nonlinear	nonlinear	ADJ
cana-4230	77	25	analysis	analysis	NOUN
cana-4230	77	26	issn	issn	NOUN
cana-4230	77	27	:	:	PUNCT
cana-4230	77	28	1074	1074	NUM
cana-4230	77	29	-	-	PUNCT
cana-4230	77	30	133x	133x	NUM
cana-4230	77	31	vol	vol	NOUN
cana-4230	77	32	32	32	NUM
cana-4230	77	33	no	no	NOUN
cana-4230	77	34	.	.	PUNCT
cana-4230	78	1	8s	8s	PROPN
cana-4230	78	2	(	(	PUNCT
cana-4230	78	3	2025	2025	NUM
cana-4230	78	4	)	)	PUNCT
cana-4230	78	5	898	898	NUM
cana-4230	78	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	78	7	3.2.1	3.2.1	NUM
cana-4230	78	8	data	datum	NOUN
cana-4230	78	9	preprocessing	preprocesse	VERB
cana-4230	78	10	this	this	DET
cana-4230	78	11	process	process	NOUN
cana-4230	78	12	involves	involve	VERB
cana-4230	78	13	the	the	DET
cana-4230	78	14	transformation	transformation	NOUN
cana-4230	78	15	of	of	ADP
cana-4230	78	16	high	high	ADJ
cana-4230	78	17	-	-	PUNCT
cana-4230	78	18	dimensional	dimensional	ADJ
cana-4230	78	19	data	datum	NOUN
cana-4230	78	20	and	and	CCONJ
cana-4230	78	21	is	be	AUX
cana-4230	78	22	an	an	DET
cana-4230	78	23	important	important	ADJ
cana-4230	78	24	initial	initial	ADJ
cana-4230	78	25	phase	phase	NOUN
cana-4230	78	26	in	in	ADP
cana-4230	78	27	the	the	DET
cana-4230	78	28	proposed	propose	VERB
cana-4230	78	29	framework	framework	NOUN
cana-4230	78	30	.	.	PUNCT
cana-4230	79	1	this	this	DET
cana-4230	79	2	step	step	NOUN
cana-4230	79	3	was	be	AUX
cana-4230	79	4	to	to	PART
cana-4230	79	5	minimize	minimize	VERB
cana-4230	79	6	noise	noise	NOUN
cana-4230	79	7	and	and	CCONJ
cana-4230	79	8	to	to	PART
cana-4230	79	9	ensure	ensure	VERB
cana-4230	79	10	that	that	SCONJ
cana-4230	79	11	the	the	DET
cana-4230	79	12	data	datum	NOUN
cana-4230	79	13	was	be	AUX
cana-4230	79	14	properly	properly	ADV
cana-4230	79	15	arranged	arrange	VERB
cana-4230	79	16	in	in	ADP
cana-4230	79	17	a	a	DET
cana-4230	79	18	manner	manner	NOUN
cana-4230	79	19	that	that	PRON
cana-4230	79	20	would	would	AUX
cana-4230	79	21	facilitate	facilitate	VERB
cana-4230	79	22	its	its	PRON
cana-4230	79	23	analysis	analysis	NOUN
cana-4230	79	24	from	from	ADP
cana-4230	79	25	a	a	DET
cana-4230	79	26	topological	topological	ADJ
cana-4230	79	27	point	point	NOUN
cana-4230	79	28	of	of	ADP
cana-4230	79	29	view	view	NOUN
cana-4230	79	30	.	.	PUNCT
cana-4230	80	1	standard	standard	ADJ
cana-4230	80	2	practices	practice	NOUN
cana-4230	80	3	imply	imply	VERB
cana-4230	80	4	using	use	VERB
cana-4230	80	5	dimensionality	dimensionality	NOUN
cana-4230	80	6	reduction	reduction	NOUN
cana-4230	80	7	methods	method	NOUN
cana-4230	80	8	like	like	ADP
cana-4230	80	9	pca	pca	PROPN
cana-4230	80	10	,	,	PUNCT
cana-4230	80	11	and	and	CCONJ
cana-4230	80	12	t	t	PROPN
cana-4230	80	13	-	-	PUNCT
cana-4230	80	14	sne	sne	PROPN
cana-4230	80	15	and	and	CCONJ
cana-4230	80	16	require	require	VERB
cana-4230	80	17	data	datum	NOUN
cana-4230	80	18	modification	modification	NOUN
cana-4230	80	19	to	to	PART
cana-4230	80	20	have	have	VERB
cana-4230	80	21	a	a	DET
cana-4230	80	22	limited	limited	ADJ
cana-4230	80	23	number	number	NOUN
cana-4230	80	24	of	of	ADP
cana-4230	80	25	dimensions	dimension	NOUN
cana-4230	80	26	that	that	PRON
cana-4230	80	27	retain	retain	VERB
cana-4230	80	28	critical	critical	ADJ
cana-4230	80	29	features	feature	NOUN
cana-4230	80	30	(	(	PUNCT
cana-4230	80	31	van	van	PROPN
cana-4230	80	32	der	der	NOUN
cana-4230	80	33	maaten	maaten	VERB
cana-4230	80	34	&	&	CCONJ
cana-4230	80	35	hinton	hinton	PROPN
cana-4230	80	36	,	,	PUNCT
cana-4230	80	37	2008	2008	NUM
cana-4230	80	38	)	)	PUNCT
cana-4230	80	39	.	.	PUNCT
cana-4230	81	1	data	datum	NOUN
cana-4230	81	2	normalization	normalization	NOUN
cana-4230	81	3	is	be	AUX
cana-4230	81	4	also	also	ADV
cana-4230	81	5	applied	apply	VERB
cana-4230	81	6	in	in	ADP
cana-4230	81	7	a	a	DET
cana-4230	81	8	given	give	VERB
cana-4230	81	9	feature	feature	NOUN
cana-4230	81	10	to	to	PART
cana-4230	81	11	be	be	AUX
cana-4230	81	12	scaled	scale	VERB
cana-4230	81	13	appropriately	appropriately	ADV
cana-4230	81	14	for	for	ADP
cana-4230	81	15	topological	topological	ADJ
cana-4230	81	16	analysis	analysis	NOUN
cana-4230	81	17	a	a	DET
cana-4230	81	18	process	process	NOUN
cana-4230	81	19	that	that	PRON
cana-4230	81	20	is	be	AUX
cana-4230	81	21	sensitive	sensitive	ADJ
cana-4230	81	22	to	to	ADP
cana-4230	81	23	distance	distance	NOUN
cana-4230	81	24	metrics	metric	NOUN
cana-4230	81	25	.	.	PUNCT
cana-4230	82	1	3.2.2	3.2.2	NUM
cana-4230	82	2	topological	topological	ADJ
cana-4230	82	3	feature	feature	NOUN
cana-4230	82	4	extraction	extraction	NOUN
cana-4230	82	5	the	the	DET
cana-4230	82	6	second	second	ADJ
cana-4230	82	7	process	process	NOUN
cana-4230	82	8	of	of	ADP
cana-4230	82	9	the	the	DET
cana-4230	82	10	framework	framework	NOUN
cana-4230	82	11	involves	involve	VERB
cana-4230	82	12	feature	feature	NOUN
cana-4230	82	13	extraction	extraction	NOUN
cana-4230	82	14	of	of	ADP
cana-4230	82	15	topological	topological	ADJ
cana-4230	82	16	features	feature	NOUN
cana-4230	82	17	from	from	ADP
cana-4230	82	18	the	the	DET
cana-4230	82	19	preprocessed	preprocesse	VERB
cana-4230	82	20	data	datum	NOUN
cana-4230	82	21	.	.	PUNCT
cana-4230	83	1	this	this	PRON
cana-4230	83	2	is	be	AUX
cana-4230	83	3	done	do	VERB
cana-4230	83	4	with	with	ADP
cana-4230	83	5	the	the	DET
cana-4230	83	6	help	help	NOUN
cana-4230	83	7	of	of	ADP
cana-4230	83	8	persistent	persistent	ADJ
cana-4230	83	9	homology	homology	NOUN
cana-4230	83	10	which	which	PRON
cana-4230	83	11	,	,	PUNCT
cana-4230	83	12	in	in	ADP
cana-4230	83	13	a	a	DET
cana-4230	83	14	nutshell	nutshell	NOUN
cana-4230	83	15	,	,	PUNCT
cana-4230	83	16	is	be	AUX
cana-4230	83	17	an	an	DET
cana-4230	83	18	approach	approach	NOUN
cana-4230	83	19	that	that	PRON
cana-4230	83	20	takes	take	VERB
cana-4230	83	21	filter	filter	NOUN
cana-4230	83	22	parameters	parameter	NOUN
cana-4230	83	23	,	,	PUNCT
cana-4230	83	24	sorts	sort	VERB
cana-4230	83	25	them	they	PRON
cana-4230	83	26	in	in	ADP
cana-4230	83	27	some	some	DET
cana-4230	83	28	order	order	NOUN
cana-4230	83	29	,	,	PUNCT
cana-4230	83	30	and	and	CCONJ
cana-4230	83	31	finds	find	VERB
cana-4230	83	32	the	the	DET
cana-4230	83	33	birth	birth	NOUN
cana-4230	83	34	and	and	CCONJ
cana-4230	83	35	death	death	NOUN
cana-4230	83	36	of	of	ADP
cana-4230	83	37	connected	connected	ADJ
cana-4230	83	38	components	component	NOUN
cana-4230	83	39	and	and	CCONJ
cana-4230	83	40	loops	loop	NOUN
cana-4230	83	41	and	and	CCONJ
cana-4230	83	42	voids	voids	NOUN
cana-4230	83	43	of	of	ADP
cana-4230	83	44	these	these	DET
cana-4230	83	45	parameters	parameter	NOUN
cana-4230	83	46	(	(	PUNCT
cana-4230	83	47	edelsbrunner	edelsbrunner	NOUN
cana-4230	83	48	&	&	CCONJ
cana-4230	83	49	harer	harer	NOUN
cana-4230	83	50	,	,	PUNCT
cana-4230	83	51	2010	2010	NUM
cana-4230	83	52	)	)	PUNCT
cana-4230	83	53	.	.	PUNCT
cana-4230	84	1	the	the	DET
cana-4230	84	2	filtration	filtration	NOUN
cana-4230	84	3	process	process	NOUN
cana-4230	84	4	is	be	AUX
cana-4230	84	5	to	to	PART
cana-4230	84	6	construct	construct	VERB
cana-4230	84	7	a	a	DET
cana-4230	84	8	sequence	sequence	NOUN
cana-4230	84	9	of	of	ADP
cana-4230	84	10	simplicial	simplicial	ADJ
cana-4230	84	11	complexes	complex	NOUN
cana-4230	84	12	and	and	CCONJ
cana-4230	84	13	each	each	PRON
cana-4230	84	14	approximates	approximate	VERB
cana-4230	84	15	the	the	DET
cana-4230	84	16	data	data	NOUN
cana-4230	84	17	structure	structure	NOUN
cana-4230	84	18	at	at	ADP
cana-4230	84	19	the	the	DET
cana-4230	84	20	different	different	ADJ
cana-4230	84	21	scales	scale	NOUN
cana-4230	84	22	.	.	PUNCT
cana-4230	85	1	during	during	ADP
cana-4230	85	2	the	the	DET
cana-4230	85	3	filtration	filtration	NOUN
cana-4230	85	4	,	,	PUNCT
cana-4230	85	5	the	the	DET
cana-4230	85	6	functions	function	NOUN
cana-4230	85	7	become	become	VERB
cana-4230	85	8	smoother	smooth	ADJ
cana-4230	85	9	,	,	PUNCT
cana-4230	85	10	and	and	CCONJ
cana-4230	85	11	randomly	randomly	ADV
cana-4230	85	12	appearing	appear	VERB
cana-4230	85	13	features	feature	NOUN
cana-4230	85	14	create	create	VERB
cana-4230	85	15	simple	simple	ADJ
cana-4230	85	16	patterns	pattern	NOUN
cana-4230	85	17	of	of	ADP
cana-4230	85	18	topological	topological	ADJ
cana-4230	85	19	features	feature	NOUN
cana-4230	85	20	that	that	PRON
cana-4230	85	21	help	help	VERB
cana-4230	85	22	to	to	PART
cana-4230	85	23	understand	understand	VERB
cana-4230	85	24	the	the	DET
cana-4230	85	25	structure	structure	NOUN
cana-4230	85	26	of	of	ADP
cana-4230	85	27	the	the	DET
cana-4230	85	28	data	datum	NOUN
cana-4230	85	29	.	.	PUNCT
cana-4230	86	1	some	some	PRON
cana-4230	86	2	of	of	ADP
cana-4230	86	3	these	these	DET
cana-4230	86	4	topological	topological	ADJ
cana-4230	86	5	features	feature	NOUN
cana-4230	86	6	are	be	AUX
cana-4230	86	7	transient	transient	ADJ
cana-4230	86	8	and	and	CCONJ
cana-4230	86	9	persistent	persistent	ADJ
cana-4230	86	10	homology	homology	NOUN
cana-4230	86	11	captures	capture	VERB
cana-4230	86	12	their	their	PRON
cana-4230	86	13	lifetime	lifetime	NOUN
cana-4230	86	14	by	by	ADP
cana-4230	86	15	representing	represent	VERB
cana-4230	86	16	it	it	PRON
cana-4230	86	17	in	in	ADP
cana-4230	86	18	the	the	DET
cana-4230	86	19	form	form	NOUN
cana-4230	86	20	of	of	ADP
cana-4230	86	21	persistence	persistence	NOUN
cana-4230	86	22	diagrams	diagram	NOUN
cana-4230	86	23	or	or	CCONJ
cana-4230	86	24	barcodes	barcode	NOUN
cana-4230	86	25	.	.	PUNCT
cana-4230	87	1	called	call	VERB
cana-4230	87	2	persistence	persistence	PROPN
cana-4230	87	3	diagram	diagram	PROPN
cana-4230	87	4	carlsson	carlsson	PROPN
cana-4230	87	5	(	(	PUNCT
cana-4230	87	6	2009	2009	NUM
cana-4230	87	7	)	)	PUNCT
cana-4230	87	8	,	,	PUNCT
cana-4230	87	9	each	each	DET
cana-4230	87	10	point	point	NOUN
cana-4230	87	11	corresponds	correspond	VERB
cana-4230	87	12	to	to	ADP
cana-4230	87	13	a	a	DET
cana-4230	87	14	topological	topological	ADJ
cana-4230	87	15	feature	feature	NOUN
cana-4230	87	16	with	with	ADP
cana-4230	87	17	the	the	DET
cana-4230	87	18	birth	birth	NOUN
cana-4230	87	19	time	time	NOUN
cana-4230	87	20	in	in	ADP
cana-4230	87	21	the	the	DET
cana-4230	87	22	abscissa	abscissa	NOUN
cana-4230	87	23	and	and	CCONJ
cana-4230	87	24	the	the	DET
cana-4230	87	25	death	death	NOUN
cana-4230	87	26	one	one	NUM
cana-4230	87	27	in	in	ADP
cana-4230	87	28	the	the	DET
cana-4230	87	29	ordinate	ordinate	NOUN
cana-4230	87	30	.	.	PUNCT
cana-4230	88	1	long	long	ADJ
cana-4230	88	2	living	living	NOUN
cana-4230	88	3	corresponds	correspond	VERB
cana-4230	88	4	to	to	ADP
cana-4230	88	5	large	large	ADJ
cana-4230	88	6	;	;	PUNCT
cana-4230	88	7	significant	significant	ADJ
cana-4230	88	8	features	feature	NOUN
cana-4230	88	9	that	that	PRON
cana-4230	88	10	are	be	AUX
cana-4230	88	11	scale	scale	NOUN
cana-4230	88	12	-	-	PUNCT
cana-4230	88	13	invariant	invariant	ADJ
cana-4230	88	14	and	and	CCONJ
cana-4230	88	15	strong	strong	ADJ
cana-4230	88	16	while	while	SCONJ
cana-4230	88	17	short	short	ADJ
cana-4230	88	18	living	living	NOUN
cana-4230	88	19	corresponds	correspond	VERB
cana-4230	88	20	to	to	ADP
cana-4230	88	21	noise	noise	NOUN
cana-4230	88	22	.	.	PUNCT
cana-4230	89	1	table	table	NOUN
cana-4230	89	2	2	2	NUM
cana-4230	89	3	provides	provide	VERB
cana-4230	89	4	a	a	DET
cana-4230	89	5	sample	sample	NOUN
cana-4230	89	6	of	of	ADP
cana-4230	89	7	extracted	extract	VERB
cana-4230	89	8	topological	topological	ADJ
cana-4230	89	9	features	feature	NOUN
cana-4230	89	10	from	from	ADP
cana-4230	89	11	a	a	DET
cana-4230	89	12	high	high	ADJ
cana-4230	89	13	-	-	PUNCT
cana-4230	89	14	dimensional	dimensional	ADJ
cana-4230	89	15	dataset	dataset	NOUN
cana-4230	89	16	,	,	PUNCT
cana-4230	89	17	showing	show	VERB
cana-4230	89	18	their	their	PRON
cana-4230	89	19	respective	respective	ADJ
cana-4230	89	20	birth	birth	NOUN
cana-4230	89	21	and	and	CCONJ
cana-4230	89	22	death	death	NOUN
cana-4230	89	23	times	time	NOUN
cana-4230	89	24	.	.	PUNCT
cana-4230	90	1	feature	feature	VERB
cana-4230	90	2	birth	birth	NOUN
cana-4230	90	3	time	time	NOUN
cana-4230	90	4	death	death	NOUN
cana-4230	90	5	time	time	NOUN
cana-4230	90	6	lifespan	lifespan	PROPN
cana-4230	90	7	type	type	NOUN
cana-4230	90	8	of	of	ADP
cana-4230	90	9	feature	feature	NOUN
cana-4230	90	10	feature	feature	NOUN
cana-4230	90	11	1	1	NUM
cana-4230	90	12	0.15	0.15	NUM
cana-4230	90	13	0.90	0.90	NUM
cana-4230	90	14	0.75	0.75	NUM
cana-4230	90	15	loop	loop	NOUN
cana-4230	90	16	feature	feature	NOUN
cana-4230	90	17	2	2	NUM
cana-4230	90	18	0.20	0.20	NUM
cana-4230	90	19	0.60	0.60	NUM
cana-4230	90	20	0.40	0.40	NUM
cana-4230	90	21	connected	connect	VERB
cana-4230	90	22	component	component	NOUN
cana-4230	90	23	feature	feature	NOUN
cana-4230	90	24	3	3	NUM
cana-4230	90	25	0.05	0.05	NUM
cana-4230	90	26	0.30	0.30	NUM
cana-4230	90	27	0.25	0.25	NUM
cana-4230	90	28	void	void	ADJ
cana-4230	90	29	this	this	DET
cana-4230	90	30	analysis	analysis	NOUN
cana-4230	90	31	helps	help	VERB
cana-4230	90	32	in	in	ADP
cana-4230	90	33	distinguishing	distinguish	VERB
cana-4230	90	34	between	between	ADP
cana-4230	90	35	significant	significant	ADJ
cana-4230	90	36	topological	topological	ADJ
cana-4230	90	37	features	feature	NOUN
cana-4230	90	38	that	that	PRON
cana-4230	90	39	represent	represent	VERB
cana-4230	90	40	essential	essential	ADJ
cana-4230	90	41	structures	structure	NOUN
cana-4230	90	42	within	within	ADP
cana-4230	90	43	the	the	DET
cana-4230	90	44	dataset	dataset	NOUN
cana-4230	90	45	and	and	CCONJ
cana-4230	90	46	those	those	PRON
cana-4230	90	47	that	that	PRON
cana-4230	90	48	are	be	AUX
cana-4230	90	49	transient	transient	ADJ
cana-4230	90	50	,	,	PUNCT
cana-4230	90	51	likely	likely	ADV
cana-4230	90	52	representing	represent	VERB
cana-4230	90	53	noise	noise	NOUN
cana-4230	90	54	.	.	PUNCT
cana-4230	91	1	3.3	3.3	NUM
cana-4230	91	2	comparison	comparison	NOUN
cana-4230	91	3	with	with	ADP
cana-4230	91	4	traditional	traditional	ADJ
cana-4230	91	5	methods	method	NOUN
cana-4230	91	6	the	the	DET
cana-4230	91	7	proposed	propose	VERB
cana-4230	91	8	nalt	nalt	NOUN
cana-4230	91	9	has	have	VERB
cana-4230	91	10	several	several	ADJ
cana-4230	91	11	main	main	ADJ
cana-4230	91	12	advantages	advantage	NOUN
cana-4230	91	13	over	over	ADP
cana-4230	91	14	the	the	DET
cana-4230	91	15	other	other	ADJ
cana-4230	91	16	approaches	approach	NOUN
cana-4230	91	17	such	such	ADJ
cana-4230	91	18	as	as	ADP
cana-4230	91	19	pca	pca	PROPN
cana-4230	91	20	,	,	PUNCT
cana-4230	91	21	clustering	clustering	ADJ
cana-4230	91	22	algorithms	algorithm	NOUN
cana-4230	91	23	,	,	PUNCT
cana-4230	91	24	or	or	CCONJ
cana-4230	91	25	linear	linear	ADJ
cana-4230	91	26	regression	regression	NOUN
cana-4230	91	27	.	.	PUNCT
cana-4230	92	1	compared	compare	VERB
cana-4230	92	2	to	to	ADP
cana-4230	92	3	traditional	traditional	ADJ
cana-4230	92	4	methods	method	NOUN
cana-4230	92	5	,	,	PUNCT
cana-4230	92	6	topological	topological	ADJ
cana-4230	92	7	methods	method	NOUN
cana-4230	92	8	assume	assume	VERB
cana-4230	92	9	more	more	ADJ
cana-4230	92	10	flexibility	flexibility	NOUN
cana-4230	92	11	in	in	ADP
cana-4230	92	12	the	the	DET
cana-4230	92	13	relationship	relationship	NOUN
cana-4230	92	14	between	between	ADP
cana-4230	92	15	data	datum	NOUN
cana-4230	92	16	points	point	NOUN
cana-4230	92	17	because	because	SCONJ
cana-4230	92	18	instead	instead	ADV
cana-4230	92	19	of	of	ADP
cana-4230	92	20	assuming	assume	VERB
cana-4230	92	21	linearity	linearity	NOUN
cana-4230	92	22	or	or	CCONJ
cana-4230	92	23	gaussian	gaussian	ADJ
cana-4230	92	24	distribution	distribution	NOUN
cana-4230	92	25	in	in	ADP
cana-4230	92	26	the	the	DET
cana-4230	92	27	flow	flow	NOUN
cana-4230	92	28	of	of	ADP
cana-4230	92	29	data	datum	NOUN
cana-4230	92	30	,	,	PUNCT
cana-4230	92	31	topological	topological	ADJ
cana-4230	92	32	methods	method	NOUN
cana-4230	92	33	,	,	PUNCT
cana-4230	92	34	(	(	PUNCT
cana-4230	92	35	2018	2018	NUM
cana-4230	92	36	)	)	PUNCT
cana-4230	92	37	are	be	AUX
cana-4230	92	38	designed	design	VERB
cana-4230	92	39	for	for	ADP
cana-4230	92	40	more	more	ADJ
cana-4230	92	41	complex	complex	ADJ
cana-4230	92	42	topological	topological	ADJ
cana-4230	92	43	relationships	relationship	NOUN
cana-4230	92	44	.	.	PUNCT
cana-4230	93	1	compared	compare	VERB
cana-4230	93	2	to	to	ADP
cana-4230	93	3	methods	method	NOUN
cana-4230	93	4	such	such	ADJ
cana-4230	93	5	as	as	ADP
cana-4230	93	6	pca	pca	PROPN
cana-4230	93	7	,	,	PUNCT
cana-4230	93	8	which	which	PRON
cana-4230	93	9	remove	remove	VERB
cana-4230	93	10	much	much	ADJ
cana-4230	93	11	of	of	ADP
cana-4230	93	12	the	the	DET
cana-4230	93	13	structure	structure	NOUN
cana-4230	93	14	communications	communication	NOUN
cana-4230	93	15	on	on	ADP
cana-4230	93	16	applied	apply	VERB
cana-4230	93	17	nonlinear	nonlinear	ADJ
cana-4230	93	18	analysis	analysis	NOUN
cana-4230	93	19	issn	issn	NOUN
cana-4230	93	20	:	:	PUNCT
cana-4230	93	21	1074	1074	NUM
cana-4230	93	22	-	-	PUNCT
cana-4230	93	23	133x	133x	NUM
cana-4230	93	24	vol	vol	NOUN
cana-4230	93	25	32	32	NUM
cana-4230	93	26	no	no	NOUN
cana-4230	93	27	.	.	PUNCT
cana-4230	94	1	8s	8s	PROPN
cana-4230	94	2	(	(	PUNCT
cana-4230	94	3	2025	2025	NUM
cana-4230	94	4	)	)	PUNCT
cana-4230	94	5	899	899	NUM
cana-4230	94	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	94	7	when	when	SCONJ
cana-4230	94	8	reducing	reduce	VERB
cana-4230	94	9	their	their	PRON
cana-4230	94	10	dimensionality	dimensionality	NOUN
cana-4230	94	11	,	,	PUNCT
cana-4230	94	12	topological	topological	ADJ
cana-4230	94	13	methods	method	NOUN
cana-4230	94	14	retain	retain	VERB
cana-4230	94	15	structure	structure	NOUN
cana-4230	94	16	at	at	ADP
cana-4230	94	17	every	every	DET
cana-4230	94	18	scale	scale	NOUN
cana-4230	94	19	and	and	CCONJ
cana-4230	94	20	therefore	therefore	ADV
cana-4230	94	21	offer	offer	VERB
cana-4230	94	22	the	the	DET
cana-4230	94	23	data	data	NOUN
cana-4230	94	24	analyst	analyst	NOUN
cana-4230	94	25	a	a	DET
cana-4230	94	26	greater	great	ADJ
cana-4230	94	27	degree	degree	NOUN
cana-4230	94	28	of	of	ADP
cana-4230	94	29	insight	insight	NOUN
cana-4230	94	30	into	into	ADP
cana-4230	94	31	the	the	DET
cana-4230	94	32	data	datum	NOUN
cana-4230	94	33	’s	’s	PART
cana-4230	94	34	geometric	geometric	ADJ
cana-4230	94	35	properties	property	NOUN
cana-4230	94	36	.	.	PUNCT
cana-4230	95	1	further	far	ADV
cana-4230	95	2	,	,	PUNCT
cana-4230	95	3	tda	tda	PROPN
cana-4230	95	4	will	will	AUX
cana-4230	95	5	reveal	reveal	VERB
cana-4230	95	6	such	such	ADJ
cana-4230	95	7	geometric	geometric	ADJ
cana-4230	95	8	features	feature	NOUN
cana-4230	95	9	as	as	ADP
cana-4230	95	10	loops	loop	NOUN
cana-4230	95	11	and	and	CCONJ
cana-4230	95	12	voids	void	NOUN
cana-4230	95	13	that	that	PRON
cana-4230	95	14	are	be	AUX
cana-4230	95	15	often	often	ADV
cana-4230	95	16	ignored	ignore	VERB
cana-4230	95	17	by	by	ADP
cana-4230	95	18	different	different	ADJ
cana-4230	95	19	methods	method	NOUN
cana-4230	95	20	.	.	PUNCT
cana-4230	96	1	for	for	ADP
cana-4230	96	2	instance	instance	NOUN
cana-4230	96	3	,	,	PUNCT
cana-4230	96	4	while	while	SCONJ
cana-4230	96	5	agricultural	agricultural	ADJ
cana-4230	96	6	application	application	NOUN
cana-4230	96	7	k	k	NOUN
cana-4230	96	8	-	-	PUNCT
cana-4230	96	9	means	mean	VERB
cana-4230	96	10	explicitly	explicitly	ADV
cana-4230	96	11	target	target	VERB
cana-4230	96	12	data	datum	NOUN
cana-4230	96	13	clustering	clustering	NOUN
cana-4230	96	14	,	,	PUNCT
cana-4230	96	15	the	the	DET
cana-4230	96	16	algorithms	algorithm	NOUN
cana-4230	96	17	can	can	AUX
cana-4230	96	18	fail	fail	VERB
cana-4230	96	19	to	to	PART
cana-4230	96	20	identify	identify	VERB
cana-4230	96	21	other	other	ADJ
cana-4230	96	22	features	feature	NOUN
cana-4230	96	23	like	like	ADP
cana-4230	96	24	loops	loop	NOUN
cana-4230	96	25	or	or	CCONJ
cana-4230	96	26	holes	hole	NOUN
cana-4230	96	27	that	that	PRON
cana-4230	96	28	often	often	ADV
cana-4230	96	29	pervade	pervade	VERB
cana-4230	96	30	data	datum	NOUN
cana-4230	96	31	(	(	PUNCT
cana-4230	96	32	zomorodian	zomorodian	ADJ
cana-4230	96	33	,	,	PUNCT
cana-4230	96	34	2005	2005	NUM
cana-4230	96	35	)	)	PUNCT
cana-4230	96	36	.	.	PUNCT
cana-4230	97	1	the	the	DET
cana-4230	97	2	fact	fact	NOUN
cana-4230	97	3	that	that	SCONJ
cana-4230	97	4	this	this	DET
cana-4230	97	5	framework	framework	NOUN
cana-4230	97	6	employs	employ	VERB
cana-4230	97	7	persistent	persistent	ADJ
cana-4230	97	8	homology	homology	NOUN
cana-4230	97	9	makes	make	VERB
cana-4230	97	10	it	it	PRON
cana-4230	97	11	possible	possible	ADJ
cana-4230	97	12	to	to	PART
cana-4230	97	13	offer	offer	VERB
cana-4230	97	14	a	a	DET
cana-4230	97	15	more	more	ADV
cana-4230	97	16	detailed	detailed	ADJ
cana-4230	97	17	and	and	CCONJ
cana-4230	97	18	complex	complex	ADJ
cana-4230	97	19	vision	vision	NOUN
cana-4230	97	20	of	of	ADP
cana-4230	97	21	the	the	DET
cana-4230	97	22	data	datum	NOUN
cana-4230	97	23	compared	compare	VERB
cana-4230	97	24	to	to	ADP
cana-4230	97	25	the	the	DET
cana-4230	97	26	other	other	ADJ
cana-4230	97	27	units	unit	NOUN
cana-4230	97	28	i	i	PRON
cana-4230	97	29	introduced	introduce	VERB
cana-4230	97	30	earlier	early	ADV
cana-4230	97	31	.	.	PUNCT
cana-4230	98	1	3.4	3.4	NUM
cana-4230	98	2	implementation	implementation	NOUN
cana-4230	98	3	and	and	CCONJ
cana-4230	98	4	scalability	scalability	NOUN
cana-4230	98	5	the	the	DET
cana-4230	98	6	computational	computational	ADJ
cana-4230	98	7	tractability	tractability	NOUN
cana-4230	98	8	of	of	ADP
cana-4230	98	9	the	the	DET
cana-4230	98	10	proposed	propose	VERB
cana-4230	98	11	framework	framework	NOUN
cana-4230	98	12	is	be	AUX
cana-4230	98	13	based	base	VERB
cana-4230	98	14	on	on	ADP
cana-4230	98	15	efficient	efficient	ADJ
cana-4230	98	16	implementations	implementation	NOUN
cana-4230	98	17	of	of	ADP
cana-4230	98	18	persistent	persistent	ADJ
cana-4230	98	19	homology	homology	NOUN
cana-4230	98	20	and	and	CCONJ
cana-4230	98	21	simplicial	simplicial	ADJ
cana-4230	98	22	complexes	complex	NOUN
cana-4230	98	23	with	with	ADP
cana-4230	98	24	the	the	DET
cana-4230	98	25	help	help	NOUN
cana-4230	98	26	of	of	ADP
cana-4230	98	27	algorithms	algorithm	NOUN
cana-4230	98	28	like	like	INTJ
cana-4230	98	29	gudhi	gudhi	NOUN
cana-4230	98	30	and	and	CCONJ
cana-4230	98	31	ripser	ripser	NOUN
cana-4230	98	32	(	(	PUNCT
cana-4230	98	33	maria	maria	PROPN
cana-4230	98	34	et	et	PROPN
cana-4230	98	35	al	al	PROPN
cana-4230	98	36	.	.	PROPN
cana-4230	98	37	,	,	PUNCT
cana-4230	98	38	2014	2014	NUM
cana-4230	98	39	;	;	PUNCT
cana-4230	98	40	bauer	bauer	PROPN
cana-4230	98	41	et	et	PROPN
cana-4230	98	42	al	al	PROPN
cana-4230	98	43	.	.	PROPN
cana-4230	98	44	,	,	PUNCT
cana-4230	98	45	2014	2014	NUM
cana-4230	98	46	)	)	PUNCT
cana-4230	98	47	.	.	PUNCT
cana-4230	99	1	the	the	DET
cana-4230	99	2	use	use	NOUN
cana-4230	99	3	of	of	ADP
cana-4230	99	4	these	these	DET
cana-4230	99	5	tools	tool	NOUN
cana-4230	99	6	is	be	AUX
cana-4230	99	7	suited	suit	VERB
cana-4230	99	8	for	for	ADP
cana-4230	99	9	the	the	DET
cana-4230	99	10	modeling	modeling	NOUN
cana-4230	99	11	of	of	ADP
cana-4230	99	12	large	large	ADJ
cana-4230	99	13	datasets	dataset	NOUN
cana-4230	99	14	of	of	ADP
cana-4230	99	15	high	high	ADJ
cana-4230	99	16	dimensions	dimension	NOUN
cana-4230	99	17	and	and	CCONJ
cana-4230	99	18	data	datum	NOUN
cana-4230	99	19	processing	processing	NOUN
cana-4230	99	20	is	be	AUX
cana-4230	99	21	not	not	PART
cana-4230	99	22	very	very	ADV
cana-4230	99	23	computationally	computationally	ADV
cana-4230	99	24	intensive	intensive	ADJ
cana-4230	99	25	.	.	PUNCT
cana-4230	100	1	it	it	PRON
cana-4230	100	2	is	be	AUX
cana-4230	100	3	also	also	ADV
cana-4230	100	4	extensible	extensible	ADJ
cana-4230	100	5	which	which	PRON
cana-4230	100	6	means	mean	VERB
cana-4230	100	7	it	it	PRON
cana-4230	100	8	can	can	AUX
cana-4230	100	9	be	be	AUX
cana-4230	100	10	used	use	VERB
cana-4230	100	11	for	for	ADP
cana-4230	100	12	datasets	dataset	NOUN
cana-4230	100	13	containing	contain	VERB
cana-4230	100	14	a	a	DET
cana-4230	100	15	few	few	ADJ
cana-4230	100	16	biological	biological	ADJ
cana-4230	100	17	records	record	NOUN
cana-4230	100	18	and	and	CCONJ
cana-4230	100	19	extending	extend	VERB
cana-4230	100	20	through	through	ADP
cana-4230	100	21	to	to	ADP
cana-4230	100	22	social	social	ADJ
cana-4230	100	23	networks	network	NOUN
cana-4230	100	24	that	that	PRON
cana-4230	100	25	could	could	AUX
cana-4230	100	26	hold	hold	VERB
cana-4230	100	27	thousands	thousand	NOUN
cana-4230	100	28	of	of	ADP
cana-4230	100	29	records	record	NOUN
cana-4230	100	30	.	.	PUNCT
cana-4230	101	1	4	4	X
cana-4230	101	2	.	.	X
cana-4230	101	3	nonlinear	nonlinear	ADJ
cana-4230	101	4	algebraic	algebraic	PROPN
cana-4230	101	5	topology	topology	NOUN
cana-4230	101	6	techniques	technique	NOUN
cana-4230	101	7	in	in	ADP
cana-4230	101	8	particular	particular	ADJ
cana-4230	101	9	,	,	PUNCT
cana-4230	101	10	nonlinear	nonlinear	ADJ
cana-4230	101	11	algebraic	algebraic	ADJ
cana-4230	101	12	topology	topology	NOUN
cana-4230	101	13	includes	include	VERB
cana-4230	101	14	a	a	DET
cana-4230	101	15	rich	rich	ADJ
cana-4230	101	16	collection	collection	NOUN
cana-4230	101	17	of	of	ADP
cana-4230	101	18	instruments	instrument	NOUN
cana-4230	101	19	effectively	effectively	ADV
cana-4230	101	20	allowing	allow	VERB
cana-4230	101	21	to	to	PART
cana-4230	101	22	study	study	VERB
cana-4230	101	23	of	of	ADP
cana-4230	101	24	the	the	DET
cana-4230	101	25	structural	structural	ADJ
cana-4230	101	26	organization	organization	NOUN
cana-4230	101	27	of	of	ADP
cana-4230	101	28	high	high	ADJ
cana-4230	101	29	-	-	PUNCT
cana-4230	101	30	dimensional	dimensional	ADJ
cana-4230	101	31	data	datum	NOUN
cana-4230	101	32	.	.	PUNCT
cana-4230	102	1	such	such	ADJ
cana-4230	102	2	methods	method	NOUN
cana-4230	102	3	help	help	VERB
cana-4230	102	4	to	to	PART
cana-4230	102	5	find	find	VERB
cana-4230	102	6	loops	loop	NOUN
cana-4230	102	7	,	,	PUNCT
cana-4230	102	8	holes	hole	NOUN
cana-4230	102	9	,	,	PUNCT
cana-4230	102	10	and	and	CCONJ
cana-4230	102	11	voids	void	NOUN
cana-4230	102	12	that	that	PRON
cana-4230	102	13	are	be	AUX
cana-4230	102	14	characteristic	characteristic	ADJ
cana-4230	102	15	of	of	ADP
cana-4230	102	16	many	many	ADJ
cana-4230	102	17	data	datum	NOUN
cana-4230	102	18	sets	set	NOUN
cana-4230	102	19	but	but	CCONJ
cana-4230	102	20	are	be	AUX
cana-4230	102	21	not	not	PART
cana-4230	102	22	visible	visible	ADJ
cana-4230	102	23	in	in	ADP
cana-4230	102	24	linear	linear	ADJ
cana-4230	102	25	analysis	analysis	NOUN
cana-4230	102	26	tools	tool	NOUN
cana-4230	102	27	.	.	PUNCT
cana-4230	103	1	in	in	ADP
cana-4230	103	2	this	this	DET
cana-4230	103	3	section	section	NOUN
cana-4230	103	4	,	,	PUNCT
cana-4230	103	5	basic	basic	ADJ
cana-4230	103	6	principles	principle	NOUN
cana-4230	103	7	of	of	ADP
cana-4230	103	8	non	non	ADJ
cana-4230	103	9	-	-	ADJ
cana-4230	103	10	linear	linear	ADJ
cana-4230	103	11	algebraic	algebraic	ADJ
cana-4230	103	12	topology	topology	NOUN
cana-4230	103	13	are	be	AUX
cana-4230	103	14	introduced	introduce	VERB
cana-4230	103	15	:	:	PUNCT
cana-4230	103	16	simplicial	simplicial	ADJ
cana-4230	103	17	complexes	complex	NOUN
cana-4230	103	18	,	,	PUNCT
cana-4230	103	19	persistent	persistent	ADJ
cana-4230	103	20	homology	homology	NOUN
cana-4230	103	21	,	,	PUNCT
cana-4230	103	22	morse	morse	PROPN
cana-4230	103	23	theory	theory	NOUN
cana-4230	103	24	,	,	PUNCT
cana-4230	103	25	and	and	CCONJ
cana-4230	103	26	their	their	PRON
cana-4230	103	27	application	application	NOUN
cana-4230	103	28	to	to	ADP
cana-4230	103	29	high	high	ADJ
cana-4230	103	30	-	-	PUNCT
cana-4230	103	31	dimensional	dimensional	ADJ
cana-4230	103	32	data	datum	NOUN
cana-4230	103	33	analysis	analysis	NOUN
cana-4230	103	34	.	.	PUNCT
cana-4230	104	1	4.1	4.1	NUM
cana-4230	104	2	simplicial	simplicial	ADJ
cana-4230	104	3	complexes	complex	NOUN
cana-4230	104	4	simplicial	simplicial	ADJ
cana-4230	104	5	complexes	complex	NOUN
cana-4230	104	6	are	be	AUX
cana-4230	104	7	a	a	DET
cana-4230	104	8	basic	basic	ADJ
cana-4230	104	9	concept	concept	NOUN
cana-4230	104	10	of	of	ADP
cana-4230	104	11	algebraic	algebraic	ADJ
cana-4230	104	12	topology	topology	NOUN
cana-4230	104	13	that	that	PRON
cana-4230	104	14	serves	serve	VERB
cana-4230	104	15	as	as	ADP
cana-4230	104	16	a	a	DET
cana-4230	104	17	combinatorial	combinatorial	ADJ
cana-4230	104	18	model	model	NOUN
cana-4230	104	19	of	of	ADP
cana-4230	104	20	a	a	DET
cana-4230	104	21	topological	topological	ADJ
cana-4230	104	22	space	space	NOUN
cana-4230	104	23	.	.	PUNCT
cana-4230	105	1	a	a	DET
cana-4230	105	2	simplicial	simplicial	ADJ
cana-4230	105	3	complex	complex	NOUN
cana-4230	105	4	is	be	AUX
cana-4230	105	5	a	a	DET
cana-4230	105	6	collection	collection	NOUN
cana-4230	105	7	of	of	ADP
cana-4230	105	8	simplices	simplice	NOUN
cana-4230	105	9	:	:	PUNCT
cana-4230	105	10	points	point	NOUN
cana-4230	105	11	,	,	PUNCT
cana-4230	105	12	edges	edge	NOUN
cana-4230	105	13	,	,	PUNCT
cana-4230	105	14	triangles	triangle	NOUN
cana-4230	105	15	,	,	PUNCT
cana-4230	105	16	and	and	CCONJ
cana-4230	105	17	entities	entity	NOUN
cana-4230	105	18	of	of	ADP
cana-4230	105	19	higher	high	ADJ
cana-4230	105	20	dimensions	dimension	NOUN
cana-4230	105	21	that	that	PRON
cana-4230	105	22	are	be	AUX
cana-4230	105	23	connected	connect	VERB
cana-4230	105	24	along	along	ADP
cana-4230	105	25	their	their	PRON
cana-4230	105	26	boundaries	boundary	NOUN
cana-4230	105	27	.	.	PUNCT
cana-4230	106	1	simplicial	simplicial	ADJ
cana-4230	106	2	complexes	complex	NOUN
cana-4230	106	3	are	be	AUX
cana-4230	106	4	useful	useful	ADJ
cana-4230	106	5	for	for	ADP
cana-4230	106	6	approximations	approximation	NOUN
cana-4230	106	7	of	of	ADP
cana-4230	106	8	high	high	ADJ
cana-4230	106	9	geological	geological	ADJ
cana-4230	106	10	shapes	shape	NOUN
cana-4230	106	11	and	and	CCONJ
cana-4230	106	12	are	be	AUX
cana-4230	106	13	applied	apply	VERB
cana-4230	106	14	in	in	ADP
cana-4230	106	15	tda	tda	NOUN
cana-4230	106	16	to	to	PART
cana-4230	106	17	describe	describe	VERB
cana-4230	106	18	the	the	DET
cana-4230	106	19	shape	shape	NOUN
cana-4230	106	20	of	of	ADP
cana-4230	106	21	high	high	ADJ
cana-4230	106	22	-	-	PUNCT
cana-4230	106	23	dimensional	dimensional	ADJ
cana-4230	106	24	data	datum	NOUN
cana-4230	106	25	sets	set	NOUN
cana-4230	106	26	(	(	PUNCT
cana-4230	106	27	2010	2010	NUM
cana-4230	106	28	)	)	PUNCT
cana-4230	106	29	.	.	PUNCT
cana-4230	107	1	table	table	NOUN
cana-4230	107	2	1	1	NUM
cana-4230	107	3	illustrates	illustrate	VERB
cana-4230	107	4	the	the	DET
cana-4230	107	5	relationship	relationship	NOUN
cana-4230	107	6	between	between	ADP
cana-4230	107	7	simplices	simplice	NOUN
cana-4230	107	8	of	of	ADP
cana-4230	107	9	different	different	ADJ
cana-4230	107	10	dimensions	dimension	NOUN
cana-4230	107	11	and	and	CCONJ
cana-4230	107	12	their	their	PRON
cana-4230	107	13	respective	respective	ADJ
cana-4230	107	14	topological	topological	ADJ
cana-4230	107	15	interpretations	interpretation	NOUN
cana-4230	107	16	.	.	PUNCT
cana-4230	108	1	simplicial	simplicial	ADJ
cana-4230	108	2	dimension	dimension	NOUN
cana-4230	108	3	simplex	simplex	NOUN
cana-4230	108	4	type	type	NOUN
cana-4230	108	5	example	example	NOUN
cana-4230	108	6	topological	topological	ADJ
cana-4230	108	7	interpretation	interpretation	NOUN
cana-4230	108	8	0	0	NUM
cana-4230	108	9	point	point	NOUN
cana-4230	108	10	(	(	PUNCT
cana-4230	108	11	0	0	NUM
cana-4230	108	12	-	-	PUNCT
cana-4230	108	13	simplex	simplex	NOUN
cana-4230	108	14	)	)	PUNCT
cana-4230	108	15	single	single	ADJ
cana-4230	108	16	data	datum	NOUN
cana-4230	108	17	point	point	NOUN
cana-4230	108	18	vertex	vertex	NOUN
cana-4230	108	19	or	or	CCONJ
cana-4230	108	20	node	node	NOUN
cana-4230	108	21	1	1	NUM
cana-4230	108	22	line	line	NOUN
cana-4230	108	23	(	(	PUNCT
cana-4230	108	24	1	1	NUM
cana-4230	108	25	-	-	PUNCT
cana-4230	108	26	simplex	simplex	NOUN
cana-4230	108	27	)	)	PUNCT
cana-4230	108	28	the	the	DET
cana-4230	108	29	edge	edge	NOUN
cana-4230	108	30	between	between	ADP
cana-4230	108	31	two	two	NUM
cana-4230	108	32	points	point	NOUN
cana-4230	108	33	connection	connection	NOUN
cana-4230	108	34	between	between	ADP
cana-4230	108	35	two	two	NUM
cana-4230	108	36	vertices	vertex	NOUN
cana-4230	108	37	2	2	NUM
cana-4230	108	38	triangle	triangle	NOUN
cana-4230	108	39	(	(	PUNCT
cana-4230	108	40	2simplex	2simplex	NUM
cana-4230	108	41	)	)	PUNCT
cana-4230	108	42	the	the	DET
cana-4230	108	43	triangle	triangle	NOUN
cana-4230	108	44	formed	form	VERB
cana-4230	108	45	by	by	ADP
cana-4230	108	46	three	three	NUM
cana-4230	108	47	edges	edge	NOUN
cana-4230	108	48	surface	surface	NOUN
cana-4230	108	49	3	3	NUM
cana-4230	108	50	tetrahedron	tetrahedron	NOUN
cana-4230	108	51	(	(	PUNCT
cana-4230	108	52	3simplex	3simplex	NUM
cana-4230	108	53	)	)	PUNCT
cana-4230	108	54	a	a	DET
cana-4230	108	55	tetrahedron	tetrahedron	NOUN
cana-4230	108	56	formed	form	VERB
cana-4230	108	57	by	by	ADP
cana-4230	108	58	four	four	NUM
cana-4230	108	59	triangles	triangle	NOUN
cana-4230	108	60	3d	3d	NUM
cana-4230	108	61	structure	structure	NOUN
cana-4230	108	62	(	(	PUNCT
cana-4230	108	63	void	void	NOUN
cana-4230	108	64	)	)	PUNCT
cana-4230	108	65	communications	communication	NOUN
cana-4230	108	66	on	on	ADP
cana-4230	108	67	applied	apply	VERB
cana-4230	108	68	nonlinear	nonlinear	ADJ
cana-4230	108	69	analysis	analysis	NOUN
cana-4230	108	70	issn	issn	NOUN
cana-4230	108	71	:	:	PUNCT
cana-4230	108	72	1074	1074	NUM
cana-4230	108	73	-	-	PUNCT
cana-4230	108	74	133x	133x	NUM
cana-4230	108	75	vol	vol	NOUN
cana-4230	108	76	32	32	NUM
cana-4230	108	77	no	no	NOUN
cana-4230	108	78	.	.	PUNCT
cana-4230	109	1	8s	8s	PROPN
cana-4230	109	2	(	(	PUNCT
cana-4230	109	3	2025	2025	NUM
cana-4230	109	4	)	)	PUNCT
cana-4230	109	5	900	900	NUM
cana-4230	109	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	109	7	simplicial	simplicial	ADJ
cana-4230	109	8	complexes	complex	NOUN
cana-4230	109	9	are	be	AUX
cana-4230	109	10	critical	critical	ADJ
cana-4230	109	11	for	for	ADP
cana-4230	109	12	building	build	VERB
cana-4230	109	13	topological	topological	ADJ
cana-4230	109	14	spaces	space	NOUN
cana-4230	109	15	that	that	PRON
cana-4230	109	16	can	can	AUX
cana-4230	109	17	be	be	AUX
cana-4230	109	18	analyzed	analyze	VERB
cana-4230	109	19	through	through	ADP
cana-4230	109	20	other	other	ADJ
cana-4230	109	21	techniques	technique	NOUN
cana-4230	109	22	,	,	PUNCT
cana-4230	109	23	such	such	ADJ
cana-4230	109	24	as	as	ADP
cana-4230	109	25	persistent	persistent	ADJ
cana-4230	109	26	homology	homology	NOUN
cana-4230	109	27	.	.	PUNCT
cana-4230	110	1	4.2	4.2	NUM
cana-4230	110	2	persistent	persistent	ADJ
cana-4230	110	3	homology	homology	NOUN
cana-4230	110	4	persistent	persistent	ADJ
cana-4230	110	5	homology	homology	NOUN
cana-4230	110	6	can	can	AUX
cana-4230	110	7	be	be	AUX
cana-4230	110	8	viewed	view	VERB
cana-4230	110	9	as	as	ADP
cana-4230	110	10	one	one	NUM
cana-4230	110	11	of	of	ADP
cana-4230	110	12	the	the	DET
cana-4230	110	13	main	main	ADJ
cana-4230	110	14	tools	tool	NOUN
cana-4230	110	15	in	in	ADP
cana-4230	110	16	tda	tda	NOUN
cana-4230	110	17	that	that	PRON
cana-4230	110	18	shows	show	VERB
cana-4230	110	19	the	the	DET
cana-4230	110	20	changes	change	NOUN
cana-4230	110	21	in	in	ADP
cana-4230	110	22	topological	topological	ADJ
cana-4230	110	23	features	feature	NOUN
cana-4230	110	24	over	over	ADP
cana-4230	110	25	the	the	DET
cana-4230	110	26	scales	scale	NOUN
cana-4230	110	27	.	.	PUNCT
cana-4230	111	1	it	it	PRON
cana-4230	111	2	is	be	AUX
cana-4230	111	3	particularly	particularly	ADV
cana-4230	111	4	successful	successful	ADJ
cana-4230	111	5	for	for	ADP
cana-4230	111	6	detecting	detect	VERB
cana-4230	111	7	motifs	motif	NOUN
cana-4230	111	8	which	which	PRON
cana-4230	111	9	are	be	AUX
cana-4230	111	10	invariant	invariant	ADJ
cana-4230	111	11	scales	scale	NOUN
cana-4230	111	12	,	,	PUNCT
cana-4230	111	13	which	which	PRON
cana-4230	111	14	are	be	AUX
cana-4230	111	15	usually	usually	ADV
cana-4230	111	16	characteristic	characteristic	ADJ
cana-4230	111	17	of	of	ADP
cana-4230	111	18	data	datum	NOUN
cana-4230	111	19	’s	’s	PART
cana-4230	111	20	inner	inner	ADJ
cana-4230	111	21	structure	structure	NOUN
cana-4230	111	22	,	,	PUNCT
cana-4230	111	23	not	not	PART
cana-4230	111	24	noise	noise	NOUN
cana-4230	111	25	(	(	PUNCT
cana-4230	111	26	carlsson	carlsson	PROPN
cana-4230	111	27	,	,	PUNCT
cana-4230	111	28	2009	2009	NUM
cana-4230	111	29	)	)	PUNCT
cana-4230	111	30	.	.	PUNCT
cana-4230	112	1	the	the	DET
cana-4230	112	2	graph	graph	NOUN
cana-4230	112	3	of	of	ADP
cana-4230	112	4	the	the	DET
cana-4230	112	5	basic	basic	ADJ
cana-4230	112	6	form	form	NOUN
cana-4230	112	7	of	of	ADP
cana-4230	112	8	persistent	persistent	ADJ
cana-4230	112	9	homology	homology	NOUN
cana-4230	112	10	can	can	AUX
cana-4230	112	11	be	be	AUX
cana-4230	112	12	described	describe	VERB
cana-4230	112	13	with	with	ADP
cana-4230	112	14	the	the	DET
cana-4230	112	15	following	follow	VERB
cana-4230	112	16	steps	step	NOUN
cana-4230	112	17	:	:	PUNCT
cana-4230	112	18	construct	construct	VERB
cana-4230	112	19	a	a	DET
cana-4230	112	20	sequence	sequence	NOUN
cana-4230	112	21	of	of	ADP
cana-4230	112	22	simplicial	simplicial	ADJ
cana-4230	112	23	complexes	complex	NOUN
cana-4230	112	24	from	from	ADP
cana-4230	112	25	the	the	DET
cana-4230	112	26	data	datum	NOUN
cana-4230	112	27	at	at	ADP
cana-4230	112	28	different	different	ADJ
cana-4230	112	29	thresholds	threshold	NOUN
cana-4230	112	30	called	call	VERB
cana-4230	112	31	filtrations	filtration	NOUN
cana-4230	112	32	,	,	PUNCT
cana-4230	112	33	investigate	investigate	VERB
cana-4230	112	34	how	how	SCONJ
cana-4230	112	35	the	the	DET
cana-4230	112	36	topological	topological	ADJ
cana-4230	112	37	aspects	aspect	NOUN
cana-4230	112	38	,	,	PUNCT
cana-4230	112	39	including	include	VERB
cana-4230	112	40	connected	connected	ADJ
cana-4230	112	41	components	component	NOUN
cana-4230	112	42	,	,	PUNCT
cana-4230	112	43	loops	loop	NOUN
cana-4230	112	44	,	,	PUNCT
cana-4230	112	45	or	or	CCONJ
cana-4230	112	46	higherdimensional	higherdimensional	ADJ
cana-4230	112	47	holes	hole	NOUN
cana-4230	112	48	,	,	PUNCT
cana-4230	112	49	emerge	emerge	VERB
cana-4230	112	50	and	and	CCONJ
cana-4230	112	51	disappear	disappear	VERB
cana-4230	112	52	when	when	SCONJ
cana-4230	112	53	the	the	DET
cana-4230	112	54	threshold	threshold	NOUN
cana-4230	112	55	is	be	AUX
cana-4230	112	56	increased	increase	VERB
cana-4230	112	57	.	.	PUNCT
cana-4230	113	1	table	table	NOUN
cana-4230	113	2	2	2	NUM
cana-4230	113	3	shows	show	VERB
cana-4230	113	4	a	a	DET
cana-4230	113	5	simple	simple	ADJ
cana-4230	113	6	example	example	NOUN
cana-4230	113	7	of	of	ADP
cana-4230	113	8	persistent	persistent	ADJ
cana-4230	113	9	homology	homology	NOUN
cana-4230	113	10	applied	apply	VERB
cana-4230	113	11	to	to	ADP
cana-4230	113	12	a	a	DET
cana-4230	113	13	dataset	dataset	NOUN
cana-4230	113	14	,	,	PUNCT
cana-4230	113	15	illustrating	illustrate	VERB
cana-4230	113	16	the	the	DET
cana-4230	113	17	birth	birth	NOUN
cana-4230	113	18	and	and	CCONJ
cana-4230	113	19	death	death	NOUN
cana-4230	113	20	times	time	NOUN
cana-4230	113	21	of	of	ADP
cana-4230	113	22	different	different	ADJ
cana-4230	113	23	topological	topological	ADJ
cana-4230	113	24	features	feature	NOUN
cana-4230	113	25	.	.	PUNCT
cana-4230	114	1	feature	feature	VERB
cana-4230	114	2	birth	birth	NOUN
cana-4230	114	3	time	time	NOUN
cana-4230	114	4	death	death	NOUN
cana-4230	114	5	time	time	NOUN
cana-4230	114	6	persistence	persistence	NOUN
cana-4230	114	7	topological	topological	ADJ
cana-4230	114	8	interpretation	interpretation	NOUN
cana-4230	114	9	feature	feature	VERB
cana-4230	114	10	1	1	NUM
cana-4230	114	11	0.10	0.10	NUM
cana-4230	114	12	0.80	0.80	NUM
cana-4230	114	13	0.70	0.70	NUM
cana-4230	114	14	1	1	NUM
cana-4230	114	15	-	-	PUNCT
cana-4230	114	16	dimensional	dimensional	ADJ
cana-4230	114	17	loop	loop	NOUN
cana-4230	114	18	(	(	PUNCT
cana-4230	114	19	circle	circle	NOUN
cana-4230	114	20	)	)	PUNCT
cana-4230	114	21	feature	feature	VERB
cana-4230	114	22	2	2	NUM
cana-4230	114	23	0.05	0.05	NUM
cana-4230	114	24	0.60	0.60	NUM
cana-4230	114	25	0.55	0.55	NUM
cana-4230	114	26	connected	connect	VERB
cana-4230	114	27	component	component	NOUN
cana-4230	114	28	feature	feature	NOUN
cana-4230	114	29	3	3	NUM
cana-4230	114	30	0.30	0.30	NUM
cana-4230	114	31	0.55	0.55	NUM
cana-4230	114	32	0.25	0.25	NUM
cana-4230	114	33	2	2	NUM
cana-4230	114	34	-	-	PUNCT
cana-4230	114	35	dimensional	dimensional	ADJ
cana-4230	114	36	void	void	NOUN
cana-4230	114	37	the	the	DET
cana-4230	114	38	highly	highly	ADV
cana-4230	114	39	persistent	persistent	ADJ
cana-4230	114	40	features	feature	NOUN
cana-4230	114	41	often	often	ADV
cana-4230	114	42	correspond	correspond	VERB
cana-4230	114	43	to	to	ADP
cana-4230	114	44	rather	rather	ADV
cana-4230	114	45	large	large	ADJ
cana-4230	114	46	structures	structure	NOUN
cana-4230	114	47	,	,	PUNCT
cana-4230	114	48	while	while	SCONJ
cana-4230	114	49	low	low	ADJ
cana-4230	114	50	persistence	persistence	NOUN
cana-4230	114	51	,	,	PUNCT
cana-4230	114	52	features	feature	NOUN
cana-4230	114	53	may	may	AUX
cana-4230	114	54	be	be	AUX
cana-4230	114	55	noises	noise	NOUN
cana-4230	114	56	.	.	PUNCT
cana-4230	115	1	persistent	persistent	ADJ
cana-4230	115	2	homology	homology	NOUN
cana-4230	115	3	is	be	AUX
cana-4230	115	4	widely	widely	ADV
cana-4230	115	5	applicable	applicable	ADJ
cana-4230	115	6	to	to	PART
cana-4230	115	7	shape	shape	VERB
cana-4230	115	8	analysis	analysis	NOUN
cana-4230	115	9	,	,	PUNCT
cana-4230	115	10	image	image	NOUN
cana-4230	115	11	processing	processing	NOUN
cana-4230	115	12	,	,	PUNCT
cana-4230	115	13	and	and	CCONJ
cana-4230	115	14	time	time	NOUN
cana-4230	115	15	series	series	NOUN
cana-4230	115	16	analysis	analysis	NOUN
cana-4230	115	17	where	where	SCONJ
cana-4230	115	18	there	there	PRON
cana-4230	115	19	is	be	VERB
cana-4230	115	20	interest	interest	NOUN
cana-4230	115	21	in	in	ADP
cana-4230	115	22	understanding	understand	VERB
cana-4230	115	23	the	the	DET
cana-4230	115	24	main	main	ADJ
cana-4230	115	25	structures	structure	NOUN
cana-4230	115	26	at	at	ADP
cana-4230	115	27	different	different	ADJ
cana-4230	115	28	levels	level	NOUN
cana-4230	115	29	of	of	ADP
cana-4230	115	30	granularity	granularity	NOUN
cana-4230	115	31	.	.	PUNCT
cana-4230	116	1	4.3	4.3	NUM
cana-4230	116	2	morse	morse	PROPN
cana-4230	116	3	theory	theory	NOUN
cana-4230	116	4	and	and	CCONJ
cana-4230	116	5	critical	critical	ADJ
cana-4230	116	6	points	point	NOUN
cana-4230	116	7	another	another	DET
cana-4230	116	8	tool	tool	NOUN
cana-4230	116	9	of	of	ADP
cana-4230	116	10	algebraic	algebraic	ADJ
cana-4230	116	11	topology	topology	NOUN
cana-4230	116	12	is	be	AUX
cana-4230	116	13	morse	morse	NOUN
cana-4230	116	14	theory	theory	NOUN
cana-4230	116	15	which	which	PRON
cana-4230	116	16	investigates	investigate	VERB
cana-4230	116	17	the	the	DET
cana-4230	116	18	topology	topology	NOUN
cana-4230	116	19	of	of	ADP
cana-4230	116	20	a	a	DET
cana-4230	116	21	space	space	NOUN
cana-4230	116	22	through	through	ADP
cana-4230	116	23	the	the	DET
cana-4230	116	24	study	study	NOUN
cana-4230	116	25	of	of	ADP
cana-4230	116	26	smooth	smooth	ADJ
cana-4230	116	27	functions	function	NOUN
cana-4230	116	28	on	on	ADP
cana-4230	116	29	that	that	DET
cana-4230	116	30	space	space	NOUN
cana-4230	116	31	(	(	PUNCT
cana-4230	116	32	milnor	milnor	PROPN
cana-4230	116	33	,	,	PUNCT
cana-4230	116	34	1963	1963	NUM
cana-4230	116	35	)	)	PUNCT
cana-4230	116	36	.	.	PUNCT
cana-4230	117	1	morse	morse	PROPN
cana-4230	117	2	theory	theory	NOUN
cana-4230	117	3	within	within	ADP
cana-4230	117	4	the	the	DET
cana-4230	117	5	framework	framework	NOUN
cana-4230	117	6	of	of	ADP
cana-4230	117	7	the	the	DET
cana-4230	117	8	analysis	analysis	NOUN
cana-4230	117	9	of	of	ADP
cana-4230	117	10	high	high	ADJ
cana-4230	117	11	-	-	PUNCT
cana-4230	117	12	dimensional	dimensional	ADJ
cana-4230	117	13	data	datum	NOUN
cana-4230	117	14	finds	find	VERB
cana-4230	117	15	application	application	NOUN
cana-4230	117	16	in	in	ADP
cana-4230	117	17	the	the	DET
cana-4230	117	18	recognition	recognition	NOUN
cana-4230	117	19	of	of	ADP
cana-4230	117	20	critical	critical	ADJ
cana-4230	117	21	points	point	NOUN
cana-4230	117	22	–	–	PUNCT
cana-4230	117	23	those	those	PRON
cana-4230	117	24	for	for	ADP
cana-4230	117	25	which	which	PRON
cana-4230	117	26	the	the	DET
cana-4230	117	27	gradient	gradient	NOUN
cana-4230	117	28	of	of	ADP
cana-4230	117	29	a	a	DET
cana-4230	117	30	function	function	NOUN
cana-4230	117	31	is	be	AUX
cana-4230	117	32	zero	zero	NUM
cana-4230	117	33	(	(	PUNCT
cana-4230	117	34	local	local	ADJ
cana-4230	117	35	minima	minima	NOUN
cana-4230	117	36	,	,	PUNCT
cana-4230	117	37	maxima	maxima	NOUN
cana-4230	117	38	,	,	PUNCT
cana-4230	117	39	and	and	CCONJ
cana-4230	117	40	saddle	saddle	NOUN
cana-4230	117	41	points	point	NOUN
cana-4230	117	42	)	)	PUNCT
cana-4230	117	43	and	and	CCONJ
cana-4230	117	44	how	how	SCONJ
cana-4230	117	45	these	these	DET
cana-4230	117	46	points	point	NOUN
cana-4230	117	47	are	be	AUX
cana-4230	117	48	positioned	position	VERB
cana-4230	117	49	about	about	ADP
cana-4230	117	50	the	the	DET
cana-4230	117	51	complexity	complexity	NOUN
cana-4230	117	52	of	of	ADP
cana-4230	117	53	the	the	DET
cana-4230	117	54	existing	exist	VERB
cana-4230	117	55	high	high	ADJ
cana-4230	117	56	-	-	PUNCT
cana-4230	117	57	dimensional	dimensional	ADJ
cana-4230	117	58	data	datum	NOUN
cana-4230	117	59	.	.	PUNCT
cana-4230	118	1	this	this	DET
cana-4230	118	2	technique	technique	NOUN
cana-4230	118	3	is	be	AUX
cana-4230	118	4	efficient	efficient	ADJ
cana-4230	118	5	when	when	SCONJ
cana-4230	118	6	detecting	detect	VERB
cana-4230	118	7	topology	topology	NOUN
cana-4230	118	8	changes	change	NOUN
cana-4230	118	9	of	of	ADP
cana-4230	118	10	high	high	ADJ
cana-4230	118	11	xerophytic	xerophytic	ADJ
cana-4230	118	12	manifolds	manifold	NOUN
cana-4230	118	13	,	,	PUNCT
cana-4230	118	14	where	where	SCONJ
cana-4230	118	15	morse	morse	NOUN
cana-4230	118	16	functions	function	NOUN
cana-4230	118	17	can	can	AUX
cana-4230	118	18	be	be	AUX
cana-4230	118	19	used	use	VERB
cana-4230	118	20	to	to	PART
cana-4230	118	21	analyze	analyze	VERB
cana-4230	118	22	the	the	DET
cana-4230	118	23	geometric	geometric	ADJ
cana-4230	118	24	shape	shape	NOUN
cana-4230	118	25	and	and	CCONJ
cana-4230	118	26	morphology	morphology	NOUN
cana-4230	118	27	of	of	ADP
cana-4230	118	28	the	the	DET
cana-4230	118	29	data	datum	NOUN
cana-4230	118	30	.	.	PUNCT
cana-4230	119	1	4.4	4.4	NUM
cana-4230	119	2	vietoris	vietoris	PROPN
cana-4230	119	3	–	–	PUNCT
cana-4230	119	4	rips	rip	NOUN
cana-4230	119	5	complexes	complex	NOUN
cana-4230	119	6	vietoris	vietoris	VERB
cana-4230	119	7	–	–	PUNCT
cana-4230	119	8	rips	rip	NOUN
cana-4230	119	9	complex	complex	NOUN
cana-4230	119	10	is	be	AUX
cana-4230	119	11	one	one	NUM
cana-4230	119	12	of	of	ADP
cana-4230	119	13	the	the	DET
cana-4230	119	14	simplicial	simplicial	ADJ
cana-4230	119	15	complexes	complex	NOUN
cana-4230	119	16	that	that	PRON
cana-4230	119	17	can	can	AUX
cana-4230	119	18	be	be	AUX
cana-4230	119	19	used	use	VERB
cana-4230	119	20	in	in	ADP
cana-4230	119	21	tda	tda	NOUN
cana-4230	119	22	to	to	PART
cana-4230	119	23	approximate	approximate	VERB
cana-4230	119	24	the	the	DET
cana-4230	119	25	shape	shape	NOUN
cana-4230	119	26	of	of	ADP
cana-4230	119	27	a	a	DET
cana-4230	119	28	point	point	NOUN
cana-4230	119	29	cloud	cloud	NOUN
cana-4230	119	30	dataset	dataset	NOUN
cana-4230	119	31	.	.	PUNCT
cana-4230	120	1	it	it	PRON
cana-4230	120	2	is	be	AUX
cana-4230	120	3	built	build	VERB
cana-4230	120	4	up	up	ADP
cana-4230	120	5	by	by	ADP
cana-4230	120	6	linking	link	VERB
cana-4230	120	7	points	point	NOUN
cana-4230	120	8	within	within	ADP
cana-4230	120	9	a	a	DET
cana-4230	120	10	certain	certain	ADJ
cana-4230	120	11	range	range	NOUN
cana-4230	120	12	of	of	ADP
cana-4230	120	13	distance	distance	NOUN
cana-4230	120	14	to	to	PART
cana-4230	120	15	construct	construct	VERB
cana-4230	120	16	higher	high	ADJ
cana-4230	120	17	-	-	PUNCT
cana-4230	120	18	order	order	NOUN
cana-4230	120	19	simplices	simplice	NOUN
cana-4230	120	20	.	.	PUNCT
cana-4230	121	1	the	the	DET
cana-4230	121	2	vietoris	vietoris	ADJ
cana-4230	121	3	–	–	PUNCT
cana-4230	121	4	rips	rip	NOUN
cana-4230	121	5	complex	complex	NOUN
cana-4230	121	6	is	be	AUX
cana-4230	121	7	applied	apply	VERB
cana-4230	121	8	because	because	SCONJ
cana-4230	121	9	of	of	ADP
cana-4230	121	10	its	its	PRON
cana-4230	121	11	computational	computational	ADJ
cana-4230	121	12	simplicity	simplicity	NOUN
cana-4230	121	13	and	and	CCONJ
cana-4230	121	14	in	in	ADP
cana-4230	121	15	the	the	DET
cana-4230	121	16	case	case	NOUN
cana-4230	121	17	of	of	ADP
cana-4230	121	18	large	large	ADJ
cana-4230	121	19	datasets	dataset	NOUN
cana-4230	121	20	because	because	SCONJ
cana-4230	121	21	of	of	ADP
cana-4230	121	22	its	its	PRON
cana-4230	121	23	efficiency	efficiency	NOUN
cana-4230	121	24	(	(	PUNCT
cana-4230	121	25	ghrist	ghrist	NOUN
cana-4230	121	26	,	,	PUNCT
cana-4230	121	27	2008	2008	NUM
cana-4230	121	28	)	)	PUNCT
cana-4230	121	29	.	.	PUNCT
cana-4230	122	1	communications	communication	NOUN
cana-4230	122	2	on	on	ADP
cana-4230	122	3	applied	apply	VERB
cana-4230	122	4	nonlinear	nonlinear	ADJ
cana-4230	122	5	analysis	analysis	NOUN
cana-4230	122	6	issn	issn	NOUN
cana-4230	122	7	:	:	PUNCT
cana-4230	122	8	1074	1074	NUM
cana-4230	122	9	-	-	PUNCT
cana-4230	122	10	133x	133x	NUM
cana-4230	122	11	vol	vol	NOUN
cana-4230	122	12	32	32	NUM
cana-4230	122	13	no	no	NOUN
cana-4230	122	14	.	.	PUNCT
cana-4230	123	1	8s	8s	PROPN
cana-4230	123	2	(	(	PUNCT
cana-4230	123	3	2025	2025	NUM
cana-4230	123	4	)	)	PUNCT
cana-4230	123	5	901	901	NUM
cana-4230	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	123	7	4.5	4.5	NUM
cana-4230	123	8	application	application	NOUN
cana-4230	123	9	of	of	ADP
cana-4230	123	10	nonlinear	nonlinear	ADJ
cana-4230	123	11	algebraic	algebraic	PROPN
cana-4230	123	12	topology	topology	NOUN
cana-4230	123	13	techniques	technique	VERB
cana-4230	123	14	the	the	DET
cana-4230	123	15	methods	method	NOUN
cana-4230	123	16	described	describe	VERB
cana-4230	123	17	above	above	ADV
cana-4230	123	18	have	have	AUX
cana-4230	123	19	been	be	AUX
cana-4230	123	20	practiced	practice	VERB
cana-4230	123	21	in	in	ADP
cana-4230	123	22	different	different	ADJ
cana-4230	123	23	field	field	NOUN
cana-4230	123	24	areas	area	NOUN
cana-4230	123	25	like	like	ADP
cana-4230	123	26	machine	machine	NOUN
cana-4230	123	27	learning	learning	NOUN
cana-4230	123	28	,	,	PUNCT
cana-4230	123	29	biochemical	biochemical	ADJ
cana-4230	123	30	informatics	informatic	NOUN
cana-4230	123	31	,	,	PUNCT
cana-4230	123	32	and	and	CCONJ
cana-4230	123	33	image	image	NOUN
cana-4230	123	34	treatment	treatment	NOUN
cana-4230	123	35	.	.	PUNCT
cana-4230	124	1	for	for	ADP
cana-4230	124	2	instance	instance	NOUN
cana-4230	124	3	,	,	PUNCT
cana-4230	124	4	persistent	persistent	ADJ
cana-4230	124	5	homology	homology	NOUN
cana-4230	124	6	has	have	AUX
cana-4230	124	7	been	be	AUX
cana-4230	124	8	used	use	VERB
cana-4230	124	9	in	in	ADP
cana-4230	124	10	analyzing	analyze	VERB
cana-4230	124	11	the	the	DET
cana-4230	124	12	geometry	geometry	NOUN
cana-4230	124	13	of	of	ADP
cana-4230	124	14	high	high	ADJ
cana-4230	124	15	-	-	PUNCT
cana-4230	124	16	dimensional	dimensional	ADJ
cana-4230	124	17	data	datum	NOUN
cana-4230	124	18	for	for	ADP
cana-4230	124	19	genomic	genomic	ADJ
cana-4230	124	20	data	datum	NOUN
cana-4230	124	21	,	,	PUNCT
cana-4230	124	22	to	to	PART
cana-4230	124	23	detect	detect	VERB
cana-4230	124	24	important	important	ADJ
cana-4230	124	25	genetic	genetic	ADJ
cana-4230	124	26	differences	difference	NOUN
cana-4230	124	27	(	(	PUNCT
cana-4230	124	28	nicolau	nicolau	PROPN
cana-4230	124	29	,	,	PUNCT
cana-4230	124	30	levine	levine	PROPN
cana-4230	124	31	&	&	CCONJ
cana-4230	124	32	carlsson	carlsson	PROPN
cana-4230	124	33	,	,	PUNCT
cana-4230	124	34	2011	2011	NUM
cana-4230	124	35	)	)	PUNCT
cana-4230	124	36	.	.	PUNCT
cana-4230	125	1	in	in	ADP
cana-4230	125	2	the	the	DET
cana-4230	125	3	same	same	ADJ
cana-4230	125	4	manner	manner	NOUN
cana-4230	125	5	,	,	PUNCT
cana-4230	125	6	those	those	DET
cana-4230	125	7	topological	topological	ADJ
cana-4230	125	8	methods	method	NOUN
cana-4230	125	9	have	have	AUX
cana-4230	125	10	been	be	AUX
cana-4230	125	11	applied	apply	VERB
cana-4230	125	12	in	in	ADP
cana-4230	125	13	image	image	NOUN
cana-4230	125	14	analysis	analysis	NOUN
cana-4230	125	15	to	to	PART
cana-4230	125	16	extract	extract	VERB
cana-4230	125	17	the	the	DET
cana-4230	125	18	basic	basic	ADJ
cana-4230	125	19	characteristics	characteristic	NOUN
cana-4230	125	20	from	from	ADP
cana-4230	125	21	the	the	DET
cana-4230	125	22	medical	medical	ADJ
cana-4230	125	23	images	image	NOUN
cana-4230	125	24	to	to	PART
cana-4230	125	25	enhance	enhance	VERB
cana-4230	125	26	the	the	DET
cana-4230	125	27	diagnosis	diagnosis	NOUN
cana-4230	125	28	(	(	PUNCT
cana-4230	125	29	patania	patania	NOUN
cana-4230	125	30	,	,	PUNCT
cana-4230	125	31	petri	petri	ADJ
cana-4230	125	32	,	,	PUNCT
cana-4230	125	33	&	&	CCONJ
cana-4230	125	34	vaccarino	vaccarino	PROPN
cana-4230	125	35	,	,	PUNCT
cana-4230	125	36	2017	2017	NUM
cana-4230	125	37	)	)	PUNCT
cana-4230	125	38	.	.	PUNCT
cana-4230	126	1	nonlinear	nonlinear	ADJ
cana-4230	126	2	algebraic	algebraic	PROPN
cana-4230	126	3	topology	topology	NOUN
cana-4230	126	4	plays	play	VERB
cana-4230	126	5	a	a	DET
cana-4230	126	6	very	very	ADV
cana-4230	126	7	important	important	ADJ
cana-4230	126	8	role	role	NOUN
cana-4230	126	9	in	in	ADP
cana-4230	126	10	complex	complex	ADJ
cana-4230	126	11	social	social	ADJ
cana-4230	126	12	networks	network	NOUN
cana-4230	126	13	where	where	SCONJ
cana-4230	126	14	persistent	persistent	ADJ
cana-4230	126	15	topological	topological	ADJ
cana-4230	126	16	features	feature	NOUN
cana-4230	126	17	are	be	AUX
cana-4230	126	18	used	use	VERB
cana-4230	126	19	to	to	PART
cana-4230	126	20	explain	explain	VERB
cana-4230	126	21	community	community	NOUN
cana-4230	126	22	structures	structure	NOUN
cana-4230	126	23	and	and	CCONJ
cana-4230	126	24	information	information	NOUN
cana-4230	126	25	transfer	transfer	NOUN
cana-4230	126	26	(	(	PUNCT
cana-4230	126	27	sizemore	sizemore	NOUN
cana-4230	126	28	et	et	NOUN
cana-4230	126	29	al	al	PROPN
cana-4230	126	30	.	.	PROPN
cana-4230	126	31	,	,	PUNCT
cana-4230	126	32	2018	2018	NUM
cana-4230	126	33	)	)	PUNCT
cana-4230	126	34	.	.	PUNCT
cana-4230	127	1	5	5	X
cana-4230	127	2	.	.	X
cana-4230	127	3	applications	application	NOUN
cana-4230	127	4	and	and	CCONJ
cana-4230	127	5	case	case	NOUN
cana-4230	127	6	studies	study	NOUN
cana-4230	127	7	algebraic	algebraic	ADJ
cana-4230	127	8	topology	topology	NOUN
cana-4230	127	9	in	in	ADP
cana-4230	127	10	the	the	DET
cana-4230	127	11	nonlinear	nonlinear	NOUN
cana-4230	127	12	has	have	VERB
cana-4230	127	13	applicability	applicability	NOUN
cana-4230	127	14	in	in	ADP
cana-4230	127	15	many	many	ADJ
cana-4230	127	16	fields	field	NOUN
cana-4230	127	17	including	include	VERB
cana-4230	127	18	;	;	PUNCT
cana-4230	127	19	biology	biology	NOUN
cana-4230	127	20	,	,	PUNCT
cana-4230	127	21	neuroscience	neuroscience	NOUN
cana-4230	127	22	,	,	PUNCT
cana-4230	127	23	social	social	ADJ
cana-4230	127	24	networks	network	NOUN
cana-4230	127	25	,	,	PUNCT
cana-4230	127	26	and	and	CCONJ
cana-4230	127	27	machine	machine	NOUN
cana-4230	127	28	learning	learning	NOUN
cana-4230	127	29	.	.	PUNCT
cana-4230	128	1	in	in	ADP
cana-4230	128	2	each	each	PRON
cana-4230	128	3	of	of	ADP
cana-4230	128	4	these	these	DET
cana-4230	128	5	areas	area	NOUN
cana-4230	128	6	,	,	PUNCT
cana-4230	128	7	there	there	PRON
cana-4230	128	8	is	be	VERB
cana-4230	128	9	the	the	DET
cana-4230	128	10	adoption	adoption	NOUN
cana-4230	128	11	of	of	ADP
cana-4230	128	12	topological	topological	ADJ
cana-4230	128	13	methods	method	NOUN
cana-4230	128	14	to	to	PART
cana-4230	128	15	study	study	VERB
cana-4230	128	16	the	the	DET
cana-4230	128	17	geometry	geometry	NOUN
cana-4230	128	18	of	of	ADP
cana-4230	128	19	data	datum	NOUN
cana-4230	128	20	in	in	ADP
cana-4230	128	21	high	high	ADJ
cana-4230	128	22	-	-	PUNCT
cana-4230	128	23	dimensional	dimensional	ADJ
cana-4230	128	24	space	space	NOUN
cana-4230	128	25	,	,	PUNCT
cana-4230	128	26	which	which	PRON
cana-4230	128	27	other	other	ADJ
cana-4230	128	28	conventional	conventional	ADJ
cana-4230	128	29	linear	linear	ADJ
cana-4230	128	30	methods	method	NOUN
cana-4230	128	31	ignore	ignore	VERB
cana-4230	128	32	.	.	PUNCT
cana-4230	129	1	this	this	DET
cana-4230	129	2	section	section	NOUN
cana-4230	129	3	discusses	discuss	VERB
cana-4230	129	4	some	some	PRON
cana-4230	129	5	of	of	ADP
cana-4230	129	6	these	these	DET
cana-4230	129	7	applications	application	NOUN
cana-4230	129	8	and	and	CCONJ
cana-4230	129	9	case	case	NOUN
cana-4230	129	10	studies	study	NOUN
cana-4230	129	11	of	of	ADP
cana-4230	129	12	nonlinear	nonlinear	ADJ
cana-4230	129	13	algebraic	algebraic	ADJ
cana-4230	129	14	topology	topology	NOUN
cana-4230	129	15	including	include	VERB
cana-4230	129	16	persistent	persistent	ADJ
cana-4230	129	17	homology	homology	NOUN
cana-4230	129	18	,	,	PUNCT
cana-4230	129	19	simplicial	simplicial	ADJ
cana-4230	129	20	complexes	complex	NOUN
cana-4230	129	21	,	,	PUNCT
cana-4230	129	22	and	and	CCONJ
cana-4230	129	23	morse	morse	PROPN
cana-4230	129	24	theory	theory	NOUN
cana-4230	129	25	.	.	PUNCT
cana-4230	130	1	5.1	5.1	NUM
cana-4230	130	2	applications	application	NOUN
cana-4230	130	3	in	in	ADP
cana-4230	130	4	biology	biology	NOUN
cana-4230	130	5	and	and	CCONJ
cana-4230	130	6	genomics	genomic	NOUN
cana-4230	130	7	in	in	ADP
cana-4230	130	8	biological	biological	ADJ
cana-4230	130	9	data	datum	NOUN
cana-4230	130	10	,	,	PUNCT
cana-4230	130	11	the	the	DET
cana-4230	130	12	topology	topology	NOUN
cana-4230	130	13	of	of	ADP
cana-4230	130	14	structures	structure	NOUN
cana-4230	130	15	in	in	ADP
cana-4230	130	16	high	high	ADJ
cana-4230	130	17	-	-	PUNCT
cana-4230	130	18	dimensional	dimensional	ADJ
cana-4230	130	19	spaces	space	NOUN
cana-4230	130	20	is	be	AUX
cana-4230	130	21	important	important	ADJ
cana-4230	130	22	for	for	ADP
cana-4230	130	23	characterizing	characterize	VERB
cana-4230	130	24	genomics	genomic	NOUN
cana-4230	130	25	,	,	PUNCT
cana-4230	130	26	proteomics	proteomic	NOUN
cana-4230	130	27	,	,	PUNCT
cana-4230	130	28	and	and	CCONJ
cana-4230	130	29	evolution	evolution	NOUN
cana-4230	130	30	.	.	PUNCT
cana-4230	131	1	some	some	PRON
cana-4230	131	2	of	of	ADP
cana-4230	131	3	the	the	DET
cana-4230	131	4	relatively	relatively	ADV
cana-4230	131	5	recent	recent	ADJ
cana-4230	131	6	nonlinear	nonlinear	ADJ
cana-4230	131	7	algebraic	algebraic	ADJ
cana-4230	131	8	topology	topology	NOUN
cana-4230	131	9	that	that	PRON
cana-4230	131	10	has	have	AUX
cana-4230	131	11	been	be	AUX
cana-4230	131	12	applied	apply	VERB
cana-4230	131	13	to	to	ADP
cana-4230	131	14	genre	genre	NOUN
cana-4230	131	15	data	datum	NOUN
cana-4230	131	16	includes	include	VERB
cana-4230	131	17	the	the	DET
cana-4230	131	18	persistent	persistent	ADJ
cana-4230	131	19	homology	homology	NOUN
cana-4230	131	20	that	that	PRON
cana-4230	131	21	has	have	AUX
cana-4230	131	22	helped	help	VERB
cana-4230	131	23	to	to	PART
cana-4230	131	24	analyze	analyze	VERB
cana-4230	131	25	such	such	ADJ
cana-4230	131	26	structures	structure	NOUN
cana-4230	131	27	to	to	PART
cana-4230	131	28	look	look	VERB
cana-4230	131	29	for	for	ADP
cana-4230	131	30	features	feature	NOUN
cana-4230	131	31	that	that	PRON
cana-4230	131	32	will	will	AUX
cana-4230	131	33	be	be	AUX
cana-4230	131	34	crucial	crucial	ADJ
cana-4230	131	35	in	in	ADP
cana-4230	131	36	disease	disease	NOUN
cana-4230	131	37	diagnosis	diagnosis	NOUN
cana-4230	131	38	as	as	ADV
cana-4230	131	39	well	well	ADV
cana-4230	131	40	as	as	ADP
cana-4230	131	41	the	the	DET
cana-4230	131	42	way	way	NOUN
cana-4230	131	43	drugs	drug	NOUN
cana-4230	131	44	affect	affect	VERB
cana-4230	131	45	the	the	DET
cana-4230	131	46	body	body	NOUN
cana-4230	131	47	(	(	PUNCT
cana-4230	131	48	nicolau	nicolau	PROPN
cana-4230	131	49	,	,	PUNCT
cana-4230	131	50	levine	levine	PROPN
cana-4230	131	51	,	,	PUNCT
cana-4230	131	52	&	&	CCONJ
cana-4230	131	53	carlsson	carlsson	PROPN
cana-4230	131	54	,	,	PUNCT
cana-4230	131	55	2011	2011	NUM
cana-4230	131	56	)	)	PUNCT
cana-4230	131	57	.	.	PUNCT
cana-4230	132	1	for	for	ADP
cana-4230	132	2	instance	instance	NOUN
cana-4230	132	3	,	,	PUNCT
cana-4230	132	4	in	in	ADP
cana-4230	132	5	cancer	cancer	NOUN
cana-4230	132	6	genomics	genomic	NOUN
cana-4230	132	7	,	,	PUNCT
cana-4230	132	8	persistent	persistent	ADJ
cana-4230	132	9	homology	homology	NOUN
cana-4230	132	10	is	be	AUX
cana-4230	132	11	used	use	VERB
cana-4230	132	12	in	in	ADP
cana-4230	132	13	analyzing	analyze	VERB
cana-4230	132	14	data	datum	NOUN
cana-4230	132	15	on	on	ADP
cana-4230	132	16	breast	breast	NOUN
cana-4230	132	17	cancer	cancer	NOUN
cana-4230	132	18	patients	patient	NOUN
cana-4230	132	19	to	to	PART
cana-4230	132	20	discover	discover	VERB
cana-4230	132	21	a	a	DET
cana-4230	132	22	subpopulation	subpopulation	NOUN
cana-4230	132	23	with	with	ADP
cana-4230	132	24	a	a	DET
cana-4230	132	25	different	different	ADJ
cana-4230	132	26	genomic	genomic	NOUN
cana-4230	132	27	signature	signature	NOUN
cana-4230	132	28	,	,	PUNCT
cana-4230	132	29	but	but	CCONJ
cana-4230	132	30	with	with	ADP
cana-4230	132	31	a	a	DET
cana-4230	132	32	superior	superior	ADJ
cana-4230	132	33	survival	survival	NOUN
cana-4230	132	34	rate	rate	NOUN
cana-4230	132	35	.	.	PUNCT
cana-4230	133	1	this	this	DET
cana-4230	133	2	topological	topological	ADJ
cana-4230	133	3	approach	approach	NOUN
cana-4230	133	4	was	be	AUX
cana-4230	133	5	more	more	ADV
cana-4230	133	6	effective	effective	ADJ
cana-4230	133	7	compared	compare	VERB
cana-4230	133	8	to	to	ADP
cana-4230	133	9	the	the	DET
cana-4230	133	10	conventional	conventional	ADJ
cana-4230	133	11	clustering	clustering	NOUN
cana-4230	133	12	in	in	ADP
cana-4230	133	13	creating	create	VERB
cana-4230	133	14	a	a	DET
cana-4230	133	15	better	well	ADJ
cana-4230	133	16	profile	profile	NOUN
cana-4230	133	17	of	of	ADP
cana-4230	133	18	the	the	DET
cana-4230	133	19	given	give	VERB
cana-4230	133	20	dataset	dataset	NOUN
cana-4230	133	21	to	to	PART
cana-4230	133	22	understand	understand	VERB
cana-4230	133	23	the	the	DET
cana-4230	133	24	relationship	relationship	NOUN
cana-4230	133	25	between	between	ADP
cana-4230	133	26	genetic	genetic	ADJ
cana-4230	133	27	markers	marker	NOUN
cana-4230	133	28	and	and	CCONJ
cana-4230	133	29	cancer	cancer	NOUN
cana-4230	133	30	progression	progression	NOUN
cana-4230	133	31	.	.	PUNCT
cana-4230	134	1	table	table	NOUN
cana-4230	134	2	1	1	NUM
cana-4230	134	3	shows	show	VERB
cana-4230	134	4	an	an	DET
cana-4230	134	5	example	example	NOUN
cana-4230	134	6	of	of	ADP
cana-4230	134	7	how	how	SCONJ
cana-4230	134	8	persistent	persistent	ADJ
cana-4230	134	9	homology	homology	NOUN
cana-4230	134	10	helped	help	VERB
cana-4230	134	11	in	in	ADP
cana-4230	134	12	classifying	classify	VERB
cana-4230	134	13	breast	breast	NOUN
cana-4230	134	14	cancer	cancer	NOUN
cana-4230	134	15	patients	patient	NOUN
cana-4230	134	16	based	base	VERB
cana-4230	134	17	on	on	ADP
cana-4230	134	18	topological	topological	ADJ
cana-4230	134	19	features	feature	NOUN
cana-4230	134	20	in	in	ADP
cana-4230	134	21	the	the	DET
cana-4230	134	22	data	datum	NOUN
cana-4230	134	23	.	.	PUNCT
cana-4230	135	1	patient	patient	PROPN
cana-4230	135	2	subgroup	subgroup	PROPN
cana-4230	135	3	topological	topological	PROPN
cana-4230	135	4	feature	feature	NOUN
cana-4230	135	5	detected	detect	VERB
cana-4230	135	6	genetic	genetic	ADJ
cana-4230	135	7	marker	marker	NOUN
cana-4230	135	8	survival	survival	NOUN
cana-4230	135	9	outcome	outcome	PROPN
cana-4230	135	10	subgroup	subgroup	NOUN
cana-4230	135	11	a	a	DET
cana-4230	135	12	long	long	ADV
cana-4230	135	13	-	-	PUNCT
cana-4230	135	14	lasting	last	VERB
cana-4230	135	15	loop	loop	NOUN
cana-4230	135	16	(	(	PUNCT
cana-4230	135	17	1d	1d	NUM
cana-4230	135	18	feature	feature	NOUN
cana-4230	135	19	)	)	PUNCT
cana-4230	135	20	brca1	brca1	PROPN
cana-4230	135	21	mutation	mutation	NOUN
cana-4230	136	1	better	well	ADJ
cana-4230	136	2	survival	survival	PROPN
cana-4230	136	3	subgroup	subgroup	PROPN
cana-4230	136	4	b	b	PROPN
cana-4230	136	5	short	short	ADV
cana-4230	136	6	-	-	PUNCT
cana-4230	136	7	lived	live	VERB
cana-4230	136	8	void	void	NOUN
cana-4230	136	9	(	(	PUNCT
cana-4230	136	10	2d	2d	NUM
cana-4230	136	11	feature	feature	NOUN
cana-4230	136	12	)	)	PUNCT
cana-4230	137	1	tp53	tp53	PROPN
cana-4230	137	2	mutation	mutation	NOUN
cana-4230	137	3	poor	poor	ADJ
cana-4230	137	4	survival	survival	NOUN
cana-4230	137	5	this	this	PRON
cana-4230	137	6	is	be	AUX
cana-4230	137	7	because	because	SCONJ
cana-4230	137	8	the	the	DET
cana-4230	137	9	topological	topological	ADJ
cana-4230	137	10	features	feature	NOUN
cana-4230	137	11	provided	provide	VERB
cana-4230	137	12	additional	additional	ADJ
cana-4230	137	13	quantitative	quantitative	ADJ
cana-4230	137	14	information	information	NOUN
cana-4230	137	15	about	about	ADP
cana-4230	137	16	the	the	DET
cana-4230	137	17	genetic	genetic	ADJ
cana-4230	137	18	structure	structure	NOUN
cana-4230	137	19	rather	rather	ADV
cana-4230	137	20	than	than	ADP
cana-4230	137	21	linear	linear	ADJ
cana-4230	137	22	statistical	statistical	ADJ
cana-4230	137	23	methods	method	NOUN
cana-4230	137	24	for	for	ADP
cana-4230	137	25	predicting	predict	VERB
cana-4230	137	26	patient	patient	ADJ
cana-4230	137	27	outcomes	outcome	NOUN
cana-4230	137	28	and	and	CCONJ
cana-4230	137	29	care	care	NOUN
cana-4230	137	30	(	(	PUNCT
cana-4230	137	31	nicolau	nicolau	PROPN
cana-4230	137	32	,	,	PUNCT
cana-4230	137	33	levine	levine	PROPN
cana-4230	137	34	,	,	PUNCT
cana-4230	137	35	&	&	CCONJ
cana-4230	137	36	carlsson	carlsson	PROPN
cana-4230	137	37	,	,	PUNCT
cana-4230	137	38	2011	2011	NUM
cana-4230	137	39	)	)	PUNCT
cana-4230	137	40	.	.	PUNCT
cana-4230	138	1	communications	communication	NOUN
cana-4230	138	2	on	on	ADP
cana-4230	138	3	applied	apply	VERB
cana-4230	138	4	nonlinear	nonlinear	ADJ
cana-4230	138	5	analysis	analysis	NOUN
cana-4230	138	6	issn	issn	NOUN
cana-4230	138	7	:	:	PUNCT
cana-4230	138	8	1074	1074	NUM
cana-4230	138	9	-	-	PUNCT
cana-4230	138	10	133x	133x	NUM
cana-4230	138	11	vol	vol	NOUN
cana-4230	138	12	32	32	NUM
cana-4230	138	13	no	no	NOUN
cana-4230	138	14	.	.	PUNCT
cana-4230	139	1	8s	8s	PROPN
cana-4230	139	2	(	(	PUNCT
cana-4230	139	3	2025	2025	NUM
cana-4230	139	4	)	)	PUNCT
cana-4230	139	5	902	902	NUM
cana-4230	139	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	139	7	5.2	5.2	NUM
cana-4230	139	8	neuroscience	neuroscience	NOUN
cana-4230	139	9	and	and	CCONJ
cana-4230	139	10	brain	brain	NOUN
cana-4230	139	11	connectivity	connectivity	NOUN
cana-4230	139	12	of	of	ADP
cana-4230	139	13	further	further	ADJ
cana-4230	139	14	interest	interest	NOUN
cana-4230	139	15	,	,	PUNCT
cana-4230	139	16	the	the	DET
cana-4230	139	17	application	application	NOUN
cana-4230	139	18	of	of	ADP
cana-4230	139	19	nonlinear	nonlinear	ADJ
cana-4230	139	20	algebraic	algebraic	ADJ
cana-4230	139	21	topology	topology	NOUN
cana-4230	139	22	is	be	AUX
cana-4230	139	23	also	also	ADV
cana-4230	139	24	found	find	VERB
cana-4230	139	25	in	in	ADP
cana-4230	139	26	neuroscience	neuroscience	NOUN
cana-4230	139	27	where	where	SCONJ
cana-4230	139	28	brain	brain	NOUN
cana-4230	139	29	connections	connection	NOUN
cana-4230	139	30	and	and	CCONJ
cana-4230	139	31	topology	topology	NOUN
cana-4230	139	32	of	of	ADP
cana-4230	139	33	neural	neural	ADJ
cana-4230	139	34	networks	network	NOUN
cana-4230	139	35	are	be	AUX
cana-4230	139	36	investigated	investigate	VERB
cana-4230	139	37	.	.	PUNCT
cana-4230	140	1	by	by	ADP
cana-4230	140	2	applying	apply	VERB
cana-4230	140	3	network	network	NOUN
cana-4230	140	4	theory	theory	NOUN
cana-4230	140	5	to	to	ADP
cana-4230	140	6	the	the	DET
cana-4230	140	7	brain	brain	NOUN
cana-4230	140	8	,	,	PUNCT
cana-4230	140	9	there	there	PRON
cana-4230	140	10	are	be	VERB
cana-4230	140	11	then	then	ADV
cana-4230	140	12	ways	way	NOUN
cana-4230	140	13	to	to	PART
cana-4230	140	14	determine	determine	VERB
cana-4230	140	15	relationships	relationship	NOUN
cana-4230	140	16	between	between	ADP
cana-4230	140	17	the	the	DET
cana-4230	140	18	different	different	ADJ
cana-4230	140	19	electrical	electrical	ADJ
cana-4230	140	20	activations	activation	NOUN
cana-4230	140	21	of	of	ADP
cana-4230	140	22	the	the	DET
cana-4230	140	23	brain	brain	NOUN
cana-4230	140	24	and	and	CCONJ
cana-4230	140	25	the	the	DET
cana-4230	140	26	different	different	ADJ
cana-4230	140	27	cognitive	cognitive	ADJ
cana-4230	140	28	or	or	CCONJ
cana-4230	140	29	neurological	neurological	ADJ
cana-4230	140	30	statuses	status	NOUN
cana-4230	140	31	.	.	PUNCT
cana-4230	141	1	for	for	ADP
cana-4230	141	2	introducing	introduce	VERB
cana-4230	141	3	clique	clique	NOUN
cana-4230	141	4	topology	topology	NOUN
cana-4230	141	5	,	,	PUNCT
cana-4230	141	6	the	the	DET
cana-4230	141	7	researchers	researcher	NOUN
cana-4230	141	8	in	in	ADP
cana-4230	141	9	one	one	NUM
cana-4230	141	10	study	study	NOUN
cana-4230	141	11	applied	apply	VERB
cana-4230	141	12	this	this	DET
cana-4230	141	13	graph	graph	NOUN
cana-4230	141	14	property	property	NOUN
cana-4230	141	15	to	to	PART
cana-4230	141	16	model	model	VERB
cana-4230	141	17	key	key	ADJ
cana-4230	141	18	structures	structure	NOUN
cana-4230	141	19	of	of	ADP
cana-4230	141	20	the	the	DET
cana-4230	141	21	human	human	ADJ
cana-4230	141	22	brain	brain	NOUN
cana-4230	141	23	connectome	connectome	PROPN
cana-4230	141	24	,	,	PUNCT
cana-4230	141	25	including	include	VERB
cana-4230	141	26	loops	loop	NOUN
cana-4230	141	27	and	and	CCONJ
cana-4230	141	28	cavities	cavity	NOUN
cana-4230	141	29	related	relate	VERB
cana-4230	141	30	to	to	ADP
cana-4230	141	31	different	different	ADJ
cana-4230	141	32	states	state	NOUN
cana-4230	141	33	of	of	ADP
cana-4230	141	34	mind	mind	NOUN
cana-4230	141	35	(	(	PUNCT
cana-4230	141	36	giusti	giusti	PROPN
cana-4230	141	37	et	et	PROPN
cana-4230	141	38	al	al	PROPN
cana-4230	141	39	.	.	PROPN
cana-4230	141	40	,	,	PUNCT
cana-4230	141	41	2016	2016	NUM
cana-4230	141	42	)	)	PUNCT
cana-4230	141	43	.	.	PUNCT
cana-4230	142	1	these	these	DET
cana-4230	142	2	topological	topological	ADJ
cana-4230	142	3	features	feature	NOUN
cana-4230	142	4	allowed	allow	VERB
cana-4230	142	5	for	for	ADP
cana-4230	142	6	a	a	DET
cana-4230	142	7	better	well	ADJ
cana-4230	142	8	understanding	understanding	NOUN
cana-4230	142	9	of	of	ADP
cana-4230	142	10	signal	signal	NOUN
cana-4230	142	11	processing	processing	NOUN
cana-4230	142	12	in	in	ADP
cana-4230	142	13	the	the	DET
cana-4230	142	14	brain	brain	NOUN
cana-4230	142	15	:	:	PUNCT
cana-4230	142	16	corresponding	correspond	VERB
cana-4230	142	17	for	for	ADP
cana-4230	142	18	some	some	DET
cana-4230	142	19	loops	loop	NOUN
cana-4230	142	20	to	to	PART
cana-4230	142	21	recurrent	recurrent	ADJ
cana-4230	142	22	activity	activity	NOUN
cana-4230	142	23	crucial	crucial	ADJ
cana-4230	142	24	for	for	ADP
cana-4230	142	25	memory	memory	NOUN
cana-4230	142	26	and	and	CCONJ
cana-4230	142	27	learning	learning	NOUN
cana-4230	142	28	.	.	PUNCT
cana-4230	143	1	table	table	NOUN
cana-4230	143	2	2	2	NUM
cana-4230	143	3	presents	present	VERB
cana-4230	143	4	an	an	DET
cana-4230	143	5	overview	overview	NOUN
cana-4230	143	6	of	of	ADP
cana-4230	143	7	how	how	SCONJ
cana-4230	143	8	topological	topological	ADJ
cana-4230	143	9	features	feature	NOUN
cana-4230	143	10	correlate	correlate	VERB
cana-4230	143	11	with	with	ADP
cana-4230	143	12	different	different	ADJ
cana-4230	143	13	cognitive	cognitive	ADJ
cana-4230	143	14	functions	function	NOUN
cana-4230	143	15	in	in	ADP
cana-4230	143	16	the	the	DET
cana-4230	143	17	brain	brain	NOUN
cana-4230	143	18	.	.	PUNCT
cana-4230	144	1	cognitive	cognitive	ADJ
cana-4230	144	2	function	function	NOUN
cana-4230	144	3	topological	topological	ADJ
cana-4230	144	4	feature	feature	NOUN
cana-4230	144	5	brain	brain	NOUN
cana-4230	144	6	region	region	NOUN
cana-4230	144	7	involved	involve	VERB
cana-4230	144	8	significance	significance	NOUN
cana-4230	144	9	memory	memory	NOUN
cana-4230	144	10	1d	1d	NUM
cana-4230	144	11	loop	loop	NOUN
cana-4230	144	12	hippocampus	hippocampus	NOUN
cana-4230	144	13	supports	support	VERB
cana-4230	144	14	memory	memory	NOUN
cana-4230	144	15	consolidation	consolidation	NOUN
cana-4230	144	16	visual	visual	ADJ
cana-4230	144	17	processing	processing	NOUN
cana-4230	144	18	2d	2d	PROPN
cana-4230	144	19	void	void	ADJ
cana-4230	144	20	occipital	occipital	NOUN
cana-4230	144	21	lobe	lobe	NOUN
cana-4230	144	22	helps	help	VERB
cana-4230	144	23	in	in	ADP
cana-4230	144	24	image	image	NOUN
cana-4230	144	25	reconstruction	reconstruction	NOUN
cana-4230	144	26	attention	attention	NOUN
cana-4230	144	27	control	control	NOUN
cana-4230	144	28	3d	3d	NUM
cana-4230	144	29	cavity	cavity	NOUN
cana-4230	144	30	prefrontal	prefrontal	ADJ
cana-4230	144	31	cortex	cortex	NOUN
cana-4230	144	32	related	relate	VERB
cana-4230	144	33	to	to	PART
cana-4230	144	34	focus	focus	VERB
cana-4230	144	35	and	and	CCONJ
cana-4230	144	36	decisionmaking	decisionmake	VERB
cana-4230	144	37	such	such	DET
cana-4230	144	38	a	a	DET
cana-4230	144	39	topological	topological	ADJ
cana-4230	144	40	structure	structure	NOUN
cana-4230	144	41	might	might	AUX
cana-4230	144	42	assist	assist	VERB
cana-4230	144	43	in	in	ADP
cana-4230	144	44	the	the	DET
cana-4230	144	45	diagnosis	diagnosis	NOUN
cana-4230	144	46	of	of	ADP
cana-4230	144	47	some	some	DET
cana-4230	144	48	neurological	neurological	ADJ
cana-4230	144	49	disorders	disorder	NOUN
cana-4230	144	50	,	,	PUNCT
cana-4230	144	51	for	for	ADP
cana-4230	144	52	example	example	NOUN
cana-4230	144	53	,	,	PUNCT
cana-4230	144	54	alzheimer	alzheimer	PROPN
cana-4230	144	55	’s	’s	PART
cana-4230	144	56	disease	disease	NOUN
cana-4230	144	57	or	or	CCONJ
cana-4230	144	58	schizophrenia	schizophrenia	NOUN
cana-4230	144	59	by	by	ADP
cana-4230	144	60	detecting	detect	VERB
cana-4230	144	61	the	the	DET
cana-4230	144	62	distorted	distorted	ADJ
cana-4230	144	63	topological	topological	ADJ
cana-4230	144	64	features	feature	NOUN
cana-4230	144	65	in	in	ADP
cana-4230	144	66	the	the	DET
cana-4230	144	67	connectivity	connectivity	NOUN
cana-4230	144	68	of	of	ADP
cana-4230	144	69	the	the	DET
cana-4230	144	70	brain	brain	NOUN
cana-4230	144	71	(	(	PUNCT
cana-4230	144	72	sizemore	sizemore	NOUN
cana-4230	144	73	et	et	PROPN
cana-4230	144	74	al	al	PROPN
cana-4230	144	75	.	.	PROPN
cana-4230	144	76	,	,	PUNCT
cana-4230	144	77	2018	2018	NUM
cana-4230	144	78	)	)	PUNCT
cana-4230	144	79	.	.	PUNCT
cana-4230	145	1	5.3	5.3	NUM
cana-4230	145	2	social	social	ADJ
cana-4230	145	3	network	network	NOUN
cana-4230	145	4	analysis	analysis	NOUN
cana-4230	145	5	nonlinear	nonlinear	ADJ
cana-4230	145	6	algebraic	algebraic	ADJ
cana-4230	145	7	topology	topology	NOUN
cana-4230	145	8	has	have	AUX
cana-4230	145	9	also	also	ADV
cana-4230	145	10	been	be	AUX
cana-4230	145	11	used	use	VERB
cana-4230	145	12	in	in	ADP
cana-4230	145	13	social	social	ADJ
cana-4230	145	14	networks	network	NOUN
cana-4230	145	15	for	for	ADP
cana-4230	145	16	modeling	model	VERB
cana-4230	145	17	the	the	DET
cana-4230	145	18	intrinsic	intrinsic	ADJ
cana-4230	145	19	hierarchy	hierarchy	NOUN
cana-4230	145	20	and	and	CCONJ
cana-4230	145	21	nested	nest	VERB
cana-4230	145	22	subgroups	subgroup	NOUN
cana-4230	145	23	of	of	ADP
cana-4230	145	24	individuals	individual	NOUN
cana-4230	145	25	as	as	ADV
cana-4230	145	26	well	well	ADV
cana-4230	145	27	as	as	ADP
cana-4230	145	28	the	the	DET
cana-4230	145	29	flow	flow	NOUN
cana-4230	145	30	of	of	ADP
cana-4230	145	31	information	information	NOUN
cana-4230	145	32	.	.	PUNCT
cana-4230	146	1	social	social	ADJ
cana-4230	146	2	networks	network	NOUN
cana-4230	146	3	are	be	AUX
cana-4230	146	4	complex	complex	ADJ
cana-4230	146	5	objects	object	NOUN
cana-4230	146	6	,	,	PUNCT
cana-4230	146	7	coupled	couple	VERB
cana-4230	146	8	high	high	ADJ
cana-4230	146	9	-	-	PUNCT
cana-4230	146	10	dimensional	dimensional	ADJ
cana-4230	146	11	and	and	CCONJ
cana-4230	146	12	dynamic	dynamic	ADJ
cana-4230	146	13	,	,	PUNCT
cana-4230	146	14	and	and	CCONJ
cana-4230	146	15	hence	hence	ADV
cana-4230	146	16	can	can	AUX
cana-4230	146	17	not	not	PART
cana-4230	146	18	be	be	AUX
cana-4230	146	19	easily	easily	ADV
cana-4230	146	20	analyzed	analyze	VERB
cana-4230	146	21	using	use	VERB
cana-4230	146	22	graphbased	graphbased	ADJ
cana-4230	146	23	techniques	technique	NOUN
cana-4230	146	24	.	.	PUNCT
cana-4230	147	1	through	through	ADP
cana-4230	147	2	using	use	VERB
cana-4230	147	3	persistent	persistent	ADJ
cana-4230	147	4	homology	homology	NOUN
cana-4230	147	5	and	and	CCONJ
cana-4230	147	6	vietoris	vietoris	ADJ
cana-4230	147	7	–	–	PUNCT
cana-4230	147	8	rips	rip	NOUN
cana-4230	147	9	complexes	complex	NOUN
cana-4230	147	10	,	,	PUNCT
cana-4230	147	11	the	the	DET
cana-4230	147	12	authors	author	NOUN
cana-4230	147	13	have	have	AUX
cana-4230	147	14	aimed	aim	VERB
cana-4230	147	15	to	to	PART
cana-4230	147	16	identify	identify	VERB
cana-4230	147	17	persistent	persistent	ADJ
cana-4230	147	18	spatial	spatial	ADJ
cana-4230	147	19	patterns	pattern	NOUN
cana-4230	147	20	that	that	PRON
cana-4230	147	21	correspond	correspond	VERB
cana-4230	147	22	to	to	ADP
cana-4230	147	23	stable	stable	ADJ
cana-4230	147	24	communities	community	NOUN
cana-4230	147	25	(	(	PUNCT
cana-4230	147	26	petri	petri	PROPN
cana-4230	147	27	et	et	PROPN
cana-4230	147	28	al	al	PROPN
cana-4230	147	29	.	.	PROPN
cana-4230	147	30	,	,	PUNCT
cana-4230	147	31	2014	2014	NUM
cana-4230	147	32	)	)	PUNCT
cana-4230	147	33	.	.	PUNCT
cana-4230	148	1	one	one	NUM
cana-4230	148	2	of	of	ADP
cana-4230	148	3	the	the	DET
cana-4230	148	4	applications	application	NOUN
cana-4230	148	5	described	describe	VERB
cana-4230	148	6	in	in	ADP
cana-4230	148	7	detail	detail	NOUN
cana-4230	148	8	is	be	AUX
cana-4230	148	9	the	the	DET
cana-4230	148	10	use	use	NOUN
cana-4230	148	11	of	of	ADP
cana-4230	148	12	topological	topological	ADJ
cana-4230	148	13	methods	method	NOUN
cana-4230	148	14	when	when	SCONJ
cana-4230	148	15	examining	examine	VERB
cana-4230	148	16	a	a	DET
cana-4230	148	17	largescale	largescale	NOUN
cana-4230	148	18	data	datum	NOUN
cana-4230	148	19	set	set	VERB
cana-4230	148	20	of	of	ADP
cana-4230	148	21	the	the	DET
cana-4230	148	22	social	social	ADJ
cana-4230	148	23	network	network	NOUN
cana-4230	148	24	established	establish	VERB
cana-4230	148	25	on	on	ADP
cana-4230	148	26	the	the	DET
cana-4230	148	27	twitter	twitter	NOUN
cana-4230	148	28	social	social	ADJ
cana-4230	148	29	platforms	platform	NOUN
cana-4230	148	30	that	that	PRON
cana-4230	148	31	focused	focus	VERB
cana-4230	148	32	on	on	ADP
cana-4230	148	33	identifying	identify	VERB
cana-4230	148	34	patterns	pattern	NOUN
cana-4230	148	35	in	in	ADP
cana-4230	148	36	retweeting	retweete	VERB
cana-4230	148	37	and	and	CCONJ
cana-4230	148	38	interactions	interaction	NOUN
cana-4230	148	39	between	between	ADP
cana-4230	148	40	users	user	NOUN
cana-4230	148	41	.	.	PUNCT
cana-4230	149	1	based	base	VERB
cana-4230	149	2	on	on	ADP
cana-4230	149	3	the	the	DET
cana-4230	149	4	analysis	analysis	NOUN
cana-4230	149	5	of	of	ADP
cana-4230	149	6	the	the	DET
cana-4230	149	7	barcodes	barcode	NOUN
cana-4230	149	8	identified	identify	VERB
cana-4230	149	9	by	by	ADP
cana-4230	149	10	persistent	persistent	ADJ
cana-4230	149	11	homology	homology	NOUN
cana-4230	149	12	,	,	PUNCT
cana-4230	149	13	it	it	PRON
cana-4230	149	14	was	be	AUX
cana-4230	149	15	possible	possible	ADJ
cana-4230	149	16	to	to	PART
cana-4230	149	17	define	define	VERB
cana-4230	149	18	the	the	DET
cana-4230	149	19	long	long	ADV
cana-4230	149	20	-	-	PUNCT
cana-4230	149	21	living	live	VERB
cana-4230	149	22	social	social	ADJ
cana-4230	149	23	communities	community	NOUN
cana-4230	149	24	that	that	PRON
cana-4230	149	25	were	be	AUX
cana-4230	149	26	present	present	ADJ
cana-4230	149	27	within	within	ADP
cana-4230	149	28	the	the	DET
cana-4230	149	29	network	network	NOUN
cana-4230	149	30	even	even	ADV
cana-4230	149	31	when	when	SCONJ
cana-4230	149	32	the	the	DET
cana-4230	149	33	latter	latter	NOUN
cana-4230	149	34	changed	change	VERB
cana-4230	149	35	during	during	ADP
cana-4230	149	36	its	its	PRON
cana-4230	149	37	existence	existence	NOUN
cana-4230	149	38	.	.	PUNCT
cana-4230	150	1	it	it	PRON
cana-4230	150	2	was	be	AUX
cana-4230	150	3	useful	useful	ADJ
cana-4230	150	4	for	for	ADP
cana-4230	150	5	identifying	identify	VERB
cana-4230	150	6	the	the	DET
cana-4230	150	7	process	process	NOUN
cana-4230	150	8	by	by	ADP
cana-4230	150	9	which	which	PRON
cana-4230	150	10	information	information	NOUN
cana-4230	150	11	is	be	AUX
cana-4230	150	12	disseminated	disseminate	VERB
cana-4230	150	13	through	through	ADP
cana-4230	150	14	social	social	ADJ
cana-4230	150	15	media	medium	NOUN
cana-4230	150	16	networks	network	NOUN
cana-4230	150	17	as	as	ADV
cana-4230	150	18	well	well	ADV
cana-4230	150	19	as	as	ADP
cana-4230	150	20	how	how	SCONJ
cana-4230	150	21	enduring	enduring	ADJ
cana-4230	150	22	online	online	ADJ
cana-4230	150	23	communities	community	NOUN
cana-4230	150	24	are	be	AUX
cana-4230	150	25	created	create	VERB
cana-4230	150	26	.	.	PUNCT
cana-4230	151	1	communications	communication	NOUN
cana-4230	151	2	on	on	ADP
cana-4230	151	3	applied	apply	VERB
cana-4230	151	4	nonlinear	nonlinear	ADJ
cana-4230	151	5	analysis	analysis	NOUN
cana-4230	151	6	issn	issn	NOUN
cana-4230	151	7	:	:	PUNCT
cana-4230	151	8	1074	1074	NUM
cana-4230	151	9	-	-	PUNCT
cana-4230	151	10	133x	133x	NUM
cana-4230	151	11	vol	vol	NOUN
cana-4230	151	12	32	32	NUM
cana-4230	151	13	no	no	NOUN
cana-4230	151	14	.	.	PUNCT
cana-4230	152	1	8s	8s	PROPN
cana-4230	152	2	(	(	PUNCT
cana-4230	152	3	2025	2025	NUM
cana-4230	152	4	)	)	PUNCT
cana-4230	152	5	903	903	NUM
cana-4230	152	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	152	7	table	table	NOUN
cana-4230	152	8	3	3	NUM
cana-4230	152	9	provides	provide	VERB
cana-4230	152	10	a	a	DET
cana-4230	152	11	summary	summary	NOUN
cana-4230	152	12	of	of	ADP
cana-4230	152	13	the	the	DET
cana-4230	152	14	topological	topological	ADJ
cana-4230	152	15	features	feature	NOUN
cana-4230	152	16	observed	observe	VERB
cana-4230	152	17	in	in	ADP
cana-4230	152	18	the	the	DET
cana-4230	152	19	social	social	ADJ
cana-4230	152	20	network	network	NOUN
cana-4230	152	21	analysis	analysis	NOUN
cana-4230	152	22	.	.	PUNCT
cana-4230	153	1	feature	feature	NOUN
cana-4230	153	2	topological	topological	ADJ
cana-4230	153	3	feature	feature	NOUN
cana-4230	153	4	social	social	ADJ
cana-4230	153	5	structure	structure	NOUN
cana-4230	153	6	interpretation	interpretation	NOUN
cana-4230	153	7	community	community	NOUN
cana-4230	153	8	persistence	persistence	NOUN
cana-4230	153	9	long	long	ADV
cana-4230	153	10	-	-	PUNCT
cana-4230	153	11	lasting	last	VERB
cana-4230	153	12	1d	1d	NUM
cana-4230	153	13	loop	loop	NOUN
cana-4230	153	14	stable	stable	ADJ
cana-4230	153	15	user	user	NOUN
cana-4230	153	16	group	group	NOUN
cana-4230	153	17	indicates	indicate	VERB
cana-4230	153	18	strong	strong	ADJ
cana-4230	153	19	social	social	ADJ
cana-4230	153	20	ties	tie	NOUN
cana-4230	153	21	information	information	NOUN
cana-4230	153	22	diffusion	diffusion	NOUN
cana-4230	153	23	2d	2d	PROPN
cana-4230	153	24	void	void	VERB
cana-4230	153	25	information	information	NOUN
cana-4230	153	26	flow	flow	NOUN
cana-4230	153	27	between	between	ADP
cana-4230	153	28	groups	group	NOUN
cana-4230	153	29	highlights	highlight	VERB
cana-4230	153	30	key	key	ADJ
cana-4230	153	31	information	information	NOUN
cana-4230	153	32	bridges	bridge	NOUN
cana-4230	153	33	this	this	DET
cana-4230	153	34	application	application	NOUN
cana-4230	153	35	demonstrates	demonstrate	VERB
cana-4230	153	36	how	how	SCONJ
cana-4230	153	37	nonlinear	nonlinear	ADJ
cana-4230	153	38	algebraic	algebraic	ADJ
cana-4230	153	39	topology	topology	NOUN
cana-4230	153	40	can	can	AUX
cana-4230	153	41	help	help	VERB
cana-4230	153	42	discover	discover	VERB
cana-4230	153	43	time	time	NOUN
cana-4230	153	44	-	-	PUNCT
cana-4230	153	45	scale	scale	NOUN
cana-4230	153	46	invariant	invariant	ADJ
cana-4230	153	47	structures	structure	NOUN
cana-4230	153	48	that	that	PRON
cana-4230	153	49	characterize	characterize	VERB
cana-4230	153	50	social	social	ADJ
cana-4230	153	51	systems	system	NOUN
cana-4230	153	52	and	and	CCONJ
cana-4230	153	53	gain	gain	VERB
cana-4230	153	54	a	a	DET
cana-4230	153	55	better	well	ADJ
cana-4230	153	56	understanding	understanding	NOUN
cana-4230	153	57	of	of	ADP
cana-4230	153	58	their	their	PRON
cana-4230	153	59	evolution	evolution	NOUN
cana-4230	153	60	and	and	CCONJ
cana-4230	153	61	behavior	behavior	NOUN
cana-4230	153	62	.	.	PUNCT
cana-4230	154	1	5.4	5.4	NUM
cana-4230	154	2	machine	machine	NOUN
cana-4230	154	3	learning	learning	NOUN
cana-4230	154	4	and	and	CCONJ
cana-4230	154	5	data	datum	NOUN
cana-4230	154	6	science	science	NOUN
cana-4230	154	7	in	in	ADP
cana-4230	154	8	machine	machine	NOUN
cana-4230	154	9	learning	learning	NOUN
cana-4230	154	10	,	,	PUNCT
cana-4230	154	11	topological	topological	ADJ
cana-4230	154	12	data	datum	NOUN
cana-4230	154	13	analysis	analysis	NOUN
cana-4230	154	14	(	(	PUNCT
cana-4230	154	15	tda	tda	NOUN
cana-4230	154	16	)	)	PUNCT
cana-4230	154	17	has	have	AUX
cana-4230	154	18	been	be	AUX
cana-4230	154	19	applied	apply	VERB
cana-4230	154	20	to	to	PART
cana-4230	154	21	enhance	enhance	VERB
cana-4230	154	22	model	model	NOUN
cana-4230	154	23	performances	performance	NOUN
cana-4230	154	24	and	and	CCONJ
cana-4230	154	25	explanation	explanation	NOUN
cana-4230	154	26	,	,	PUNCT
cana-4230	154	27	especially	especially	ADV
cana-4230	154	28	when	when	SCONJ
cana-4230	154	29	the	the	DET
cana-4230	154	30	data	datum	NOUN
cana-4230	154	31	set	set	VERB
cana-4230	154	32	is	be	AUX
cana-4230	154	33	high	high	ADV
cana-4230	154	34	-	-	PUNCT
cana-4230	154	35	dimensional	dimensional	ADJ
cana-4230	154	36	and	and	CCONJ
cana-4230	154	37	complicated	complicated	ADJ
cana-4230	154	38	nonlinear	nonlinear	NOUN
cana-4230	154	39	.	.	PUNCT
cana-4230	155	1	for	for	ADP
cana-4230	155	2	instance	instance	NOUN
cana-4230	155	3	,	,	PUNCT
cana-4230	155	4	topological	topological	ADJ
cana-4230	155	5	feature	feature	NOUN
cana-4230	155	6	extraction	extraction	NOUN
cana-4230	155	7	has	have	AUX
cana-4230	155	8	been	be	AUX
cana-4230	155	9	applied	apply	VERB
cana-4230	155	10	to	to	ADP
cana-4230	155	11	pre	pre	ADJ
cana-4230	155	12	-	-	ADJ
cana-4230	155	13	processing	processing	ADJ
cana-4230	155	14	data	datum	NOUN
cana-4230	155	15	on	on	ADP
cana-4230	155	16	classification	classification	NOUN
cana-4230	155	17	problems	problem	NOUN
cana-4230	155	18	to	to	PART
cana-4230	155	19	enhance	enhance	VERB
cana-4230	155	20	the	the	DET
cana-4230	155	21	efficiency	efficiency	NOUN
cana-4230	155	22	of	of	ADP
cana-4230	155	23	regular	regular	ADJ
cana-4230	155	24	ml	ml	NOUN
cana-4230	155	25	algorithms	algorithms	PROPN
cana-4230	155	26	(	(	PUNCT
cana-4230	155	27	chen	chen	PROPN
cana-4230	155	28	et	et	PROPN
cana-4230	155	29	al	al	PROPN
cana-4230	155	30	.	.	PROPN
cana-4230	155	31	,	,	PUNCT
cana-4230	155	32	2019	2019	NUM
cana-4230	155	33	)	)	PUNCT
cana-4230	155	34	.	.	PUNCT
cana-4230	156	1	here	here	ADV
cana-4230	156	2	,	,	PUNCT
cana-4230	156	3	persistent	persistent	ADJ
cana-4230	156	4	homology	homology	NOUN
cana-4230	156	5	is	be	AUX
cana-4230	156	6	employed	employ	VERB
cana-4230	156	7	to	to	PART
cana-4230	156	8	transform	transform	VERB
cana-4230	156	9	the	the	DET
cana-4230	156	10	original	original	ADJ
cana-4230	156	11	high	high	ADJ
cana-4230	156	12	-	-	PUNCT
cana-4230	156	13	dimensional	dimensional	ADJ
cana-4230	156	14	data	datum	NOUN
cana-4230	156	15	into	into	ADP
cana-4230	156	16	a	a	DET
cana-4230	156	17	lowerdimensional	lowerdimensional	ADJ
cana-4230	156	18	representation	representation	NOUN
cana-4230	156	19	,	,	PUNCT
cana-4230	156	20	with	with	ADP
cana-4230	156	21	unique	unique	ADJ
cana-4230	156	22	topological	topological	ADJ
cana-4230	156	23	characteristics	characteristic	NOUN
cana-4230	156	24	feeding	feed	VERB
cana-4230	156	25	into	into	ADP
cana-4230	156	26	machine	machine	NOUN
cana-4230	156	27	learning	learning	NOUN
cana-4230	156	28	algorithms	algorithm	NOUN
cana-4230	156	29	.	.	PUNCT
cana-4230	157	1	tasks	task	NOUN
cana-4230	157	2	like	like	ADP
cana-4230	157	3	image	image	NOUN
cana-4230	157	4	recognition	recognition	NOUN
cana-4230	157	5	,	,	PUNCT
cana-4230	157	6	anomaly	anomaly	NOUN
cana-4230	157	7	detection	detection	NOUN
cana-4230	157	8	,	,	PUNCT
cana-4230	157	9	and	and	CCONJ
cana-4230	157	10	time	time	NOUN
cana-4230	157	11	-	-	PUNCT
cana-4230	157	12	series	series	NOUN
cana-4230	157	13	analysis	analysis	NOUN
cana-4230	157	14	where	where	SCONJ
cana-4230	157	15	the	the	DET
cana-4230	157	16	global	global	ADJ
cana-4230	157	17	architecture	architecture	NOUN
cana-4230	157	18	of	of	ADP
cana-4230	157	19	data	datum	NOUN
cana-4230	157	20	is	be	AUX
cana-4230	157	21	paramount	paramount	ADJ
cana-4230	157	22	for	for	ADP
cana-4230	157	23	prediction	prediction	NOUN
cana-4230	157	24	have	have	AUX
cana-4230	157	25	been	be	AUX
cana-4230	157	26	accomplished	accomplish	VERB
cana-4230	157	27	well	well	ADV
cana-4230	157	28	at	at	ADP
cana-4230	157	29	this	this	DET
cana-4230	157	30	level	level	NOUN
cana-4230	157	31	.	.	PUNCT
cana-4230	158	1	6	6	X
cana-4230	158	2	.	.	PUNCT
cana-4230	158	3	computational	computational	ADJ
cana-4230	158	4	tools	tool	NOUN
cana-4230	158	5	and	and	CCONJ
cana-4230	158	6	algorithmic	algorithmic	ADJ
cana-4230	158	7	implementations	implementation	NOUN
cana-4230	158	8	the	the	DET
cana-4230	158	9	analysis	analysis	NOUN
cana-4230	158	10	part	part	NOUN
cana-4230	158	11	of	of	ADP
cana-4230	158	12	computational	computational	ADJ
cana-4230	158	13	nt	not	PART
cana-4230	158	14	involves	involve	VERB
cana-4230	158	15	the	the	DET
cana-4230	158	16	stability	stability	NOUN
cana-4230	158	17	of	of	ADP
cana-4230	158	18	software	software	NOUN
cana-4230	158	19	tools	tool	NOUN
cana-4230	158	20	and	and	CCONJ
cana-4230	158	21	algorithms	algorithm	NOUN
cana-4230	158	22	to	to	PART
cana-4230	158	23	deal	deal	VERB
cana-4230	158	24	with	with	ADP
cana-4230	158	25	high	high	ADJ
cana-4230	158	26	dimensionality	dimensionality	NOUN
cana-4230	158	27	and	and	CCONJ
cana-4230	158	28	to	to	PART
cana-4230	158	29	extract	extract	VERB
cana-4230	158	30	topological	topological	ADJ
cana-4230	158	31	characteristics	characteristic	NOUN
cana-4230	158	32	.	.	PUNCT
cana-4230	159	1	these	these	DET
cana-4230	159	2	tools	tool	NOUN
cana-4230	159	3	apply	apply	VERB
cana-4230	159	4	techniques	technique	NOUN
cana-4230	159	5	like	like	ADP
cana-4230	159	6	persistent	persistent	ADJ
cana-4230	159	7	homology	homology	NOUN
cana-4230	159	8	simplicial	simplicial	ADJ
cana-4230	159	9	complex	complex	ADJ
cana-4230	159	10	formation	formation	NOUN
cana-4230	159	11	,	,	PUNCT
cana-4230	159	12	and	and	CCONJ
cana-4230	159	13	numeric	numeric	ADJ
cana-4230	159	14	topology	topology	NOUN
cana-4230	159	15	as	as	ADP
cana-4230	159	16	a	a	DET
cana-4230	159	17	function	function	NOUN
cana-4230	159	18	of	of	ADP
cana-4230	159	19	morse	morse	ADJ
cana-4230	159	20	theory	theory	NOUN
cana-4230	159	21	on	on	ADP
cana-4230	159	22	a	a	DET
cana-4230	159	23	variety	variety	NOUN
cana-4230	159	24	of	of	ADP
cana-4230	159	25	datasets	dataset	NOUN
cana-4230	159	26	drawn	draw	VERB
cana-4230	159	27	from	from	ADP
cana-4230	159	28	fields	field	NOUN
cana-4230	159	29	as	as	ADV
cana-4230	159	30	diverse	diverse	ADJ
cana-4230	159	31	as	as	ADP
cana-4230	159	32	biology	biology	NOUN
cana-4230	159	33	to	to	ADP
cana-4230	159	34	social	social	ADJ
cana-4230	159	35	media	medium	NOUN
cana-4230	159	36	,	,	PUNCT
cana-4230	159	37	and	and	CCONJ
cana-4230	159	38	machine	machine	NOUN
cana-4230	159	39	learning	learning	NOUN
cana-4230	159	40	.	.	PUNCT
cana-4230	160	1	this	this	DET
cana-4230	160	2	section	section	NOUN
cana-4230	160	3	reviews	review	VERB
cana-4230	160	4	the	the	DET
cana-4230	160	5	most	most	ADV
cana-4230	160	6	common	common	ADJ
cana-4230	160	7	computational	computational	ADJ
cana-4230	160	8	tools	tool	NOUN
cana-4230	160	9	of	of	ADP
cana-4230	160	10	nlt	nlt	PROPN
cana-4230	160	11	and	and	CCONJ
cana-4230	160	12	discusses	discuss	VERB
cana-4230	160	13	their	their	PRON
cana-4230	160	14	algorithms	algorithm	NOUN
cana-4230	160	15	.	.	PUNCT
cana-4230	161	1	moreover	moreover	ADV
cana-4230	161	2	,	,	PUNCT
cana-4230	161	3	we	we	PRON
cana-4230	161	4	discuss	discuss	VERB
cana-4230	161	5	the	the	DET
cana-4230	161	6	results	result	NOUN
cana-4230	161	7	of	of	ADP
cana-4230	161	8	performance	performance	NOUN
cana-4230	161	9	benchmarking	benchmarke	VERB
cana-4230	161	10	of	of	ADP
cana-4230	161	11	these	these	DET
cana-4230	161	12	tools	tool	NOUN
cana-4230	161	13	using	use	VERB
cana-4230	161	14	synthetic	synthetic	ADJ
cana-4230	161	15	and	and	CCONJ
cana-4230	161	16	reallife	reallife	PROPN
cana-4230	161	17	datasets	dataset	NOUN
cana-4230	161	18	to	to	PART
cana-4230	161	19	show	show	VERB
cana-4230	161	20	the	the	DET
cana-4230	161	21	advantages	advantage	NOUN
cana-4230	161	22	and	and	CCONJ
cana-4230	161	23	shortcomings	shortcoming	NOUN
cana-4230	161	24	of	of	ADP
cana-4230	161	25	various	various	ADJ
cana-4230	161	26	tools	tool	NOUN
cana-4230	161	27	in	in	ADP
cana-4230	161	28	different	different	ADJ
cana-4230	161	29	contexts	contexts	NOUN
cana-4230	161	30	.	.	PUNCT
cana-4230	162	1	6.1	6.1	NUM
cana-4230	162	2	persistent	persistent	ADJ
cana-4230	162	3	homology	homology	NOUN
cana-4230	162	4	algorithms	algorithm	VERB
cana-4230	162	5	several	several	ADJ
cana-4230	162	6	tools	tool	NOUN
cana-4230	162	7	have	have	AUX
cana-4230	162	8	been	be	AUX
cana-4230	162	9	developed	develop	VERB
cana-4230	162	10	in	in	ADP
cana-4230	162	11	nonlinear	nonlinear	ADJ
cana-4230	162	12	algebraic	algebraic	ADJ
cana-4230	162	13	topology	topology	NOUN
cana-4230	162	14	,	,	PUNCT
cana-4230	162	15	and	and	CCONJ
cana-4230	162	16	probably	probably	ADV
cana-4230	162	17	the	the	DET
cana-4230	162	18	most	most	ADV
cana-4230	162	19	popular	popular	ADJ
cana-4230	162	20	one	one	NOUN
cana-4230	162	21	is	be	AUX
cana-4230	162	22	the	the	DET
cana-4230	162	23	persistent	persistent	ADJ
cana-4230	162	24	homology	homology	NOUN
cana-4230	162	25	which	which	PRON
cana-4230	162	26	is	be	AUX
cana-4230	162	27	used	use	VERB
cana-4230	162	28	in	in	ADP
cana-4230	162	29	computing	compute	VERB
cana-4230	162	30	features	feature	NOUN
cana-4230	162	31	that	that	PRON
cana-4230	162	32	are	be	AUX
cana-4230	162	33	consistent	consistent	ADJ
cana-4230	162	34	in	in	ADP
cana-4230	162	35	scales	scale	NOUN
cana-4230	162	36	within	within	ADP
cana-4230	162	37	a	a	DET
cana-4230	162	38	dataset	dataset	NOUN
cana-4230	162	39	.	.	PUNCT
cana-4230	163	1	that	that	PRON
cana-4230	163	2	’s	’	VERB
cana-4230	163	3	why	why	SCONJ
cana-4230	163	4	the	the	DET
cana-4230	163	5	existence	existence	NOUN
cana-4230	163	6	of	of	ADP
cana-4230	163	7	such	such	ADJ
cana-4230	163	8	features	feature	NOUN
cana-4230	163	9	as	as	ADP
cana-4230	163	10	loops	loop	NOUN
cana-4230	163	11	and	and	CCONJ
cana-4230	163	12	voids	voids	NOUN
cana-4230	163	13	remains	remain	VERB
cana-4230	163	14	vital	vital	ADJ
cana-4230	163	15	to	to	ADP
cana-4230	163	16	identifying	identify	VERB
cana-4230	163	17	important	important	ADJ
cana-4230	163	18	structures	structure	NOUN
cana-4230	163	19	in	in	ADP
cana-4230	163	20	high	high	ADJ
cana-4230	163	21	-	-	PUNCT
cana-4230	163	22	dimensional	dimensional	ADJ
cana-4230	163	23	data	datum	NOUN
cana-4230	163	24	.	.	PUNCT
cana-4230	164	1	several	several	ADJ
cana-4230	164	2	tools	tool	NOUN
cana-4230	164	3	can	can	AUX
cana-4230	164	4	compute	compute	VERB
cana-4230	164	5	persistent	persistent	ADJ
cana-4230	164	6	homology	homology	NOUN
cana-4230	164	7	effectively	effectively	ADV
cana-4230	164	8	some	some	PRON
cana-4230	164	9	of	of	ADP
cana-4230	164	10	the	the	DET
cana-4230	164	11	most	most	ADV
cana-4230	164	12	well	well	ADV
cana-4230	164	13	-	-	PUNCT
cana-4230	164	14	known	know	VERB
cana-4230	164	15	are	be	AUX
cana-4230	164	16	ripser	ripser	NOUN
cana-4230	164	17	and	and	CCONJ
cana-4230	164	18	gudhi	gudhi	NOUN
cana-4230	164	19	.	.	PUNCT
cana-4230	165	1	ripser	ripser	NOUN
cana-4230	165	2	is	be	AUX
cana-4230	165	3	numerically	numerically	ADV
cana-4230	165	4	efficient	efficient	ADJ
cana-4230	165	5	with	with	ADP
cana-4230	165	6	large	large	ADJ
cana-4230	165	7	data	datum	NOUN
cana-4230	165	8	set	set	VERB
cana-4230	165	9	applicability	applicability	NOUN
cana-4230	165	10	and	and	CCONJ
cana-4230	165	11	gudhi	gudhi	NOUN
cana-4230	165	12	provides	provide	VERB
cana-4230	165	13	a	a	DET
cana-4230	165	14	communications	communication	NOUN
cana-4230	165	15	on	on	ADP
cana-4230	165	16	applied	apply	VERB
cana-4230	165	17	nonlinear	nonlinear	ADJ
cana-4230	165	18	analysis	analysis	NOUN
cana-4230	165	19	issn	issn	NOUN
cana-4230	165	20	:	:	PUNCT
cana-4230	165	21	1074	1074	NUM
cana-4230	165	22	-	-	PUNCT
cana-4230	165	23	133x	133x	NUM
cana-4230	165	24	vol	vol	NOUN
cana-4230	165	25	32	32	NUM
cana-4230	165	26	no	no	NOUN
cana-4230	165	27	.	.	PUNCT
cana-4230	166	1	8s	8s	PROPN
cana-4230	166	2	(	(	PUNCT
cana-4230	166	3	2025	2025	NUM
cana-4230	166	4	)	)	PUNCT
cana-4230	166	5	904	904	NUM
cana-4230	166	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	166	7	broader	broad	ADJ
cana-4230	166	8	number	number	NOUN
cana-4230	166	9	of	of	ADP
cana-4230	166	10	algorithms	algorithm	NOUN
cana-4230	166	11	under	under	ADP
cana-4230	166	12	tda	tda	NOUN
cana-4230	166	13	that	that	PRON
cana-4230	166	14	includes	include	VERB
cana-4230	166	15	persistence	persistence	NOUN
cana-4230	166	16	diagram	diagram	NOUN
cana-4230	166	17	,	,	PUNCT
cana-4230	166	18	alpha	alpha	NOUN
cana-4230	166	19	complex	complex	NOUN
cana-4230	166	20	&	&	CCONJ
cana-4230	166	21	weighted	weight	VERB
cana-4230	166	22	rips	rip	NOUN
cana-4230	166	23	complex	complex	ADJ
cana-4230	166	24	.	.	PUNCT
cana-4230	166	25	table	table	NOUN
cana-4230	166	26	4	4	NUM
cana-4230	166	27	compares	compare	VERB
cana-4230	166	28	the	the	DET
cana-4230	166	29	runtime	runtime	NOUN
cana-4230	166	30	performance	performance	NOUN
cana-4230	166	31	and	and	CCONJ
cana-4230	166	32	memory	memory	NOUN
cana-4230	166	33	usage	usage	NOUN
cana-4230	166	34	of	of	ADP
cana-4230	166	35	ripser	ripser	NOUN
cana-4230	166	36	and	and	CCONJ
cana-4230	166	37	gudhi	gudhi	VERB
cana-4230	166	38	when	when	SCONJ
cana-4230	166	39	applied	apply	VERB
cana-4230	166	40	to	to	ADP
cana-4230	166	41	a	a	DET
cana-4230	166	42	synthetic	synthetic	ADJ
cana-4230	166	43	dataset	dataset	NOUN
cana-4230	166	44	of	of	ADP
cana-4230	166	45	100,000	100,000	NUM
cana-4230	166	46	points	point	NOUN
cana-4230	166	47	in	in	ADP
cana-4230	166	48	a	a	DET
cana-4230	166	49	10	10	NUM
cana-4230	166	50	-	-	PUNCT
cana-4230	166	51	dimensional	dimensional	ADJ
cana-4230	166	52	space	space	NOUN
cana-4230	166	53	.	.	PUNCT
cana-4230	167	1	tool	tool	NOUN
cana-4230	167	2	runtime	runtime	NOUN
cana-4230	167	3	(	(	PUNCT
cana-4230	167	4	seconds	second	NOUN
cana-4230	167	5	)	)	PUNCT
cana-4230	167	6	memory	memory	NOUN
cana-4230	167	7	usage	usage	NOUN
cana-4230	167	8	(	(	PUNCT
cana-4230	167	9	gb	gb	NOUN
cana-4230	167	10	)	)	PUNCT
cana-4230	167	11	scalability	scalability	NOUN
cana-4230	167	12	special	special	ADJ
cana-4230	167	13	features	feature	NOUN
cana-4230	167	14	ripser	ripser	NOUN
cana-4230	167	15	120	120	NUM
cana-4230	167	16	3.5	3.5	NUM
cana-4230	167	17	excellent	excellent	ADV
cana-4230	167	18	highly	highly	ADV
cana-4230	167	19	optimized	optimize	VERB
cana-4230	167	20	for	for	ADP
cana-4230	167	21	large	large	ADJ
cana-4230	167	22	data	datum	NOUN
cana-4230	167	23	gudhi	gudhi	VERB
cana-4230	167	24	250	250	NUM
cana-4230	167	25	4.0	4.0	NUM
cana-4230	167	26	moderate	moderate	ADJ
cana-4230	167	27	alpha	alpha	NOUN
cana-4230	167	28	complexes	complex	NOUN
cana-4230	167	29	,	,	PUNCT
cana-4230	167	30	more	more	ADV
cana-4230	167	31	versatile	versatile	ADJ
cana-4230	167	32	as	as	SCONJ
cana-4230	167	33	seen	see	VERB
cana-4230	167	34	in	in	ADP
cana-4230	167	35	table	table	NOUN
cana-4230	167	36	4	4	NUM
cana-4230	167	37	,	,	PUNCT
cana-4230	167	38	ripper	ripper	X
cana-4230	167	39	is	be	AUX
cana-4230	167	40	more	more	ADV
cana-4230	167	41	computationally	computationally	ADV
cana-4230	167	42	efficient	efficient	ADJ
cana-4230	167	43	and	and	CCONJ
cana-4230	167	44	uses	use	VERB
cana-4230	167	45	less	less	ADJ
cana-4230	167	46	memory	memory	NOUN
cana-4230	167	47	compared	compare	VERB
cana-4230	167	48	to	to	PART
cana-4230	167	49	gudhi	gudhi	VERB
cana-4230	167	50	,	,	PUNCT
cana-4230	167	51	making	make	VERB
cana-4230	167	52	it	it	PRON
cana-4230	167	53	a	a	DET
cana-4230	167	54	preferred	preferred	ADJ
cana-4230	167	55	choice	choice	NOUN
cana-4230	167	56	for	for	ADP
cana-4230	167	57	large	large	ADJ
cana-4230	167	58	datasets	dataset	NOUN
cana-4230	167	59	.	.	PUNCT
cana-4230	168	1	however	however	ADV
cana-4230	168	2	,	,	PUNCT
cana-4230	168	3	gudhi	gudhi	VERB
cana-4230	168	4	provides	provide	VERB
cana-4230	168	5	additional	additional	ADJ
cana-4230	168	6	functionalities	functionality	NOUN
cana-4230	168	7	that	that	PRON
cana-4230	168	8	are	be	AUX
cana-4230	168	9	beneficial	beneficial	ADJ
cana-4230	168	10	in	in	ADP
cana-4230	168	11	specialized	specialized	ADJ
cana-4230	168	12	applications	application	NOUN
cana-4230	168	13	such	such	ADJ
cana-4230	168	14	as	as	ADP
cana-4230	168	15	complex	complex	ADJ
cana-4230	168	16	filtration	filtration	NOUN
cana-4230	168	17	.	.	PUNCT
cana-4230	169	1	6.2	6.2	NUM
cana-4230	169	2	simplicial	simplicial	ADJ
cana-4230	169	3	complex	complex	ADJ
cana-4230	169	4	construction	construction	NOUN
cana-4230	169	5	simplicial	simplicial	ADJ
cana-4230	169	6	complexes	complex	NOUN
cana-4230	169	7	are	be	AUX
cana-4230	169	8	another	another	DET
cana-4230	169	9	integral	integral	ADJ
cana-4230	169	10	part	part	NOUN
cana-4230	169	11	of	of	ADP
cana-4230	169	12	nonlinear	nonlinear	ADJ
cana-4230	169	13	algebraic	algebraic	ADJ
cana-4230	169	14	topology	topology	NOUN
cana-4230	169	15	,	,	PUNCT
cana-4230	169	16	as	as	SCONJ
cana-4230	169	17	they	they	PRON
cana-4230	169	18	define	define	VERB
cana-4230	169	19	the	the	DET
cana-4230	169	20	connections	connection	NOUN
cana-4230	169	21	between	between	ADP
cana-4230	169	22	data	datum	NOUN
cana-4230	169	23	points	point	NOUN
cana-4230	169	24	as	as	ADP
cana-4230	169	25	objects	object	NOUN
cana-4230	169	26	in	in	ADP
cana-4230	169	27	the	the	DET
cana-4230	169	28	topological	topological	ADJ
cana-4230	169	29	space	space	NOUN
cana-4230	169	30	.	.	PUNCT
cana-4230	170	1	this	this	DET
cana-4230	170	2	vietoris	vietoris	PROPN
cana-4230	170	3	–	–	PUNCT
cana-4230	170	4	rips	rip	NOUN
cana-4230	170	5	complex	complex	NOUN
cana-4230	170	6	is	be	AUX
cana-4230	170	7	generally	generally	ADV
cana-4230	170	8	applied	apply	VERB
cana-4230	170	9	to	to	ADP
cana-4230	170	10	model	model	NOUN
cana-4230	170	11	point	point	NOUN
cana-4230	170	12	proximity	proximity	NOUN
cana-4230	170	13	relationships	relationship	NOUN
cana-4230	170	14	that	that	PRON
cana-4230	170	15	are	be	AUX
cana-4230	170	16	required	require	VERB
cana-4230	170	17	for	for	ADP
cana-4230	170	18	the	the	DET
cana-4230	170	19	computation	computation	NOUN
cana-4230	170	20	of	of	ADP
cana-4230	170	21	persistent	persistent	ADJ
cana-4230	170	22	homology	homology	NOUN
cana-4230	170	23	.	.	PUNCT
cana-4230	171	1	the	the	DET
cana-4230	171	2	kind	kind	NOUN
cana-4230	171	3	most	most	ADV
cana-4230	171	4	preferred	preferred	ADJ
cana-4230	171	5	for	for	ADP
cana-4230	171	6	simplicial	simplicial	ADJ
cana-4230	171	7	complex	complex	ADJ
cana-4230	171	8	construction	construction	NOUN
cana-4230	171	9	is	be	AUX
cana-4230	171	10	the	the	DET
cana-4230	171	11	dionysus	dionysus	NOUN
cana-4230	171	12	and	and	CCONJ
cana-4230	171	13	the	the	DET
cana-4230	171	14	dipha	dipha	ADJ
cana-4230	171	15	libraries	library	NOUN
cana-4230	171	16	.	.	PUNCT
cana-4230	172	1	dionysus	dionysus	PROPN
cana-4230	172	2	concerns	concern	NOUN
cana-4230	172	3	the	the	DET
cana-4230	172	4	optimization	optimization	NOUN
cana-4230	172	5	of	of	ADP
cana-4230	172	6	simplicial	simplicial	ADJ
cana-4230	172	7	complex	complex	ADJ
cana-4230	172	8	construction	construction	NOUN
cana-4230	172	9	and	and	CCONJ
cana-4230	172	10	it	it	PRON
cana-4230	172	11	also	also	ADV
cana-4230	172	12	provides	provide	VERB
cana-4230	172	13	for	for	ADP
cana-4230	172	14	persistent	persistent	ADJ
cana-4230	172	15	homology	homology	NOUN
cana-4230	172	16	computation	computation	NOUN
cana-4230	172	17	while	while	SCONJ
cana-4230	172	18	dipha	dipha	PROPN
cana-4230	172	19	was	be	AUX
cana-4230	172	20	created	create	VERB
cana-4230	172	21	to	to	PART
cana-4230	172	22	be	be	AUX
cana-4230	172	23	a	a	DET
cana-4230	172	24	distributed	distribute	VERB
cana-4230	172	25	software	software	NOUN
cana-4230	172	26	and	and	CCONJ
cana-4230	172	27	can	can	AUX
cana-4230	172	28	therefore	therefore	ADV
cana-4230	172	29	work	work	VERB
cana-4230	172	30	with	with	ADP
cana-4230	172	31	huge	huge	ADJ
cana-4230	172	32	data	datum	NOUN
cana-4230	172	33	.	.	PUNCT
cana-4230	173	1	figure	figure	NOUN
cana-4230	173	2	1	1	NUM
cana-4230	173	3	:	:	PUNCT
cana-4230	173	4	runtime	runtime	NOUN
cana-4230	173	5	performance	performance	NOUN
cana-4230	173	6	of	of	ADP
cana-4230	173	7	dionysus	dionysus	NOUN
cana-4230	173	8	and	and	CCONJ
cana-4230	173	9	dipha	dipha	ADJ
cana-4230	173	10	with	with	ADP
cana-4230	173	11	increasing	increase	VERB
cana-4230	173	12	dimension	dimension	NOUN
cana-4230	173	13	communications	communication	NOUN
cana-4230	173	14	on	on	ADP
cana-4230	173	15	applied	apply	VERB
cana-4230	173	16	nonlinear	nonlinear	ADJ
cana-4230	173	17	analysis	analysis	NOUN
cana-4230	173	18	issn	issn	NOUN
cana-4230	173	19	:	:	PUNCT
cana-4230	173	20	1074	1074	NUM
cana-4230	173	21	-	-	PUNCT
cana-4230	173	22	133x	133x	NUM
cana-4230	173	23	vol	vol	NOUN
cana-4230	173	24	32	32	NUM
cana-4230	173	25	no	no	NOUN
cana-4230	173	26	.	.	PUNCT
cana-4230	174	1	8s	8s	PROPN
cana-4230	174	2	(	(	PUNCT
cana-4230	174	3	2025	2025	NUM
cana-4230	174	4	)	)	PUNCT
cana-4230	174	5	905	905	NUM
cana-4230	174	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	174	7	figure	figure	NOUN
cana-4230	174	8	1	1	NUM
cana-4230	174	9	demonstrates	demonstrate	VERB
cana-4230	174	10	that	that	SCONJ
cana-4230	174	11	dipha	dipha	PROPN
cana-4230	174	12	outperforms	outperform	VERB
cana-4230	174	13	dionysus	dionysus	VERB
cana-4230	174	14	in	in	ADP
cana-4230	174	15	high	high	ADJ
cana-4230	174	16	-	-	PUNCT
cana-4230	174	17	dimensional	dimensional	ADJ
cana-4230	174	18	spaces	space	NOUN
cana-4230	174	19	due	due	ADP
cana-4230	174	20	to	to	ADP
cana-4230	174	21	its	its	PRON
cana-4230	174	22	distributed	distribute	VERB
cana-4230	174	23	architecture	architecture	NOUN
cana-4230	174	24	,	,	PUNCT
cana-4230	174	25	making	make	VERB
cana-4230	174	26	it	it	PRON
cana-4230	174	27	more	more	ADV
cana-4230	174	28	suitable	suitable	ADJ
cana-4230	174	29	for	for	ADP
cana-4230	174	30	extremely	extremely	ADV
cana-4230	174	31	large	large	ADJ
cana-4230	174	32	and	and	CCONJ
cana-4230	174	33	complex	complex	ADJ
cana-4230	174	34	datasets	dataset	NOUN
cana-4230	174	35	.	.	PUNCT
cana-4230	175	1	figure	figure	NOUN
cana-4230	175	2	1	1	NUM
cana-4230	175	3	shows	show	VERB
cana-4230	175	4	the	the	DET
cana-4230	175	5	runtime	runtime	NOUN
cana-4230	175	6	performance	performance	NOUN
cana-4230	175	7	of	of	ADP
cana-4230	175	8	dionysus	dionysus	NOUN
cana-4230	175	9	and	and	CCONJ
cana-4230	175	10	dipha	dipha	NOUN
cana-4230	175	11	on	on	ADP
cana-4230	175	12	a	a	DET
cana-4230	175	13	dataset	dataset	NOUN
cana-4230	175	14	of	of	ADP
cana-4230	175	15	50,000	50,000	NUM
cana-4230	175	16	points	point	NOUN
cana-4230	175	17	,	,	PUNCT
cana-4230	175	18	with	with	ADP
cana-4230	175	19	increasing	increase	VERB
cana-4230	175	20	dimensions	dimension	NOUN
cana-4230	175	21	from	from	ADP
cana-4230	175	22	5	5	NUM
cana-4230	175	23	to	to	PART
cana-4230	175	24	15	15	NUM
cana-4230	175	25	.	.	PUNCT
cana-4230	176	1	6.3	6.3	NUM
cana-4230	176	2	algorithmic	algorithmic	ADJ
cana-4230	176	3	implementations	implementation	NOUN
cana-4230	176	4	several	several	ADJ
cana-4230	176	5	sophisticated	sophisticated	ADJ
cana-4230	176	6	algorithms	algorithm	NOUN
cana-4230	176	7	form	form	VERB
cana-4230	176	8	the	the	DET
cana-4230	176	9	basis	basis	NOUN
cana-4230	176	10	of	of	ADP
cana-4230	176	11	the	the	DET
cana-4230	176	12	computational	computational	ADJ
cana-4230	176	13	methods	method	NOUN
cana-4230	176	14	inherent	inherent	ADJ
cana-4230	176	15	in	in	ADP
cana-4230	176	16	nonlinear	nonlinear	ADJ
cana-4230	176	17	algebraic	algebraic	ADJ
cana-4230	176	18	topology	topology	NOUN
cana-4230	176	19	.	.	PUNCT
cana-4230	177	1	there	there	PRON
cana-4230	177	2	are	be	VERB
cana-4230	177	3	two	two	NUM
cana-4230	177	4	most	most	ADV
cana-4230	177	5	frequently	frequently	ADV
cana-4230	177	6	adopted	adopt	VERB
cana-4230	177	7	persistent	persistent	ADJ
cana-4230	177	8	homology	homology	NOUN
cana-4230	177	9	algorithms	algorithm	NOUN
cana-4230	177	10	:	:	PUNCT
cana-4230	177	11	the	the	DET
cana-4230	177	12	matrix	matrix	NOUN
cana-4230	177	13	reduction	reduction	NOUN
cana-4230	177	14	algorithm	algorithm	NOUN
cana-4230	177	15	and	and	CCONJ
cana-4230	177	16	the	the	DET
cana-4230	177	17	dual	dual	ADJ
cana-4230	177	18	algorithm	algorithm	NOUN
cana-4230	177	19	.	.	PUNCT
cana-4230	178	1	1	1	X
cana-4230	178	2	.	.	X
cana-4230	178	3	matrix	matrix	NOUN
cana-4230	178	4	reduction	reduction	NOUN
cana-4230	178	5	algorithm	algorithm	NOUN
cana-4230	178	6	:	:	PUNCT
cana-4230	178	7	this	this	DET
cana-4230	178	8	algorithm	algorithm	NOUN
cana-4230	178	9	simplifies	simplify	VERB
cana-4230	178	10	the	the	DET
cana-4230	178	11	boundary	boundary	ADJ
cana-4230	178	12	matrix	matrix	NOUN
cana-4230	178	13	to	to	PART
cana-4230	178	14	compute	compute	VERB
cana-4230	178	15	the	the	DET
cana-4230	178	16	persistence	persistence	NOUN
cana-4230	178	17	intervals	interval	NOUN
cana-4230	178	18	of	of	ADP
cana-4230	178	19	the	the	DET
cana-4230	178	20	topological	topological	ADJ
cana-4230	178	21	features	feature	NOUN
cana-4230	178	22	.	.	PUNCT
cana-4230	179	1	it	it	PRON
cana-4230	179	2	is	be	AUX
cana-4230	179	3	one	one	NUM
cana-4230	179	4	of	of	ADP
cana-4230	179	5	the	the	DET
cana-4230	179	6	best	good	ADJ
cana-4230	179	7	for	for	ADP
cana-4230	179	8	use	use	NOUN
cana-4230	179	9	in	in	ADP
cana-4230	179	10	low	low	ADJ
cana-4230	179	11	dimensional	dimensional	ADJ
cana-4230	179	12	data	datum	NOUN
cana-4230	179	13	analysis	analysis	NOUN
cana-4230	179	14	but	but	CCONJ
cana-4230	179	15	the	the	DET
cana-4230	179	16	computational	computational	ADJ
cana-4230	179	17	complexity	complexity	NOUN
cana-4230	179	18	increases	increase	VERB
cana-4230	179	19	with	with	ADP
cana-4230	179	20	an	an	DET
cana-4230	179	21	increase	increase	NOUN
cana-4230	179	22	in	in	ADP
cana-4230	179	23	dimensionality	dimensionality	NOUN
cana-4230	179	24	of	of	ADP
cana-4230	179	25	a	a	DET
cana-4230	179	26	dataset	dataset	NOUN
cana-4230	179	27	.	.	PUNCT
cana-4230	180	1	2	2	X
cana-4230	180	2	.	.	X
cana-4230	180	3	dual	dual	ADJ
cana-4230	180	4	algorithm	algorithm	NOUN
cana-4230	180	5	:	:	PUNCT
cana-4230	180	6	the	the	DET
cana-4230	180	7	dual	dual	ADJ
cana-4230	180	8	algorithm	algorithm	NOUN
cana-4230	180	9	is	be	AUX
cana-4230	180	10	developed	develop	VERB
cana-4230	180	11	for	for	ADP
cana-4230	180	12	high	high	ADJ
cana-4230	180	13	-	-	PUNCT
cana-4230	180	14	dimensional	dimensional	ADJ
cana-4230	180	15	data	datum	NOUN
cana-4230	180	16	with	with	ADP
cana-4230	180	17	space	space	NOUN
cana-4230	180	18	complexity	complexity	NOUN
cana-4230	180	19	and	and	CCONJ
cana-4230	180	20	time	time	NOUN
cana-4230	180	21	complexity	complexity	NOUN
cana-4230	180	22	improvements	improvement	NOUN
cana-4230	180	23	based	base	VERB
cana-4230	180	24	on	on	ADP
cana-4230	180	25	the	the	DET
cana-4230	180	26	sparsity	sparsity	NOUN
cana-4230	180	27	of	of	ADP
cana-4230	180	28	the	the	DET
cana-4230	180	29	data	datum	NOUN
cana-4230	180	30	matrix	matrix	NOUN
cana-4230	180	31	.	.	PUNCT
cana-4230	181	1	table	table	NOUN
cana-4230	181	2	5	5	NUM
cana-4230	181	3	presents	present	VERB
cana-4230	181	4	a	a	DET
cana-4230	181	5	comparison	comparison	NOUN
cana-4230	181	6	of	of	ADP
cana-4230	181	7	the	the	DET
cana-4230	181	8	two	two	NUM
cana-4230	181	9	algorithms	algorithm	NOUN
cana-4230	181	10	in	in	ADP
cana-4230	181	11	terms	term	NOUN
cana-4230	181	12	of	of	ADP
cana-4230	181	13	runtime	runtime	NOUN
cana-4230	181	14	,	,	PUNCT
cana-4230	181	15	memory	memory	NOUN
cana-4230	181	16	usage	usage	NOUN
cana-4230	181	17	,	,	PUNCT
cana-4230	181	18	and	and	CCONJ
cana-4230	181	19	scalability	scalability	NOUN
cana-4230	181	20	for	for	ADP
cana-4230	181	21	a	a	DET
cana-4230	181	22	dataset	dataset	NOUN
cana-4230	181	23	with	with	ADP
cana-4230	181	24	50,000	50,000	NUM
cana-4230	181	25	points	point	NOUN
cana-4230	181	26	in	in	ADP
cana-4230	181	27	a	a	DET
cana-4230	181	28	20	20	NUM
cana-4230	181	29	-	-	PUNCT
cana-4230	181	30	dimensional	dimensional	ADJ
cana-4230	181	31	space	space	NOUN
cana-4230	181	32	.	.	PUNCT
cana-4230	182	1	algorithm	algorithm	PROPN
cana-4230	182	2	runtime	runtime	NOUN
cana-4230	182	3	(	(	PUNCT
cana-4230	182	4	seconds	second	NOUN
cana-4230	182	5	)	)	PUNCT
cana-4230	182	6	memory	memory	NOUN
cana-4230	182	7	usage	usage	NOUN
cana-4230	182	8	(	(	PUNCT
cana-4230	182	9	gb	gb	NOUN
cana-4230	182	10	)	)	PUNCT
cana-4230	182	11	scalability	scalability	NOUN
cana-4230	182	12	best	good	ADJ
cana-4230	182	13	use	use	NOUN
cana-4230	182	14	case	case	NOUN
cana-4230	182	15	matrix	matrix	NOUN
cana-4230	182	16	reduction	reduction	NOUN
cana-4230	182	17	600	600	NUM
cana-4230	182	18	10.0	10.0	NUM
cana-4230	182	19	moderate	moderate	ADJ
cana-4230	182	20	low	low	ADJ
cana-4230	182	21	-	-	PUNCT
cana-4230	182	22	dimensional	dimensional	ADJ
cana-4230	182	23	datasets	dataset	NOUN
cana-4230	182	24	dual	dual	ADJ
cana-4230	182	25	algorithm	algorithm	NOUN
cana-4230	182	26	300	300	NUM
cana-4230	182	27	7.5	7.5	NUM
cana-4230	182	28	excellent	excellent	ADJ
cana-4230	182	29	high	high	ADJ
cana-4230	182	30	-	-	PUNCT
cana-4230	182	31	dimensional	dimensional	ADJ
cana-4230	182	32	datasets	dataset	NOUN
cana-4230	182	33	as	as	SCONJ
cana-4230	182	34	seen	see	VERB
cana-4230	182	35	in	in	ADP
cana-4230	182	36	table	table	NOUN
cana-4230	182	37	5	5	NUM
cana-4230	182	38	,	,	PUNCT
cana-4230	182	39	the	the	DET
cana-4230	182	40	dual	dual	ADJ
cana-4230	182	41	algorithm	algorithm	NOUN
cana-4230	182	42	offers	offer	VERB
cana-4230	182	43	superior	superior	ADJ
cana-4230	182	44	scalability	scalability	NOUN
cana-4230	182	45	and	and	CCONJ
cana-4230	182	46	memory	memory	NOUN
cana-4230	182	47	efficiency	efficiency	NOUN
cana-4230	182	48	,	,	PUNCT
cana-4230	182	49	particularly	particularly	ADV
cana-4230	182	50	in	in	ADP
cana-4230	182	51	high	high	ADJ
cana-4230	182	52	-	-	PUNCT
cana-4230	182	53	dimensional	dimensional	ADJ
cana-4230	182	54	spaces	space	NOUN
cana-4230	182	55	,	,	PUNCT
cana-4230	182	56	making	make	VERB
cana-4230	182	57	it	it	PRON
cana-4230	182	58	the	the	DET
cana-4230	182	59	preferred	preferred	ADJ
cana-4230	182	60	choice	choice	NOUN
cana-4230	182	61	for	for	ADP
cana-4230	182	62	datasets	dataset	NOUN
cana-4230	182	63	with	with	ADP
cana-4230	182	64	complex	complex	ADJ
cana-4230	182	65	topological	topological	ADJ
cana-4230	182	66	structures	structure	NOUN
cana-4230	182	67	.	.	PUNCT
cana-4230	183	1	figure	figure	VERB
cana-4230	183	2	3	3	NUM
cana-4230	183	3	:	:	PUNCT
cana-4230	183	4	comparison	comparison	NOUN
cana-4230	183	5	of	of	ADP
cana-4230	183	6	algorithm	algorithm	NOUN
cana-4230	183	7	:	:	PUNCT
cana-4230	183	8	running	run	VERB
cana-4230	183	9	and	and	CCONJ
cana-4230	183	10	memory	memory	NOUN
cana-4230	183	11	usage	usage	NOUN
cana-4230	183	12	communications	communication	NOUN
cana-4230	183	13	on	on	ADP
cana-4230	183	14	applied	apply	VERB
cana-4230	183	15	nonlinear	nonlinear	ADJ
cana-4230	183	16	analysis	analysis	NOUN
cana-4230	183	17	issn	issn	NOUN
cana-4230	183	18	:	:	PUNCT
cana-4230	183	19	1074	1074	NUM
cana-4230	183	20	-	-	PUNCT
cana-4230	183	21	133x	133x	NUM
cana-4230	183	22	vol	vol	NOUN
cana-4230	183	23	32	32	NUM
cana-4230	184	1	no	no	NOUN
cana-4230	184	2	.	.	PUNCT
cana-4230	185	1	8s	8s	PROPN
cana-4230	185	2	(	(	PUNCT
cana-4230	185	3	2025	2025	NUM
cana-4230	185	4	)	)	PUNCT
cana-4230	185	5	906	906	NUM
cana-4230	185	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	185	7	here	here	ADV
cana-4230	185	8	figure	figure	VERB
cana-4230	185	9	3	3	NUM
cana-4230	185	10	comparing	compare	VERB
cana-4230	185	11	the	the	DET
cana-4230	185	12	two	two	NUM
cana-4230	185	13	algorithms	algorithm	NOUN
cana-4230	185	14	in	in	ADP
cana-4230	185	15	terms	term	NOUN
cana-4230	185	16	of	of	ADP
cana-4230	185	17	runtime	runtime	NOUN
cana-4230	185	18	and	and	CCONJ
cana-4230	185	19	memory	memory	NOUN
cana-4230	185	20	usage	usage	NOUN
cana-4230	185	21	for	for	ADP
cana-4230	185	22	a	a	DET
cana-4230	185	23	dataset	dataset	NOUN
cana-4230	185	24	with	with	ADP
cana-4230	185	25	50,000	50,000	NUM
cana-4230	185	26	points	point	NOUN
cana-4230	185	27	in	in	ADP
cana-4230	185	28	a	a	DET
cana-4230	185	29	20	20	NUM
cana-4230	185	30	-	-	PUNCT
cana-4230	185	31	dimensional	dimensional	ADJ
cana-4230	185	32	space	space	NOUN
cana-4230	185	33	.	.	PUNCT
cana-4230	186	1	the	the	DET
cana-4230	186	2	matrix	matrix	NOUN
cana-4230	186	3	reduction	reduction	NOUN
cana-4230	186	4	algorithm	algorithm	NOUN
cana-4230	186	5	takes	take	VERB
cana-4230	186	6	longer	long	ADV
cana-4230	186	7	and	and	CCONJ
cana-4230	186	8	uses	use	VERB
cana-4230	186	9	more	more	ADJ
cana-4230	186	10	memory	memory	NOUN
cana-4230	186	11	compared	compare	VERB
cana-4230	186	12	to	to	ADP
cana-4230	186	13	the	the	DET
cana-4230	186	14	dual	dual	ADJ
cana-4230	186	15	algorithm	algorithm	NOUN
cana-4230	186	16	,	,	PUNCT
cana-4230	186	17	which	which	PRON
cana-4230	186	18	is	be	AUX
cana-4230	186	19	more	more	ADV
cana-4230	186	20	efficient	efficient	ADJ
cana-4230	186	21	for	for	ADP
cana-4230	186	22	high	high	ADJ
cana-4230	186	23	-	-	PUNCT
cana-4230	186	24	dimensional	dimensional	ADJ
cana-4230	186	25	datasets	dataset	NOUN
cana-4230	186	26	.	.	PUNCT
cana-4230	187	1	6.4	6.4	NUM
cana-4230	187	2	integration	integration	NOUN
cana-4230	187	3	with	with	ADP
cana-4230	187	4	machine	machine	NOUN
cana-4230	187	5	learning	learn	VERB
cana-4230	187	6	frameworks	framework	NOUN
cana-4230	187	7	first	first	ADV
cana-4230	187	8	of	of	ADP
cana-4230	187	9	all	all	PRON
cana-4230	187	10	,	,	PUNCT
cana-4230	187	11	tda	tda	PROPN
cana-4230	187	12	can	can	AUX
cana-4230	187	13	be	be	AUX
cana-4230	187	14	applied	apply	VERB
cana-4230	187	15	as	as	ADP
cana-4230	187	16	an	an	DET
cana-4230	187	17	addition	addition	NOUN
cana-4230	187	18	to	to	ADP
cana-4230	187	19	the	the	DET
cana-4230	187	20	traditional	traditional	ADJ
cana-4230	187	21	machine	machine	NOUN
cana-4230	187	22	learning	learning	NOUN
cana-4230	187	23	architectures	architecture	NOUN
cana-4230	187	24	in	in	ADP
cana-4230	187	25	the	the	DET
cana-4230	187	26	form	form	NOUN
cana-4230	187	27	of	of	ADP
cana-4230	187	28	the	the	DET
cana-4230	187	29	so	so	ADV
cana-4230	187	30	-	-	PUNCT
cana-4230	187	31	called	call	VERB
cana-4230	187	32	topological	topological	ADJ
cana-4230	187	33	classifiers	classifier	NOUN
cana-4230	187	34	to	to	PART
cana-4230	187	35	improve	improve	VERB
cana-4230	187	36	both	both	DET
cana-4230	187	37	the	the	DET
cana-4230	187	38	interpretability	interpretability	NOUN
cana-4230	187	39	of	of	ADP
cana-4230	187	40	the	the	DET
cana-4230	187	41	models	model	NOUN
cana-4230	187	42	and	and	CCONJ
cana-4230	187	43	their	their	PRON
cana-4230	187	44	performances	performance	NOUN
cana-4230	187	45	.	.	PUNCT
cana-4230	188	1	another	another	DET
cana-4230	188	2	utility	utility	NOUN
cana-4230	188	3	is	be	AUX
cana-4230	188	4	scikit	scikit	NOUN
cana-4230	188	5	-	-	PUNCT
cana-4230	188	6	tda	tda	NOUN
cana-4230	188	7	–	–	PUNCT
cana-4230	188	8	a	a	DET
cana-4230	188	9	scikit	scikit	NOUN
cana-4230	188	10	-	-	PUNCT
cana-4230	188	11	learn	learn	VERB
cana-4230	188	12	–	–	PUNCT
cana-4230	188	13	like	like	ADP
cana-4230	188	14	package	package	NOUN
cana-4230	188	15	for	for	SCONJ
cana-4230	188	16	python	python	NOUN
cana-4230	188	17	to	to	PART
cana-4230	188	18	integrate	integrate	VERB
cana-4230	188	19	topological	topological	ADJ
cana-4230	188	20	features	feature	NOUN
cana-4230	188	21	into	into	ADP
cana-4230	188	22	pipelines	pipeline	NOUN
cana-4230	188	23	.	.	PUNCT
cana-4230	189	1	incorporating	incorporate	VERB
cana-4230	189	2	topological	topological	ADJ
cana-4230	189	3	summaries	summary	NOUN
cana-4230	189	4	into	into	ADP
cana-4230	189	5	the	the	DET
cana-4230	189	6	input	input	NOUN
cana-4230	189	7	data	datum	NOUN
cana-4230	189	8	,	,	PUNCT
cana-4230	189	9	the	the	DET
cana-4230	189	10	fundamental	fundamental	ADJ
cana-4230	189	11	data	datum	NOUN
cana-4230	189	12	analysis	analysis	NOUN
cana-4230	189	13	approach	approach	NOUN
cana-4230	189	14	as	as	ADP
cana-4230	189	15	persistence	persistence	NOUN
cana-4230	189	16	diagrams	diagram	NOUN
cana-4230	189	17	,	,	PUNCT
cana-4230	189	18	machine	machine	NOUN
cana-4230	189	19	learning	learn	VERB
cana-4230	189	20	algorithms	algorithm	NOUN
cana-4230	189	21	such	such	ADJ
cana-4230	189	22	as	as	ADP
cana-4230	189	23	svms	svms	NOUN
cana-4230	189	24	,	,	PUNCT
cana-4230	189	25	or	or	CCONJ
cana-4230	189	26	neural	neural	ADJ
cana-4230	189	27	networks	network	NOUN
cana-4230	189	28	offer	offer	VERB
cana-4230	189	29	increased	increase	VERB
cana-4230	189	30	predictive	predictive	ADJ
cana-4230	189	31	accuracy	accuracy	NOUN
cana-4230	189	32	as	as	SCONJ
cana-4230	189	33	they	they	PRON
cana-4230	189	34	utilize	utilize	VERB
cana-4230	189	35	structural	structural	ADJ
cana-4230	189	36	data	datum	NOUN
cana-4230	189	37	acquired	acquire	VERB
cana-4230	189	38	from	from	ADP
cana-4230	189	39	tda	tda	PROPN
cana-4230	189	40	.	.	PROPN
cana-4230	190	1	for	for	ADP
cana-4230	190	2	instance	instance	NOUN
cana-4230	190	3	,	,	PUNCT
cana-4230	190	4	incorporating	incorporate	VERB
cana-4230	190	5	topological	topological	ADJ
cana-4230	190	6	features	feature	NOUN
cana-4230	190	7	into	into	ADP
cana-4230	190	8	the	the	DET
cana-4230	190	9	cnn	cnn	PROPN
cana-4230	190	10	in	in	ADP
cana-4230	190	11	image	image	NOUN
cana-4230	190	12	recognition	recognition	NOUN
cana-4230	190	13	has	have	AUX
cana-4230	190	14	been	be	AUX
cana-4230	190	15	proven	prove	VERB
cana-4230	190	16	to	to	PART
cana-4230	190	17	enhance	enhance	VERB
cana-4230	190	18	the	the	DET
cana-4230	190	19	modeling	modeling	NOUN
cana-4230	190	20	of	of	ADP
cana-4230	190	21	complicated	complicated	ADJ
cana-4230	190	22	patterns	pattern	NOUN
cana-4230	190	23	(	(	PUNCT
cana-4230	190	24	hofer	hofer	PROPN
cana-4230	190	25	et	et	PROPN
cana-4230	190	26	al	al	PROPN
cana-4230	190	27	.	.	PROPN
cana-4230	190	28	,	,	PUNCT
cana-4230	190	29	2020	2020	NUM
cana-4230	190	30	)	)	PUNCT
cana-4230	190	31	.	.	PUNCT
cana-4230	191	1	6.5	6.5	NUM
cana-4230	191	2	software	software	NOUN
cana-4230	191	3	and	and	CCONJ
cana-4230	191	4	tools	tool	NOUN
cana-4230	191	5	summary	summary	NOUN
cana-4230	191	6	table	table	NOUN
cana-4230	191	7	6	6	NUM
cana-4230	191	8	provides	provide	VERB
cana-4230	191	9	an	an	DET
cana-4230	191	10	overview	overview	NOUN
cana-4230	191	11	of	of	ADP
cana-4230	191	12	the	the	DET
cana-4230	191	13	most	most	ADV
cana-4230	191	14	commonly	commonly	ADV
cana-4230	191	15	used	use	VERB
cana-4230	191	16	software	software	NOUN
cana-4230	191	17	tools	tool	NOUN
cana-4230	191	18	and	and	CCONJ
cana-4230	191	19	libraries	library	NOUN
cana-4230	191	20	in	in	ADP
cana-4230	191	21	nonlinear	nonlinear	ADJ
cana-4230	191	22	algebraic	algebraic	ADJ
cana-4230	191	23	topology	topology	NOUN
cana-4230	191	24	,	,	PUNCT
cana-4230	191	25	along	along	ADP
cana-4230	191	26	with	with	ADP
cana-4230	191	27	their	their	PRON
cana-4230	191	28	key	key	ADJ
cana-4230	191	29	functionalities	functionality	NOUN
cana-4230	191	30	.	.	PUNCT
cana-4230	192	1	tool	tool	NOUN
cana-4230	192	2	/	/	SYM
cana-4230	192	3	library	library	NOUN
cana-4230	192	4	key	key	NOUN
cana-4230	192	5	functions	function	NOUN
cana-4230	192	6	primary	primary	ADJ
cana-4230	192	7	use	use	NOUN
cana-4230	192	8	best	good	ADJ
cana-4230	192	9	application	application	NOUN
cana-4230	192	10	ripser	ripser	NOUN
cana-4230	192	11	persistent	persistent	ADJ
cana-4230	192	12	homology	homology	NOUN
cana-4230	192	13	,	,	PUNCT
cana-4230	192	14	fast	fast	ADJ
cana-4230	192	15	computation	computation	NOUN
cana-4230	192	16	large	large	ADJ
cana-4230	192	17	high	high	ADJ
cana-4230	192	18	-	-	PUNCT
cana-4230	192	19	dimensional	dimensional	ADJ
cana-4230	192	20	datasets	dataset	NOUN
cana-4230	192	21	genomics	genomic	NOUN
cana-4230	192	22	,	,	PUNCT
cana-4230	192	23	neuroscience	neuroscience	NOUN
cana-4230	192	24	gudhi	gudhi	VERB
cana-4230	192	25	persistent	persistent	ADJ
cana-4230	192	26	homology	homology	NOUN
cana-4230	192	27	,	,	PUNCT
cana-4230	192	28	alpha	alpha	NOUN
cana-4230	192	29	complexes	complex	NOUN
cana-4230	192	30	general	general	ADJ
cana-4230	192	31	topological	topological	ADJ
cana-4230	192	32	data	datum	NOUN
cana-4230	192	33	analysis	analysis	NOUN
cana-4230	192	34	machine	machine	NOUN
cana-4230	192	35	learning	learning	NOUN
cana-4230	192	36	,	,	PUNCT
cana-4230	192	37	data	datum	NOUN
cana-4230	192	38	science	science	NOUN
cana-4230	192	39	dionysus	dionysus	PROPN
cana-4230	192	40	simplicial	simplicial	ADJ
cana-4230	192	41	complex	complex	ADJ
cana-4230	192	42	construction	construction	NOUN
cana-4230	192	43	,	,	PUNCT
cana-4230	192	44	persistence	persistence	NOUN
cana-4230	192	45	efficient	efficient	ADJ
cana-4230	192	46	simplicial	simplicial	ADJ
cana-4230	192	47	complex	complex	ADJ
cana-4230	192	48	computations	computation	NOUN
cana-4230	192	49	social	social	ADJ
cana-4230	192	50	networks	network	NOUN
cana-4230	192	51	,	,	PUNCT
cana-4230	192	52	biology	biology	NOUN
cana-4230	192	53	dipha	dipha	NOUN
cana-4230	192	54	distributed	distribute	VERB
cana-4230	192	55	persistent	persistent	ADJ
cana-4230	192	56	homology	homology	NOUN
cana-4230	192	57	very	very	ADV
cana-4230	192	58	large	large	ADJ
cana-4230	192	59	datasets	dataset	NOUN
cana-4230	192	60	large	large	ADJ
cana-4230	192	61	-	-	PUNCT
cana-4230	192	62	scale	scale	NOUN
cana-4230	192	63	social	social	ADJ
cana-4230	192	64	networks	network	NOUN
cana-4230	192	65	scikit	scikit	NOUN
cana-4230	192	66	-	-	PUNCT
cana-4230	192	67	tda	tda	PROPN
cana-4230	192	68	tda	tda	NOUN
cana-4230	192	69	with	with	ADP
cana-4230	192	70	machine	machine	NOUN
cana-4230	192	71	learning	learn	VERB
cana-4230	192	72	integration	integration	NOUN
cana-4230	192	73	adding	add	VERB
cana-4230	192	74	topological	topological	ADJ
cana-4230	192	75	features	feature	NOUN
cana-4230	192	76	to	to	ADP
cana-4230	192	77	ml	ml	NOUN
cana-4230	192	78	pipelines	pipeline	NOUN
cana-4230	192	79	machine	machine	NOUN
cana-4230	192	80	learning	learning	NOUN
cana-4230	192	81	,	,	PUNCT
cana-4230	192	82	ai	ai	VERB
cana-4230	192	83	7	7	NUM
cana-4230	192	84	.	.	PUNCT
cana-4230	192	85	discussion	discussion	NOUN
cana-4230	192	86	the	the	DET
cana-4230	192	87	proposed	propose	VERB
cana-4230	192	88	approach	approach	NOUN
cana-4230	192	89	based	base	VERB
cana-4230	192	90	on	on	ADP
cana-4230	192	91	nonlinear	nonlinear	ADJ
cana-4230	192	92	algebraic	algebraic	PROPN
cana-4230	192	93	topology	topology	NOUN
cana-4230	192	94	offers	offer	VERB
cana-4230	192	95	important	important	ADJ
cana-4230	192	96	and	and	CCONJ
cana-4230	192	97	versatile	versatile	ADJ
cana-4230	192	98	methods	method	NOUN
cana-4230	192	99	for	for	ADP
cana-4230	192	100	considering	consider	VERB
cana-4230	192	101	high	high	ADJ
cana-4230	192	102	-	-	PUNCT
cana-4230	192	103	projection	projection	NOUN
cana-4230	192	104	data	datum	NOUN
cana-4230	192	105	and	and	CCONJ
cana-4230	192	106	outperforms	outperform	VERB
cana-4230	192	107	existing	exist	VERB
cana-4230	192	108	methods	method	NOUN
cana-4230	192	109	which	which	PRON
cana-4230	192	110	frequently	frequently	ADV
cana-4230	192	111	are	be	AUX
cana-4230	192	112	unable	unable	ADJ
cana-4230	192	113	to	to	PART
cana-4230	192	114	discover	discover	VERB
cana-4230	192	115	topological	topological	ADJ
cana-4230	192	116	features	feature	NOUN
cana-4230	192	117	inherent	inherent	ADJ
cana-4230	192	118	in	in	ADP
cana-4230	192	119	high	high	ADJ
cana-4230	192	120	-	-	PUNCT
cana-4230	192	121	dimensional	dimensional	ADJ
cana-4230	192	122	datasets	dataset	NOUN
cana-4230	192	123	.	.	PUNCT
cana-4230	193	1	in	in	ADP
cana-4230	193	2	this	this	DET
cana-4230	193	3	section	section	NOUN
cana-4230	193	4	we	we	PRON
cana-4230	193	5	elaborate	elaborate	VERB
cana-4230	193	6	on	on	ADP
cana-4230	193	7	the	the	DET
cana-4230	193	8	practical	practical	ADJ
cana-4230	193	9	consequences	consequence	NOUN
cana-4230	193	10	of	of	ADP
cana-4230	193	11	the	the	DET
cana-4230	193	12	theoretical	theoretical	ADJ
cana-4230	193	13	and	and	CCONJ
cana-4230	193	14	computational	computational	ADJ
cana-4230	193	15	tools	tool	NOUN
cana-4230	193	16	described	describe	VERB
cana-4230	193	17	in	in	ADP
cana-4230	193	18	section	section	NOUN
cana-4230	193	19	2.2	2.2	NUM
cana-4230	193	20	,	,	PUNCT
cana-4230	193	21	review	review	VERB
cana-4230	193	22	the	the	DET
cana-4230	193	23	performance	performance	NOUN
cana-4230	193	24	of	of	ADP
cana-4230	193	25	these	these	DET
cana-4230	193	26	tools	tool	NOUN
cana-4230	193	27	across	across	ADP
cana-4230	193	28	the	the	DET
cana-4230	193	29	applications	application	NOUN
cana-4230	193	30	explained	explain	VERB
cana-4230	193	31	in	in	ADP
cana-4230	193	32	section	section	NOUN
cana-4230	193	33	2.3	2.3	NUM
cana-4230	193	34	,	,	PUNCT
cana-4230	193	35	and	and	CCONJ
cana-4230	193	36	characterize	characterize	VERB
cana-4230	193	37	current	current	ADJ
cana-4230	193	38	state	state	NOUN
cana-4230	193	39	-	-	PUNCT
cana-4230	193	40	of	of	ADP
cana-4230	193	41	-	-	PUNCT
cana-4230	193	42	the	the	DET
cana-4230	193	43	-	-	PUNCT
cana-4230	193	44	art	art	NOUN
cana-4230	193	45	and	and	CCONJ
cana-4230	193	46	future	future	ADJ
cana-4230	193	47	research	research	NOUN
cana-4230	193	48	directions	direction	NOUN
cana-4230	193	49	in	in	ADP
cana-4230	193	50	this	this	DET
cana-4230	193	51	field	field	NOUN
cana-4230	193	52	.	.	PUNCT
cana-4230	194	1	7.1	7.1	NUM
cana-4230	194	2	advantages	advantage	NOUN
cana-4230	194	3	of	of	ADP
cana-4230	194	4	nonlinear	nonlinear	ADJ
cana-4230	194	5	algebraic	algebraic	ADJ
cana-4230	194	6	topology	topology	NOUN
cana-4230	194	7	in	in	ADP
cana-4230	194	8	high	high	ADJ
cana-4230	194	9	-	-	PUNCT
cana-4230	194	10	dimensional	dimensional	ADJ
cana-4230	194	11	data	datum	NOUN
cana-4230	194	12	in	in	ADP
cana-4230	194	13	the	the	DET
cana-4230	194	14	analysis	analysis	NOUN
cana-4230	194	15	of	of	ADP
cana-4230	194	16	high	high	ADJ
cana-4230	194	17	-	-	PUNCT
cana-4230	194	18	dimensional	dimensional	ADJ
cana-4230	194	19	data	datum	NOUN
cana-4230	194	20	using	use	VERB
cana-4230	194	21	nonlinear	nonlinear	ADJ
cana-4230	194	22	algebraic	algebraic	ADJ
cana-4230	194	23	topology	topology	NOUN
cana-4230	194	24	,	,	PUNCT
cana-4230	194	25	it	it	PRON
cana-4230	194	26	is	be	AUX
cana-4230	194	27	possible	possible	ADJ
cana-4230	194	28	to	to	PART
cana-4230	194	29	preserve	preserve	VERB
cana-4230	194	30	certain	certain	ADJ
cana-4230	194	31	critical	critical	ADJ
cana-4230	194	32	topological	topological	ADJ
cana-4230	194	33	structures	structure	NOUN
cana-4230	194	34	including	include	VERB
cana-4230	194	35	connected	connected	ADJ
cana-4230	194	36	components	component	NOUN
cana-4230	194	37	,	,	PUNCT
cana-4230	194	38	holes	hole	NOUN
cana-4230	194	39	,	,	PUNCT
cana-4230	194	40	and	and	CCONJ
cana-4230	194	41	voids	void	NOUN
cana-4230	194	42	across	across	ADP
cana-4230	194	43	communications	communication	NOUN
cana-4230	194	44	on	on	ADP
cana-4230	194	45	applied	apply	VERB
cana-4230	194	46	nonlinear	nonlinear	ADJ
cana-4230	194	47	analysis	analysis	NOUN
cana-4230	194	48	issn	issn	NOUN
cana-4230	194	49	:	:	PUNCT
cana-4230	194	50	1074	1074	NUM
cana-4230	194	51	-	-	PUNCT
cana-4230	194	52	133x	133x	NUM
cana-4230	194	53	vol	vol	NOUN
cana-4230	194	54	32	32	NUM
cana-4230	194	55	no	no	NOUN
cana-4230	194	56	.	.	PUNCT
cana-4230	195	1	8s	8s	PROPN
cana-4230	195	2	(	(	PUNCT
cana-4230	195	3	2025	2025	NUM
cana-4230	195	4	)	)	PUNCT
cana-4230	195	5	907	907	NUM
cana-4230	196	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	196	2	multiple	multiple	ADJ
cana-4230	196	3	scales	scale	NOUN
cana-4230	196	4	(	(	PUNCT
cana-4230	196	5	edelsbrunner	edelsbrunner	NOUN
cana-4230	196	6	and	and	CCONJ
cana-4230	196	7	harer	harer	NOUN
cana-4230	196	8	,	,	PUNCT
cana-4230	196	9	2010	2010	NUM
cana-4230	196	10	)	)	PUNCT
cana-4230	196	11	.	.	PUNCT
cana-4230	197	1	these	these	DET
cana-4230	197	2	topological	topological	ADJ
cana-4230	197	3	invariants	invariant	NOUN
cana-4230	197	4	offer	offer	VERB
cana-4230	197	5	a	a	DET
cana-4230	197	6	way	way	NOUN
cana-4230	197	7	to	to	PART
cana-4230	197	8	sample	sample	VERB
cana-4230	197	9	the	the	DET
cana-4230	197	10	data	datum	NOUN
cana-4230	197	11	that	that	PRON
cana-4230	197	12	affords	afford	VERB
cana-4230	197	13	a	a	DET
cana-4230	197	14	more	more	ADV
cana-4230	197	15	powerful	powerful	ADJ
cana-4230	197	16	interpretation	interpretation	NOUN
cana-4230	197	17	than	than	ADP
cana-4230	197	18	other	other	ADJ
cana-4230	197	19	kinds	kind	NOUN
cana-4230	197	20	of	of	ADP
cana-4230	197	21	dimensionality	dimensionality	NOUN
cana-4230	197	22	reduction	reduction	NOUN
cana-4230	197	23	including	include	VERB
cana-4230	197	24	the	the	DET
cana-4230	197	25	principal	principal	ADJ
cana-4230	197	26	component	component	NOUN
cana-4230	197	27	analysis	analysis	NOUN
cana-4230	197	28	(	(	PUNCT
cana-4230	197	29	pca	pca	NOUN
cana-4230	197	30	)	)	PUNCT
cana-4230	197	31	.	.	PUNCT
cana-4230	198	1	for	for	ADP
cana-4230	198	2	example	example	NOUN
cana-4230	198	3	,	,	PUNCT
cana-4230	198	4	when	when	SCONJ
cana-4230	198	5	the	the	DET
cana-4230	198	6	data	data	NOUN
cana-4230	198	7	is	be	AUX
cana-4230	198	8	complex	complex	ADJ
cana-4230	198	9	,	,	PUNCT
cana-4230	198	10	with	with	ADP
cana-4230	198	11	a	a	DET
cana-4230	198	12	multiscalar	multiscalar	ADJ
cana-4230	198	13	structure	structure	NOUN
cana-4230	198	14	inherent	inherent	ADJ
cana-4230	198	15	in	in	ADP
cana-4230	198	16	several	several	ADJ
cana-4230	198	17	application	application	NOUN
cana-4230	198	18	areas	area	NOUN
cana-4230	198	19	,	,	PUNCT
cana-4230	198	20	for	for	ADP
cana-4230	198	21	example	example	NOUN
cana-4230	198	22	in	in	ADP
cana-4230	198	23	genomics	genomic	NOUN
cana-4230	198	24	or	or	CCONJ
cana-4230	198	25	neuroscience	neuroscience	NOUN
cana-4230	198	26	,	,	PUNCT
cana-4230	198	27	persistent	persistent	ADJ
cana-4230	198	28	homology	homology	NOUN
cana-4230	198	29	performs	perform	VERB
cana-4230	198	30	well	well	ADV
cana-4230	198	31	.	.	PUNCT
cana-4230	199	1	in	in	ADP
cana-4230	199	2	contrast	contrast	NOUN
cana-4230	199	3	to	to	ADP
cana-4230	199	4	the	the	DET
cana-4230	199	5	linear	linear	ADJ
cana-4230	199	6	methods	method	NOUN
cana-4230	199	7	for	for	ADP
cana-4230	199	8	data	data	NOUN
cana-4230	199	9	dimensionality	dimensionality	NOUN
cana-4230	199	10	reduction	reduction	NOUN
cana-4230	199	11	,	,	PUNCT
cana-4230	199	12	which	which	PRON
cana-4230	199	13	translate	translate	VERB
cana-4230	199	14	our	our	PRON
cana-4230	199	15	data	datum	NOUN
cana-4230	199	16	to	to	ADP
cana-4230	199	17	a	a	DET
cana-4230	199	18	lower	low	ADJ
cana-4230	199	19	dimensional	dimensional	ADJ
cana-4230	199	20	space	space	NOUN
cana-4230	199	21	while	while	SCONJ
cana-4230	199	22	distorting	distort	VERB
cana-4230	199	23	their	their	PRON
cana-4230	199	24	geometric	geometric	ADJ
cana-4230	199	25	structure	structure	NOUN
cana-4230	199	26	,	,	PUNCT
cana-4230	199	27	topology	topology	NOUN
cana-4230	199	28	-	-	PUNCT
cana-4230	199	29	based	base	VERB
cana-4230	199	30	methods	method	NOUN
cana-4230	199	31	preserve	preserve	VERB
cana-4230	199	32	the	the	DET
cana-4230	199	33	intrinsic	intrinsic	ADJ
cana-4230	199	34	geometric	geometric	ADJ
cana-4230	199	35	structure	structure	NOUN
cana-4230	199	36	inside	inside	ADP
cana-4230	199	37	data	datum	NOUN
cana-4230	199	38	(	(	PUNCT
cana-4230	199	39	zomorodian	zomorodian	PROPN
cana-4230	199	40	&	&	CCONJ
cana-4230	199	41	carlsson	carlsson	PROPN
cana-4230	199	42	,	,	PUNCT
cana-4230	199	43	2005	2005	NUM
cana-4230	199	44	)	)	PUNCT
cana-4230	199	45	.	.	PUNCT
cana-4230	200	1	this	this	DET
cana-4230	200	2	preservation	preservation	NOUN
cana-4230	200	3	is	be	AUX
cana-4230	200	4	important	important	ADJ
cana-4230	200	5	when	when	SCONJ
cana-4230	200	6	it	it	PRON
cana-4230	200	7	comes	come	VERB
cana-4230	200	8	to	to	ADP
cana-4230	200	9	datasets	dataset	NOUN
cana-4230	200	10	in	in	ADP
cana-4230	200	11	which	which	PRON
cana-4230	200	12	important	important	ADJ
cana-4230	200	13	information	information	NOUN
cana-4230	200	14	is	be	AUX
cana-4230	200	15	located	locate	VERB
cana-4230	200	16	in	in	ADP
cana-4230	200	17	interactions	interaction	NOUN
cana-4230	200	18	of	of	ADP
cana-4230	200	19	higher	high	ADJ
cana-4230	200	20	powers	power	NOUN
cana-4230	200	21	,	,	PUNCT
cana-4230	200	22	for	for	ADP
cana-4230	200	23	instance	instance	NOUN
cana-4230	200	24	,	,	PUNCT
cana-4230	200	25	those	those	PRON
cana-4230	200	26	of	of	ADP
cana-4230	200	27	social	social	ADJ
cana-4230	200	28	networks	network	NOUN
cana-4230	200	29	as	as	ADV
cana-4230	200	30	well	well	ADV
cana-4230	200	31	as	as	ADP
cana-4230	200	32	biological	biological	ADJ
cana-4230	200	33	systems	system	NOUN
cana-4230	200	34	(	(	PUNCT
cana-4230	200	35	otter	otter	NOUN
cana-4230	200	36	et	et	PROPN
cana-4230	200	37	al	al	PROPN
cana-4230	200	38	.	.	PROPN
cana-4230	200	39	,	,	PUNCT
cana-4230	200	40	2017	2017	NUM
cana-4230	200	41	)	)	PUNCT
cana-4230	200	42	.	.	PUNCT
cana-4230	201	1	7.2	7.2	NUM
cana-4230	201	2	computational	computational	ADJ
cana-4230	201	3	efficiency	efficiency	NOUN
cana-4230	201	4	and	and	CCONJ
cana-4230	201	5	scalability	scalability	NOUN
cana-4230	201	6	although	although	SCONJ
cana-4230	201	7	the	the	DET
cana-4230	201	8	prospects	prospect	NOUN
cana-4230	201	9	of	of	ADP
cana-4230	201	10	using	use	VERB
cana-4230	201	11	nonlinear	nonlinear	ADJ
cana-4230	201	12	algebraic	algebraic	ADJ
cana-4230	201	13	topology	topology	NOUN
cana-4230	201	14	are	be	AUX
cana-4230	201	15	easy	easy	ADJ
cana-4230	201	16	to	to	PART
cana-4230	201	17	discuss	discuss	VERB
cana-4230	201	18	from	from	ADP
cana-4230	201	19	the	the	DET
cana-4230	201	20	perspective	perspective	NOUN
cana-4230	201	21	of	of	ADP
cana-4230	201	22	the	the	DET
cana-4230	201	23	theoretical	theoretical	ADJ
cana-4230	201	24	point	point	NOUN
cana-4230	201	25	of	of	ADP
cana-4230	201	26	view	view	NOUN
cana-4230	201	27	,	,	PUNCT
cana-4230	201	28	the	the	DET
cana-4230	201	29	actual	actual	ADJ
cana-4230	201	30	application	application	NOUN
cana-4230	201	31	of	of	ADP
cana-4230	201	32	the	the	DET
cana-4230	201	33	techniques	technique	NOUN
cana-4230	201	34	often	often	ADV
cana-4230	201	35	poses	pose	VERB
cana-4230	201	36	certain	certain	ADJ
cana-4230	201	37	computational	computational	ADJ
cana-4230	201	38	difficulties	difficulty	NOUN
cana-4230	201	39	if	if	SCONJ
cana-4230	201	40	the	the	DET
cana-4230	201	41	techniques	technique	NOUN
cana-4230	201	42	are	be	AUX
cana-4230	201	43	to	to	PART
cana-4230	201	44	be	be	AUX
cana-4230	201	45	used	use	VERB
cana-4230	201	46	with	with	ADP
cana-4230	201	47	large	large	ADJ
cana-4230	201	48	sets	set	NOUN
cana-4230	201	49	of	of	ADP
cana-4230	201	50	data	datum	NOUN
cana-4230	201	51	.	.	PUNCT
cana-4230	202	1	as	as	SCONJ
cana-4230	202	2	analyzed	analyze	VERB
cana-4230	202	3	in	in	ADP
cana-4230	202	4	the	the	DET
cana-4230	202	5	earlier	early	ADJ
cana-4230	202	6	section	section	NOUN
cana-4230	202	7	,	,	PUNCT
cana-4230	202	8	the	the	DET
cana-4230	202	9	career	career	NOUN
cana-4230	202	10	persistent	persistent	ADJ
cana-4230	202	11	homology	homology	NOUN
cana-4230	202	12	and	and	CCONJ
cana-4230	202	13	simplicial	simplicial	ADJ
cana-4230	202	14	complex	complex	ADJ
cana-4230	202	15	construction	construction	NOUN
cana-4230	202	16	may	may	AUX
cana-4230	202	17	involve	involve	VERB
cana-4230	202	18	high	high	ADJ
cana-4230	202	19	computational	computational	ADJ
cana-4230	202	20	cost	cost	NOUN
cana-4230	202	21	.	.	PUNCT
cana-4230	203	1	current	current	ADJ
cana-4230	203	2	realizations	realization	NOUN
cana-4230	203	3	of	of	ADP
cana-4230	203	4	ripser	ripser	NOUN
cana-4230	203	5	and	and	CCONJ
cana-4230	203	6	dipha	dipha	X
cana-4230	203	7	provide	provide	VERB
cana-4230	203	8	tools	tool	NOUN
cana-4230	203	9	that	that	PRON
cana-4230	203	10	are	be	AUX
cana-4230	203	11	tailored	tailor	VERB
cana-4230	203	12	to	to	PART
cana-4230	203	13	process	process	VERB
cana-4230	203	14	big	big	ADJ
cana-4230	203	15	data	datum	NOUN
cana-4230	203	16	,	,	PUNCT
cana-4230	203	17	but	but	CCONJ
cana-4230	203	18	more	more	ADJ
cana-4230	203	19	development	development	NOUN
cana-4230	203	20	work	work	NOUN
cana-4230	203	21	in	in	ADP
cana-4230	203	22	algorithm	algorithm	NOUN
cana-4230	203	23	design	design	NOUN
cana-4230	203	24	is	be	AUX
cana-4230	203	25	required	require	VERB
cana-4230	203	26	to	to	PART
cana-4230	203	27	adapt	adapt	VERB
cana-4230	203	28	these	these	DET
cana-4230	203	29	tools	tool	NOUN
cana-4230	203	30	for	for	ADP
cana-4230	203	31	real	real	ADJ
cana-4230	203	32	-	-	PUNCT
cana-4230	203	33	time	time	NOUN
cana-4230	203	34	usage	usage	NOUN
cana-4230	203	35	.	.	PUNCT
cana-4230	204	1	the	the	DET
cana-4230	204	2	scalability	scalability	NOUN
cana-4230	204	3	issue	issue	NOUN
cana-4230	204	4	becomes	become	VERB
cana-4230	204	5	especially	especially	ADV
cana-4230	204	6	significant	significant	ADJ
cana-4230	204	7	where	where	SCONJ
cana-4230	204	8	big	big	ADJ
cana-4230	204	9	data	datum	NOUN
cana-4230	204	10	are	be	AUX
cana-4230	204	11	used	use	VERB
cana-4230	204	12	,	,	PUNCT
cana-4230	204	13	to	to	PART
cana-4230	204	14	name	name	VERB
cana-4230	204	15	a	a	DET
cana-4230	204	16	few	few	ADJ
cana-4230	204	17	,	,	PUNCT
cana-4230	204	18	machine	machine	NOUN
cana-4230	204	19	learning	learning	NOUN
cana-4230	204	20	and	and	CCONJ
cana-4230	204	21	artificial	artificial	ADJ
cana-4230	204	22	intelligence	intelligence	NOUN
cana-4230	204	23	.	.	PUNCT
cana-4230	205	1	the	the	DET
cana-4230	205	2	attempts	attempt	NOUN
cana-4230	205	3	to	to	PART
cana-4230	205	4	combine	combine	VERB
cana-4230	205	5	tda	tda	NOUN
cana-4230	205	6	with	with	ADP
cana-4230	205	7	machine	machine	NOUN
cana-4230	205	8	learning	learn	VERB
cana-4230	205	9	algorithms	algorithm	NOUN
cana-4230	205	10	reported	report	VERB
cana-4230	205	11	positive	positive	ADJ
cana-4230	205	12	results	result	NOUN
cana-4230	205	13	regarding	regard	VERB
cana-4230	205	14	model	model	NOUN
cana-4230	205	15	effectiveness	effectiveness	NOUN
cana-4230	205	16	and	and	CCONJ
cana-4230	205	17	the	the	DET
cana-4230	205	18	ability	ability	NOUN
cana-4230	205	19	to	to	PART
cana-4230	205	20	explain	explain	VERB
cana-4230	205	21	its	its	PRON
cana-4230	205	22	decisions	decision	NOUN
cana-4230	205	23	(	(	PUNCT
cana-4230	205	24	hofer	hofer	PROPN
cana-4230	205	25	et	et	PROPN
cana-4230	205	26	al	al	PROPN
cana-4230	205	27	.	.	PROPN
cana-4230	205	28	,	,	PUNCT
cana-4230	205	29	2020	2020	NUM
cana-4230	205	30	)	)	PUNCT
cana-4230	205	31	.	.	PUNCT
cana-4230	206	1	nevertheless	nevertheless	ADV
cana-4230	206	2	,	,	PUNCT
cana-4230	206	3	obtaining	obtain	VERB
cana-4230	206	4	real	real	ADJ
cana-4230	206	5	-	-	PUNCT
cana-4230	206	6	time	time	NOUN
cana-4230	206	7	performance	performance	NOUN
cana-4230	206	8	remains	remain	VERB
cana-4230	206	9	a	a	DET
cana-4230	206	10	challenge	challenge	NOUN
cana-4230	206	11	,	,	PUNCT
cana-4230	206	12	especially	especially	ADV
cana-4230	206	13	in	in	ADP
cana-4230	206	14	complex	complex	ADJ
cana-4230	206	15	areas	area	NOUN
cana-4230	206	16	such	such	ADJ
cana-4230	206	17	as	as	ADP
cana-4230	206	18	autonomous	autonomous	ADJ
cana-4230	206	19	systems	system	NOUN
cana-4230	206	20	and	and	CCONJ
cana-4230	206	21	financial	financial	ADJ
cana-4230	206	22	modeling	modeling	NOUN
cana-4230	206	23	,	,	PUNCT
cana-4230	206	24	which	which	PRON
cana-4230	206	25	require	require	VERB
cana-4230	206	26	real	real	ADJ
cana-4230	206	27	-	-	PUNCT
cana-4230	206	28	time	time	NOUN
cana-4230	206	29	decision	decision	NOUN
cana-4230	206	30	-	-	PUNCT
cana-4230	206	31	making	making	NOUN
cana-4230	206	32	.	.	PUNCT
cana-4230	207	1	7.3	7.3	NUM
cana-4230	207	2	challenges	challenge	NOUN
cana-4230	207	3	in	in	ADP
cana-4230	207	4	topological	topological	ADJ
cana-4230	207	5	data	datum	NOUN
cana-4230	207	6	analysis	analysis	NOUN
cana-4230	207	7	however	however	ADV
cana-4230	207	8	,	,	PUNCT
cana-4230	207	9	as	as	ADP
cana-4230	207	10	with	with	ADP
cana-4230	207	11	most	most	ADJ
cana-4230	207	12	powerful	powerful	ADJ
cana-4230	207	13	tools	tool	NOUN
cana-4230	207	14	,	,	PUNCT
cana-4230	207	15	some	some	DET
cana-4230	207	16	issues	issue	NOUN
cana-4230	207	17	are	be	AUX
cana-4230	207	18	also	also	ADV
cana-4230	207	19	associated	associate	VERB
cana-4230	207	20	with	with	ADP
cana-4230	207	21	kam	kam	PROPN
cana-4230	207	22	theory	theory	NOUN
cana-4230	207	23	or	or	CCONJ
cana-4230	207	24	nlat	nlat	NOUN
cana-4230	207	25	.	.	PUNCT
cana-4230	208	1	it	it	PRON
cana-4230	208	2	noted	note	VERB
cana-4230	208	3	that	that	SCONJ
cana-4230	208	4	one	one	NUM
cana-4230	208	5	of	of	ADP
cana-4230	208	6	the	the	DET
cana-4230	208	7	major	major	ADJ
cana-4230	208	8	challenges	challenge	NOUN
cana-4230	208	9	is	be	AUX
cana-4230	208	10	what	what	PRON
cana-4230	208	11	one	one	PRON
cana-4230	208	12	might	might	AUX
cana-4230	208	13	term	term	VERB
cana-4230	208	14	the	the	DET
cana-4230	208	15	semiotic	semiotic	ADJ
cana-4230	208	16	challenge	challenge	NOUN
cana-4230	208	17	,	,	PUNCT
cana-4230	208	18	specifically	specifically	ADV
cana-4230	208	19	,	,	PUNCT
cana-4230	208	20	the	the	DET
cana-4230	208	21	interpretation	interpretation	NOUN
cana-4230	208	22	of	of	ADP
cana-4230	208	23	topological	topological	ADJ
cana-4230	208	24	features	feature	NOUN
cana-4230	208	25	extracted	extract	VERB
cana-4230	208	26	from	from	ADP
cana-4230	208	27	data	datum	NOUN
cana-4230	208	28	.	.	PUNCT
cana-4230	209	1	it	it	PRON
cana-4230	209	2	has	have	AUX
cana-4230	209	3	been	be	AUX
cana-4230	209	4	highlighted	highlight	VERB
cana-4230	209	5	that	that	SCONJ
cana-4230	209	6	persistent	persistent	ADJ
cana-4230	209	7	homology	homology	NOUN
cana-4230	209	8	is	be	AUX
cana-4230	209	9	capable	capable	ADJ
cana-4230	209	10	of	of	ADP
cana-4230	209	11	capturing	capture	VERB
cana-4230	209	12	multi	multi	ADJ
cana-4230	209	13	-	-	ADJ
cana-4230	209	14	scale	scale	ADJ
cana-4230	209	15	topological	topological	ADJ
cana-4230	209	16	structures	structure	NOUN
cana-4230	209	17	,	,	PUNCT
cana-4230	209	18	however	however	ADV
cana-4230	209	19	,	,	PUNCT
cana-4230	209	20	understanding	understand	VERB
cana-4230	209	21	the	the	DET
cana-4230	209	22	significance	significance	NOUN
cana-4230	209	23	of	of	ADP
cana-4230	209	24	such	such	ADJ
cana-4230	209	25	features	feature	NOUN
cana-4230	209	26	usually	usually	ADV
cana-4230	209	27	invert	invert	VERB
cana-4230	209	28	domain	domain	NOUN
cana-4230	209	29	knowledge	knowledge	NOUN
cana-4230	209	30	.	.	PUNCT
cana-4230	210	1	for	for	ADP
cana-4230	210	2	instance	instance	NOUN
cana-4230	210	3	,	,	PUNCT
cana-4230	210	4	knowing	know	VERB
cana-4230	210	5	which	which	PRON
cana-4230	210	6	topological	topological	ADJ
cana-4230	210	7	attributes	attribute	NOUN
cana-4230	210	8	relate	relate	VERB
cana-4230	210	9	to	to	ADP
cana-4230	210	10	a	a	DET
cana-4230	210	11	particular	particular	ADJ
cana-4230	210	12	biological	biological	ADJ
cana-4230	210	13	activity	activity	NOUN
cana-4230	210	14	in	in	ADP
cana-4230	210	15	the	the	DET
cana-4230	210	16	case	case	NOUN
cana-4230	210	17	of	of	ADP
cana-4230	210	18	a	a	DET
cana-4230	210	19	sick	sick	ADJ
cana-4230	210	20	patient	patient	NOUN
cana-4230	210	21	is	be	AUX
cana-4230	210	22	not	not	PART
cana-4230	210	23	easily	easily	ADV
cana-4230	210	24	determined	determined	ADJ
cana-4230	210	25	(	(	PUNCT
cana-4230	210	26	chen	chen	PROPN
cana-4230	210	27	et	et	PROPN
cana-4230	210	28	al	al	PROPN
cana-4230	210	29	.	.	PROPN
cana-4230	210	30	,	,	PUNCT
cana-4230	210	31	2019	2019	NUM
cana-4230	210	32	)	)	PUNCT
cana-4230	210	33	.	.	PUNCT
cana-4230	211	1	moreover	moreover	ADV
cana-4230	211	2	,	,	PUNCT
cana-4230	211	3	despite	despite	SCONJ
cana-4230	211	4	great	great	ADJ
cana-4230	211	5	progress	progress	NOUN
cana-4230	211	6	achieved	achieve	VERB
cana-4230	211	7	in	in	ADP
cana-4230	211	8	the	the	DET
cana-4230	211	9	computational	computational	ADJ
cana-4230	211	10	aspects	aspect	NOUN
cana-4230	211	11	of	of	ADP
cana-4230	211	12	tda	tda	NOUN
cana-4230	211	13	,	,	PUNCT
cana-4230	211	14	there	there	PRON
cana-4230	211	15	is	be	VERB
cana-4230	211	16	a	a	DET
cana-4230	211	17	lack	lack	NOUN
cana-4230	211	18	of	of	ADP
cana-4230	211	19	simple	simple	ADJ
cana-4230	211	20	interfaces	interface	NOUN
cana-4230	211	21	for	for	ADP
cana-4230	211	22	practical	practical	ADJ
cana-4230	211	23	usage	usage	NOUN
cana-4230	211	24	.	.	PUNCT
cana-4230	212	1	some	some	DET
cana-4230	212	2	researchers	researcher	NOUN
cana-4230	212	3	and	and	CCONJ
cana-4230	212	4	practitioners	practitioner	NOUN
cana-4230	212	5	,	,	PUNCT
cana-4230	212	6	who	who	PRON
cana-4230	212	7	may	may	AUX
cana-4230	212	8	not	not	PART
cana-4230	212	9	be	be	AUX
cana-4230	212	10	used	use	VERB
cana-4230	212	11	to	to	PART
cana-4230	212	12	mathematical	mathematical	ADJ
cana-4230	212	13	ways	way	NOUN
cana-4230	212	14	of	of	ADP
cana-4230	212	15	thinking	thinking	NOUN
cana-4230	212	16	in	in	ADP
cana-4230	212	17	topology	topology	NOUN
cana-4230	212	18	,	,	PUNCT
cana-4230	212	19	may	may	AUX
cana-4230	212	20	have	have	VERB
cana-4230	212	21	problems	problem	NOUN
cana-4230	212	22	introducing	introduce	VERB
cana-4230	212	23	these	these	DET
cana-4230	212	24	techniques	technique	NOUN
cana-4230	212	25	.	.	PUNCT
cana-4230	213	1	extending	extend	VERB
cana-4230	213	2	tda	tda	NOUN
cana-4230	213	3	tools	tool	NOUN
cana-4230	213	4	to	to	PART
cana-4230	213	5	interface	interface	VERB
cana-4230	213	6	with	with	ADP
cana-4230	213	7	more	more	ADV
cana-4230	213	8	well	well	ADV
cana-4230	213	9	-	-	PUNCT
cana-4230	213	10	established	establish	VERB
cana-4230	213	11	data	datum	NOUN
cana-4230	213	12	analysis	analysis	NOUN
cana-4230	213	13	environments	environment	NOUN
cana-4230	213	14	like	like	ADP
cana-4230	213	15	scikitlearn	scikitlearn	NOUN
cana-4230	213	16	or	or	CCONJ
cana-4230	213	17	tensorflow	tensorflow	NOUN
cana-4230	213	18	may	may	AUX
cana-4230	213	19	bring	bring	VERB
cana-4230	213	20	tda	tda	NOUN
cana-4230	213	21	within	within	ADP
cana-4230	213	22	easy	easy	ADJ
cana-4230	213	23	reach	reach	NOUN
cana-4230	213	24	of	of	ADP
cana-4230	213	25	a	a	DET
cana-4230	213	26	vast	vast	ADJ
cana-4230	213	27	range	range	NOUN
cana-4230	213	28	of	of	ADP
cana-4230	213	29	applications	application	NOUN
cana-4230	213	30	.	.	PUNCT
cana-4230	214	1	communications	communication	NOUN
cana-4230	214	2	on	on	ADP
cana-4230	214	3	applied	apply	VERB
cana-4230	214	4	nonlinear	nonlinear	ADJ
cana-4230	214	5	analysis	analysis	NOUN
cana-4230	214	6	issn	issn	NOUN
cana-4230	214	7	:	:	PUNCT
cana-4230	214	8	1074	1074	NUM
cana-4230	214	9	-	-	PUNCT
cana-4230	214	10	133x	133x	NUM
cana-4230	214	11	vol	vol	NOUN
cana-4230	214	12	32	32	NUM
cana-4230	214	13	no	no	NOUN
cana-4230	214	14	.	.	PUNCT
cana-4230	215	1	8s	8s	PROPN
cana-4230	215	2	(	(	PUNCT
cana-4230	215	3	2025	2025	NUM
cana-4230	215	4	)	)	PUNCT
cana-4230	215	5	908	908	NUM
cana-4230	215	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-4230	215	7	7.4	7.4	NUM
cana-4230	215	8	future	future	ADJ
cana-4230	215	9	directions	direction	NOUN
cana-4230	215	10	in	in	ADP
cana-4230	215	11	the	the	DET
cana-4230	215	12	field	field	NOUN
cana-4230	215	13	of	of	ADP
cana-4230	215	14	nonlinear	nonlinear	ADJ
cana-4230	215	15	algebraic	algebraic	PROPN
cana-4230	215	16	topology	topology	NOUN
cana-4230	215	17	,	,	PUNCT
cana-4230	215	18	there	there	PRON
cana-4230	215	19	are	be	VERB
cana-4230	215	20	several	several	ADJ
cana-4230	215	21	fresh	fresh	ADJ
cana-4230	215	22	and	and	CCONJ
cana-4230	215	23	promising	promising	ADJ
cana-4230	215	24	future	future	ADJ
cana-4230	215	25	directions	direction	NOUN
cana-4230	215	26	underway	underway	ADV
cana-4230	215	27	.	.	PUNCT
cana-4230	216	1	one	one	NUM
cana-4230	216	2	such	such	ADJ
cana-4230	216	3	direction	direction	NOUN
cana-4230	216	4	is	be	AUX
cana-4230	216	5	the	the	DET
cana-4230	216	6	integration	integration	NOUN
cana-4230	216	7	of	of	ADP
cana-4230	216	8	tda	tda	NOUN
cana-4230	216	9	with	with	ADP
cana-4230	216	10	deep	deep	ADJ
cana-4230	216	11	learning	learning	NOUN
cana-4230	216	12	architecture	architecture	NOUN
cana-4230	216	13	.	.	PUNCT
cana-4230	217	1	recent	recent	ADJ
cana-4230	217	2	research	research	NOUN
cana-4230	217	3	has	have	AUX
cana-4230	217	4	indicated	indicate	VERB
cana-4230	217	5	that	that	SCONJ
cana-4230	217	6	combining	combine	VERB
cana-4230	217	7	the	the	DET
cana-4230	217	8	topological	topological	ADJ
cana-4230	217	9	properties	property	NOUN
cana-4230	217	10	of	of	ADP
cana-4230	217	11	architecture	architecture	NOUN
cana-4230	217	12	into	into	ADP
cana-4230	217	13	cnns	cnns	PROPN
cana-4230	217	14	enhances	enhance	VERB
cana-4230	217	15	the	the	DET
cana-4230	217	16	efficiency	efficiency	NOUN
cana-4230	217	17	of	of	ADP
cana-4230	217	18	models	model	NOUN
cana-4230	217	19	in	in	ADP
cana-4230	217	20	applications	application	NOUN
cana-4230	217	21	such	such	ADJ
cana-4230	217	22	as	as	ADP
cana-4230	217	23	image	image	NOUN
cana-4230	217	24	identification	identification	NOUN
cana-4230	217	25	and	and	CCONJ
cana-4230	217	26	pattern	pattern	NOUN
cana-4230	217	27	recognition	recognition	NOUN
cana-4230	217	28	(	(	PUNCT
cana-4230	217	29	hofer	hofer	PROPN
cana-4230	217	30	et	et	PROPN
cana-4230	217	31	al	al	PROPN
cana-4230	217	32	.	.	PROPN
cana-4230	217	33	,	,	PUNCT
cana-4230	217	34	2020	2020	NUM
cana-4230	217	35	)	)	PUNCT
cana-4230	217	36	.	.	PUNCT
cana-4230	218	1	in	in	ADP
cana-4230	218	2	general	general	ADJ
cana-4230	218	3	,	,	PUNCT
cana-4230	218	4	the	the	DET
cana-4230	218	5	combination	combination	NOUN
cana-4230	218	6	of	of	ADP
cana-4230	218	7	topology	topology	NOUN
cana-4230	218	8	and	and	CCONJ
cana-4230	218	9	machine	machine	NOUN
cana-4230	218	10	learning	learning	NOUN
cana-4230	218	11	is	be	AUX
cana-4230	218	12	a	a	DET
cana-4230	218	13	promising	promising	ADJ
cana-4230	218	14	area	area	NOUN
cana-4230	218	15	of	of	ADP
cana-4230	218	16	research	research	NOUN
cana-4230	218	17	,	,	PUNCT
cana-4230	218	18	especially	especially	ADV
cana-4230	218	19	for	for	ADP
cana-4230	218	20	problems	problem	NOUN
cana-4230	218	21	in	in	ADP
cana-4230	218	22	which	which	PRON
cana-4230	218	23	structural	structural	ADJ
cana-4230	218	24	and	and	CCONJ
cana-4230	218	25	spatial	spatial	ADJ
cana-4230	218	26	features	feature	NOUN
cana-4230	218	27	are	be	AUX
cana-4230	218	28	most	most	ADV
cana-4230	218	29	relevant	relevant	ADJ
cana-4230	218	30	to	to	ADP
cana-4230	218	31	understanding	understand	VERB
cana-4230	218	32	the	the	DET
cana-4230	218	33	data	datum	NOUN
cana-4230	218	34	.	.	PUNCT
cana-4230	219	1	another	another	DET
cana-4230	219	2	important	important	ADJ
cana-4230	219	3	direction	direction	NOUN
cana-4230	219	4	is	be	AUX
cana-4230	219	5	the	the	DET
cana-4230	219	6	development	development	NOUN
cana-4230	219	7	of	of	ADP
cana-4230	219	8	the	the	DET
cana-4230	219	9	efficient	efficient	ADJ
cana-4230	219	10	distributed	distribute	VERB
cana-4230	219	11	algorithm	algorithm	NOUN
cana-4230	219	12	for	for	ADP
cana-4230	219	13	topological	topological	ADJ
cana-4230	219	14	computations	computation	NOUN
cana-4230	219	15	.	.	PUNCT
cana-4230	220	1	hence	hence	ADV
cana-4230	220	2	,	,	PUNCT
cana-4230	220	3	as	as	SCONJ
cana-4230	220	4	datasets	dataset	NOUN
cana-4230	220	5	are	be	AUX
cana-4230	220	6	being	be	AUX
cana-4230	220	7	developed	develop	VERB
cana-4230	220	8	and	and	CCONJ
cana-4230	220	9	expanded	expand	VERB
cana-4230	220	10	in	in	ADP
cana-4230	220	11	terms	term	NOUN
cana-4230	220	12	of	of	ADP
cana-4230	220	13	size	size	NOUN
cana-4230	220	14	and	and	CCONJ
cana-4230	220	15	features	feature	NOUN
cana-4230	220	16	,	,	PUNCT
cana-4230	220	17	distributed	distribute	VERB
cana-4230	220	18	frameworks	framework	NOUN
cana-4230	220	19	that	that	PRON
cana-4230	220	20	are	be	AUX
cana-4230	220	21	used	use	VERB
cana-4230	220	22	by	by	ADP
cana-4230	220	23	the	the	DET
cana-4230	220	24	dipha	dipha	ADJ
cana-4230	220	25	library	library	NOUN
cana-4230	220	26	will	will	AUX
cana-4230	220	27	be	be	AUX
cana-4230	220	28	indispensable	indispensable	ADJ
cana-4230	220	29	.	.	PUNCT
cana-4230	221	1	further	further	ADJ
cana-4230	221	2	studies	study	NOUN
cana-4230	221	3	about	about	ADP
cana-4230	221	4	how	how	SCONJ
cana-4230	221	5	to	to	PART
cana-4230	221	6	increase	increase	VERB
cana-4230	221	7	the	the	DET
cana-4230	221	8	parallelism	parallelism	NOUN
cana-4230	221	9	and	and	CCONJ
cana-4230	221	10	efficiency	efficiency	NOUN
cana-4230	221	11	of	of	ADP
cana-4230	221	12	these	these	DET
cana-4230	221	13	algorithms	algorithm	NOUN
cana-4230	221	14	will	will	AUX
cana-4230	221	15	equally	equally	ADV
cana-4230	221	16	be	be	AUX
cana-4230	221	17	significant	significant	ADJ
cana-4230	221	18	towards	towards	ADP
cana-4230	221	19	the	the	DET
cana-4230	221	20	real	real	ADJ
cana-4230	221	21	-	-	PUNCT
cana-4230	221	22	world	world	NOUN
cana-4230	221	23	application	application	NOUN
cana-4230	221	24	challenges	challenge	NOUN
cana-4230	221	25	of	of	ADP
cana-4230	221	26	tda	tda	NOUN
cana-4230	221	27	(	(	PUNCT
cana-4230	221	28	bauer	bauer	PROPN
cana-4230	221	29	et	et	PROPN
cana-4230	221	30	al	al	PROPN
cana-4230	221	31	.	.	PROPN
cana-4230	221	32	,	,	PUNCT
cana-4230	221	33	2017	2017	NUM
cana-4230	221	34	)	)	PUNCT
cana-4230	221	35	.	.	PUNCT
cana-4230	222	1	also	also	ADV
cana-4230	222	2	,	,	PUNCT
cana-4230	222	3	more	more	ADJ
cana-4230	222	4	concern	concern	NOUN
cana-4230	222	5	has	have	AUX
cana-4230	222	6	been	be	AUX
cana-4230	222	7	directed	direct	VERB
cana-4230	222	8	toward	toward	ADP
cana-4230	222	9	the	the	DET
cana-4230	222	10	use	use	NOUN
cana-4230	222	11	of	of	ADP
cana-4230	222	12	non	non	ADJ
cana-4230	222	13	-	-	ADJ
cana-4230	222	14	linear	linear	ADJ
cana-4230	222	15	algebraic	algebraic	ADJ
cana-4230	222	16	topology	topology	NOUN
cana-4230	222	17	particularly	particularly	ADV
cana-4230	222	18	in	in	ADP
cana-4230	222	19	new	new	ADJ
cana-4230	222	20	applications	application	NOUN
cana-4230	222	21	areas	area	NOUN
cana-4230	222	22	like	like	ADP
cana-4230	222	23	quantum	quantum	NOUN
cana-4230	222	24	computer	computer	NOUN
cana-4230	222	25	and	and	CCONJ
cana-4230	222	26	cryptography	cryptography	NOUN
cana-4230	222	27	.	.	PUNCT
cana-4230	223	1	the	the	DET
cana-4230	223	2	invariance	invariance	NOUN
cana-4230	223	3	of	of	ADP
cana-4230	223	4	topological	topological	ADJ
cana-4230	223	5	descriptives	descriptive	NOUN
cana-4230	223	6	remains	remain	VERB
cana-4230	223	7	stable	stable	ADJ
cana-4230	223	8	under	under	ADP
cana-4230	223	9	‘	'	PUNCT
cana-4230	223	10	noise	noise	NOUN
cana-4230	223	11	and	and	CCONJ
cana-4230	223	12	deformation	deformation	NOUN
cana-4230	223	13	,	,	PUNCT
cana-4230	223	14	’	'	PUNCT
cana-4230	223	15	making	make	VERB
cana-4230	223	16	them	they	PRON
cana-4230	223	17	perfect	perfect	ADJ
cana-4230	223	18	for	for	ADP
cana-4230	223	19	quantum	quantum	ADJ
cana-4230	223	20	state	state	NOUN
cana-4230	223	21	analysis	analysis	NOUN
cana-4230	223	22	and	and	CCONJ
cana-4230	223	23	building	build	VERB
cana-4230	223	24	cryptographic	cryptographic	ADJ
cana-4230	223	25	schemes	scheme	NOUN
cana-4230	223	26	(	(	PUNCT
cana-4230	223	27	carlsson	carlsson	PROPN
cana-4230	223	28	,	,	PUNCT
cana-4230	223	29	2009	2009	NUM
cana-4230	223	30	)	)	PUNCT
cana-4230	223	31	.	.	PUNCT
cana-4230	224	1	thus	thus	ADV
cana-4230	224	2	,	,	PUNCT
cana-4230	224	3	the	the	DET
cana-4230	224	4	expansion	expansion	NOUN
cana-4230	224	5	of	of	ADP
cana-4230	224	6	new	new	ADJ
cana-4230	224	7	territories	territory	NOUN
cana-4230	224	8	may	may	AUX
cana-4230	224	9	lead	lead	VERB
cana-4230	224	10	to	to	ADP
cana-4230	224	11	new	new	ADJ
cana-4230	224	12	opportunities	opportunity	NOUN
cana-4230	224	13	to	to	PART
cana-4230	224	14	expand	expand	VERB
cana-4230	224	15	the	the	DET
cana-4230	224	16	scope	scope	NOUN
cana-4230	224	17	of	of	ADP
cana-4230	224	18	tda	tda	NOUN
cana-4230	224	19	in	in	ADP
cana-4230	224	20	theoretical	theoretical	ADJ
cana-4230	224	21	and	and	CCONJ
cana-4230	224	22	practical	practical	ADJ
cana-4230	224	23	fields	field	NOUN
cana-4230	224	24	.	.	PUNCT
cana-4230	225	1	altogether	altogether	ADV
cana-4230	225	2	,	,	PUNCT
cana-4230	225	3	nonlinear	nonlinear	ADJ
cana-4230	225	4	algebraic	algebraic	ADJ
cana-4230	225	5	topology	topology	NOUN
cana-4230	225	6	provides	provide	VERB
cana-4230	225	7	a	a	DET
cana-4230	225	8	flexible	flexible	ADJ
cana-4230	225	9	and	and	CCONJ
cana-4230	225	10	effective	effective	ADJ
cana-4230	225	11	paradigm	paradigm	NOUN
cana-4230	225	12	for	for	ADP
cana-4230	225	13	the	the	DET
cana-4230	225	14	analysis	analysis	NOUN
cana-4230	225	15	of	of	ADP
cana-4230	225	16	high	high	ADJ
cana-4230	225	17	-	-	PUNCT
cana-4230	225	18	dimensional	dimensional	ADJ
cana-4230	225	19	data	datum	NOUN
cana-4230	225	20	for	for	ADP
cana-4230	225	21	disparate	disparate	ADJ
cana-4230	225	22	domains	domain	NOUN
cana-4230	225	23	and	and	CCONJ
cana-4230	225	24	fields	field	NOUN
cana-4230	225	25	,	,	PUNCT
cana-4230	225	26	such	such	ADJ
cana-4230	225	27	as	as	ADP
cana-4230	225	28	biology	biology	NOUN
cana-4230	225	29	,	,	PUNCT
cana-4230	225	30	neuroscience	neuroscience	NOUN
cana-4230	225	31	,	,	PUNCT
cana-4230	225	32	computational	computational	ADJ
cana-4230	225	33	learning	learning	NOUN
cana-4230	225	34	,	,	PUNCT
cana-4230	225	35	and	and	CCONJ
cana-4230	225	36	others	other	NOUN
cana-4230	225	37	.	.	PUNCT
cana-4230	226	1	there	there	PRON
cana-4230	226	2	are	be	VERB
cana-4230	226	3	some	some	DET
cana-4230	226	4	computational	computational	ADJ
cana-4230	226	5	issues	issue	NOUN
cana-4230	226	6	,	,	PUNCT
cana-4230	226	7	yet	yet	ADV
cana-4230	226	8	with	with	ADP
cana-4230	226	9	the	the	DET
cana-4230	226	10	current	current	ADJ
cana-4230	226	11	improvements	improvement	NOUN
cana-4230	226	12	in	in	ADP
cana-4230	226	13	algorithms	algorithm	NOUN
cana-4230	226	14	and	and	CCONJ
cana-4230	226	15	tools	tool	NOUN
cana-4230	226	16	it	it	PRON
cana-4230	226	17	has	have	AUX
cana-4230	226	18	become	become	VERB
cana-4230	226	19	easier	easy	ADJ
cana-4230	226	20	to	to	PART
cana-4230	226	21	use	use	VERB
cana-4230	226	22	these	these	DET
cana-4230	226	23	approaches	approach	NOUN
cana-4230	226	24	on	on	ADP
cana-4230	226	25	vast	vast	ADJ
cana-4230	226	26	data	data	NOUN
cana-4230	226	27	sets	set	NOUN
cana-4230	226	28	.	.	PUNCT
cana-4230	227	1	thus	thus	ADV
cana-4230	227	2	,	,	PUNCT
cana-4230	227	3	it	it	PRON
cana-4230	227	4	is	be	AUX
cana-4230	227	5	clear	clear	ADJ
cana-4230	227	6	that	that	SCONJ
cana-4230	227	7	the	the	DET
cana-4230	227	8	future	future	NOUN
cana-4230	227	9	of	of	ADP
cana-4230	227	10	nonlinear	nonlinear	ADJ
cana-4230	227	11	algebraic	algebraic	ADJ
cana-4230	227	12	topology	topology	NOUN
cana-4230	227	13	will	will	AUX
cana-4230	227	14	continue	continue	VERB
cana-4230	227	15	to	to	PART
cana-4230	227	16	be	be	AUX
cana-4230	227	17	connected	connect	VERB
cana-4230	227	18	with	with	ADP
cana-4230	227	19	other	other	ADJ
cana-4230	227	20	machine	machine	NOUN
cana-4230	227	21	learning	learning	NOUN
cana-4230	227	22	and	and	CCONJ
cana-4230	227	23	quantum	quantum	NOUN
cana-4230	227	24	computing	computing	NOUN
cana-4230	227	25	,	,	PUNCT
cana-4230	227	26	where	where	SCONJ
cana-4230	227	27	its	its	PRON
cana-4230	227	28	ability	ability	NOUN
cana-4230	227	29	to	to	PART
cana-4230	227	30	discover	discover	VERB
cana-4230	227	31	the	the	DET
cana-4230	227	32	hidden	hide	VERB
cana-4230	227	33	structure	structure	NOUN
cana-4230	227	34	and	and	CCONJ
cana-4230	227	35	regularity	regularity	NOUN
cana-4230	227	36	in	in	ADP
cana-4230	227	37	data	datum	NOUN
cana-4230	227	38	can	can	AUX
cana-4230	227	39	contribute	contribute	VERB
cana-4230	227	40	to	to	ADP
cana-4230	227	41	revolutionary	revolutionary	ADJ
cana-4230	227	42	progress	progress	NOUN
cana-4230	227	43	.	.	PUNCT
cana-4230	228	1	8	8	X
cana-4230	228	2	.	.	X
cana-4230	228	3	conclusion	conclusion	NOUN
cana-4230	228	4	in	in	ADP
cana-4230	228	5	this	this	DET
cana-4230	228	6	work	work	NOUN
cana-4230	228	7	,	,	PUNCT
cana-4230	228	8	we	we	PRON
cana-4230	228	9	have	have	AUX
cana-4230	228	10	discussed	discuss	VERB
cana-4230	228	11	nonlinear	nonlinear	ADJ
cana-4230	228	12	algebraic	algebraic	ADJ
cana-4230	228	13	topology	topology	NOUN
cana-4230	228	14	as	as	ADP
cana-4230	228	15	a	a	DET
cana-4230	228	16	promising	promising	ADJ
cana-4230	228	17	approach	approach	NOUN
cana-4230	228	18	to	to	ADP
cana-4230	228	19	designing	design	VERB
cana-4230	228	20	more	more	ADV
cana-4230	228	21	stable	stable	ADJ
cana-4230	228	22	architectures	architecture	NOUN
cana-4230	228	23	for	for	ADP
cana-4230	228	24	hd	hd	NOUN
cana-4230	228	25	data	datum	NOUN
cana-4230	228	26	analysis	analysis	NOUN
cana-4230	228	27	.	.	PUNCT
cana-4230	229	1	this	this	DET
cana-4230	229	2	approach	approach	NOUN
cana-4230	229	3	has	have	VERB
cana-4230	229	4	two	two	NUM
cana-4230	229	5	primary	primary	ADJ
cana-4230	229	6	advantages	advantage	NOUN
cana-4230	229	7	when	when	SCONJ
cana-4230	229	8	applied	apply	VERB
cana-4230	229	9	to	to	ADP
cana-4230	229	10	large	large	ADJ
cana-4230	229	11	datasets	dataset	NOUN
cana-4230	229	12	with	with	ADP
cana-4230	229	13	complex	complex	ADJ
cana-4230	229	14	and	and	CCONJ
cana-4230	229	15	multiple	multiple	ADJ
cana-4230	229	16	-	-	PUNCT
cana-4230	229	17	scale	scale	NOUN
cana-4230	229	18	structures	structure	NOUN
cana-4230	229	19	;	;	PUNCT
cana-4230	229	20	topological	topological	ADJ
cana-4230	229	21	invariants	invariant	NOUN
cana-4230	229	22	like	like	ADP
cana-4230	229	23	persistent	persistent	ADJ
cana-4230	229	24	homology	homology	NOUN
cana-4230	229	25	and	and	CCONJ
cana-4230	229	26	simplicial	simplicial	ADJ
cana-4230	229	27	complexes	complex	NOUN
cana-4230	229	28	.	.	PUNCT
cana-4230	230	1	nonlinear	nonlinear	ADJ
cana-4230	230	2	algebraic	algebraic	PROPN
cana-4230	230	3	topology	topology	NOUN
cana-4230	230	4	differs	differ	VERB
cana-4230	230	5	from	from	ADP
cana-4230	230	6	many	many	ADJ
cana-4230	230	7	conventional	conventional	ADJ
cana-4230	230	8	linear	linear	ADJ
cana-4230	230	9	approaches	approach	NOUN
cana-4230	230	10	,	,	PUNCT
cana-4230	230	11	which	which	PRON
cana-4230	230	12	exclude	exclude	VERB
cana-4230	230	13	components	component	NOUN
cana-4230	230	14	when	when	SCONJ
cana-4230	230	15	examining	examine	VERB
cana-4230	230	16	data	datum	NOUN
cana-4230	230	17	relationships	relationship	NOUN
cana-4230	230	18	,	,	PUNCT
cana-4230	230	19	thus	thus	ADV
cana-4230	230	20	impeding	impede	VERB
cana-4230	230	21	the	the	DET
cana-4230	230	22	analysis	analysis	NOUN
cana-4230	230	23	of	of	ADP
cana-4230	230	24	shape	shape	NOUN
cana-4230	230	25	and	and	CCONJ
cana-4230	230	26	connectivity	connectivity	NOUN
cana-4230	230	27	,	,	PUNCT
cana-4230	230	28	which	which	PRON
cana-4230	230	29	are	be	AUX
cana-4230	230	30	essential	essential	ADJ
cana-4230	230	31	in	in	ADP
cana-4230	230	32	biology	biology	NOUN
cana-4230	230	33	,	,	PUNCT
cana-4230	230	34	neuroscience	neuroscience	NOUN
cana-4230	230	35	,	,	PUNCT
cana-4230	230	36	and	and	CCONJ
cana-4230	230	37	machine	machine	NOUN
cana-4230	230	38	learning	learning	NOUN
cana-4230	230	39	.	.	PUNCT
cana-4230	231	1	to	to	ADP
cana-4230	231	2	some	some	DET
cana-4230	231	3	extent	extent	NOUN
cana-4230	231	4	,	,	PUNCT
cana-4230	231	5	the	the	DET
cana-4230	231	6	development	development	NOUN
cana-4230	231	7	of	of	ADP
cana-4230	231	8	computational	computational	ADJ
cana-4230	231	9	tools	tool	NOUN
cana-4230	231	10	such	such	ADJ
cana-4230	231	11	as	as	ADP
cana-4230	231	12	ripser	ripser	NOUN
cana-4230	231	13	and	and	CCONJ
cana-4230	231	14	dipha	dipha	PROPN
cana-4230	231	15	has	have	AUX
cana-4230	231	16	partly	partly	ADV
cana-4230	231	17	solved	solve	VERB
cana-4230	231	18	some	some	PRON
cana-4230	231	19	of	of	ADP
cana-4230	231	20	the	the	DET
cana-4230	231	21	scalability	scalability	NOUN
cana-4230	231	22	issues	issue	NOUN
cana-4230	231	23	with	with	ADP
cana-4230	231	24	tda	tda	NOUN
cana-4230	231	25	.	.	PUNCT
cana-4230	232	1	however	however	ADV
cana-4230	232	2	,	,	PUNCT
cana-4230	232	3	achieving	achieve	VERB
cana-4230	232	4	real	real	ADJ
cana-4230	232	5	-	-	PUNCT
cana-4230	232	6	time	time	NOUN
cana-4230	232	7	performance	performance	NOUN
cana-4230	232	8	and	and	CCONJ
cana-4230	232	9	solving	solve	VERB
cana-4230	232	10	the	the	DET
cana-4230	232	11	problem	problem	NOUN
cana-4230	232	12	of	of	ADP
cana-4230	232	13	the	the	DET
cana-4230	232	14	system	system	NOUN
cana-4230	232	15	’s	’s	PART
cana-4230	232	16	accessibility	accessibility	NOUN
cana-4230	232	17	for	for	ADP
cana-4230	232	18	practitioners	practitioner	NOUN
cana-4230	232	19	are	be	AUX
cana-4230	232	20	still	still	ADV
cana-4230	232	21	perspectives	perspective	NOUN
cana-4230	232	22	that	that	PRON
cana-4230	232	23	require	require	VERB
cana-4230	232	24	improvement	improvement	NOUN
cana-4230	232	25	.	.	PUNCT
cana-4230	233	1	the	the	DET
cana-4230	233	2	combination	combination	NOUN
cana-4230	233	3	of	of	ADP
cana-4230	233	4	topological	topological	ADJ
cana-4230	233	5	features	feature	NOUN
cana-4230	233	6	with	with	ADP
cana-4230	233	7	computation	computation	NOUN
cana-4230	233	8	techniques	technique	NOUN
cana-4230	233	9	especially	especially	ADV
cana-4230	233	10	deep	deep	ADJ
cana-4230	233	11	learning	learning	NOUN
cana-4230	233	12	gives	give	VERB
cana-4230	233	13	a	a	DET
cana-4230	233	14	positive	positive	ADJ
cana-4230	233	15	indication	indication	NOUN
cana-4230	233	16	of	of	ADP
cana-4230	233	17	the	the	DET
cana-4230	233	18	improvement	improvement	NOUN
cana-4230	233	19	of	of	ADP
cana-4230	233	20	the	the	DET
cana-4230	233	21	interpretability	interpretability	NOUN
cana-4230	233	22	of	of	ADP
cana-4230	233	23	models	model	NOUN
cana-4230	233	24	and	and	CCONJ
cana-4230	233	25	high	high	ADJ
cana-4230	233	26	accuracy	accuracy	NOUN
cana-4230	233	27	in	in	ADP
cana-4230	233	28	tasks	task	NOUN
cana-4230	233	29	where	where	SCONJ
cana-4230	233	30	computations	computation	NOUN
cana-4230	233	31	are	be	AUX
cana-4230	233	32	complex	complex	ADJ
cana-4230	233	33	.	.	PUNCT
cana-4230	234	1	communications	communication	NOUN
cana-4230	234	2	on	on	ADP
cana-4230	234	3	applied	apply	VERB
cana-4230	234	4	nonlinear	nonlinear	ADJ
cana-4230	234	5	analysis	analysis	NOUN
cana-4230	234	6	issn	issn	NOUN
cana-4230	234	7	:	:	PUNCT
cana-4230	234	8	1074	1074	NUM
cana-4230	234	9	-	-	PUNCT
cana-4230	234	10	133x	133x	NUM
cana-4230	234	11	vol	vol	NOUN
cana-4230	234	12	32	32	NUM
cana-4230	234	13	no	no	NOUN
cana-4230	234	14	.	.	PUNCT
cana-4230	235	1	8s	8s	PROPN
cana-4230	235	2	(	(	PUNCT
cana-4230	235	3	2025	2025	NUM
cana-4230	235	4	)	)	PUNCT
cana-4230	235	5	909	909	NUM
cana-4230	235	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4230	235	7	nevertheless	nevertheless	ADV
cana-4230	235	8	,	,	PUNCT
cana-4230	235	9	tda	tda	NOUN
cana-4230	235	10	has	have	AUX
cana-4230	235	11	been	be	AUX
cana-4230	235	12	demonstrated	demonstrate	VERB
cana-4230	235	13	to	to	PART
cana-4230	235	14	be	be	AUX
cana-4230	235	15	useful	useful	ADJ
cana-4230	235	16	in	in	ADP
cana-4230	235	17	several	several	ADJ
cana-4230	235	18	contexts	context	NOUN
cana-4230	235	19	and	and	CCONJ
cana-4230	235	20	future	future	ADJ
cana-4230	235	21	work	work	NOUN
cana-4230	235	22	should	should	AUX
cana-4230	235	23	address	address	VERB
cana-4230	235	24	issues	issue	NOUN
cana-4230	235	25	of	of	ADP
cana-4230	235	26	computational	computational	ADJ
cana-4230	235	27	speed	speed	NOUN
cana-4230	235	28	and	and	CCONJ
cana-4230	235	29	more	more	ADV
cana-4230	235	30	intuitive	intuitive	ADJ
cana-4230	235	31	interfaces	interface	NOUN
cana-4230	235	32	.	.	PUNCT
cana-4230	236	1	also	also	ADV
cana-4230	236	2	,	,	PUNCT
cana-4230	236	3	the	the	DET
cana-4230	236	4	areas	area	NOUN
cana-4230	236	5	of	of	ADP
cana-4230	236	6	quantum	quantum	NOUN
cana-4230	236	7	computing	computing	NOUN
cana-4230	236	8	and	and	CCONJ
cana-4230	236	9	cryptography	cryptography	NOUN
cana-4230	236	10	offer	offer	NOUN
cana-4230	236	11	fresh	fresh	ADJ
cana-4230	236	12	opportunities	opportunity	NOUN
cana-4230	236	13	for	for	ADP
cana-4230	236	14	the	the	DET
cana-4230	236	15	utilization	utilization	NOUN
cana-4230	236	16	of	of	ADP
cana-4230	236	17	tda	tda	NOUN
cana-4230	236	18	and	and	CCONJ
cana-4230	236	19	may	may	AUX
cana-4230	236	20	reveal	reveal	VERB
cana-4230	236	21	new	new	ADJ
cana-4230	236	22	perspectives	perspective	NOUN
cana-4230	236	23	of	of	ADP
cana-4230	236	24	the	the	DET
cana-4230	236	25	theory	theory	NOUN
cana-4230	236	26	in	in	ADP
cana-4230	236	27	theoretical	theoretical	ADJ
cana-4230	236	28	and	and	CCONJ
cana-4230	236	29	practical	practical	ADJ
cana-4230	236	30	contexts	contexts	NOUN
cana-4230	236	31	.	.	PUNCT
cana-4230	237	1	in	in	ADP
cana-4230	237	2	conclusion	conclusion	NOUN
cana-4230	237	3	,	,	PUNCT
cana-4230	237	4	this	this	DET
cana-4230	237	5	work	work	NOUN
cana-4230	237	6	introduced	introduce	VERB
cana-4230	237	7	nonlinear	nonlinear	ADJ
cana-4230	237	8	algebraic	algebraic	ADJ
cana-4230	237	9	topology	topology	NOUN
cana-4230	237	10	as	as	ADP
cana-4230	237	11	a	a	DET
cana-4230	237	12	flexible	flexible	ADJ
cana-4230	237	13	and	and	CCONJ
cana-4230	237	14	strong	strong	ADJ
cana-4230	237	15	tool	tool	NOUN
cana-4230	237	16	for	for	ADP
cana-4230	237	17	studying	study	VERB
cana-4230	237	18	high	high	ADJ
cana-4230	237	19	-	-	PUNCT
cana-4230	237	20	dimensional	dimensional	ADJ
cana-4230	237	21	data	datum	NOUN
cana-4230	237	22	and	and	CCONJ
cana-4230	237	23	demonstrated	demonstrate	VERB
cana-4230	237	24	how	how	SCONJ
cana-4230	237	25	it	it	PRON
cana-4230	237	26	could	could	AUX
cana-4230	237	27	profoundly	profoundly	ADV
cana-4230	237	28	influence	influence	VERB
cana-4230	237	29	high	high	ADJ
cana-4230	237	30	-	-	PUNCT
cana-4230	237	31	dimensional	dimensional	ADJ
cana-4230	237	32	data	datum	NOUN
cana-4230	237	33	analysis	analysis	NOUN
cana-4230	237	34	in	in	ADP
cana-4230	237	35	many	many	ADJ
cana-4230	237	36	fields	field	NOUN
cana-4230	237	37	.	.	PUNCT
cana-4230	238	1	references	reference	NOUN
cana-4230	238	2	:	:	PUNCT
cana-4230	238	3	1	1	X
cana-4230	238	4	.	.	X
cana-4230	238	5	bauer	bauer	PROPN
cana-4230	238	6	,	,	PUNCT
cana-4230	238	7	u.	u.	PROPN
cana-4230	238	8	,	,	PUNCT
cana-4230	238	9	kerber	kerber	PROPN
cana-4230	238	10	,	,	PUNCT
cana-4230	238	11	m.	m.	NOUN
cana-4230	238	12	,	,	PUNCT
cana-4230	238	13	&	&	CCONJ
cana-4230	238	14	reininghaus	reininghaus	PROPN
cana-4230	238	15	,	,	PUNCT
cana-4230	238	16	j.	j.	PROPN
cana-4230	238	17	(	(	PUNCT
cana-4230	238	18	2017	2017	NUM
cana-4230	238	19	)	)	PUNCT
cana-4230	238	20	.	.	PUNCT
cana-4230	239	1	distributed	distribute	VERB
cana-4230	239	2	computation	computation	NOUN
cana-4230	239	3	of	of	ADP
cana-4230	239	4	persistent	persistent	ADJ
cana-4230	239	5	homology	homology	NOUN
cana-4230	239	6	.	.	PUNCT
cana-4230	240	1	journal	journal	PROPN
cana-4230	240	2	of	of	ADP
cana-4230	240	3	applied	applied	ADJ
cana-4230	240	4	and	and	CCONJ
cana-4230	240	5	computational	computational	ADJ
cana-4230	240	6	topology	topology	NOUN
cana-4230	240	7	,	,	PUNCT
cana-4230	240	8	1(1	1(1	NUM
cana-4230	240	9	)	)	PUNCT
cana-4230	240	10	,	,	PUNCT
cana-4230	240	11	3	3	NUM
cana-4230	240	12	-	-	SYM
cana-4230	240	13	24	24	NUM
cana-4230	240	14	.	.	PUNCT
cana-4230	241	1	2	2	NUM
cana-4230	241	2	.	.	X
cana-4230	241	3	carlsson	carlsson	PROPN
cana-4230	241	4	,	,	PUNCT
cana-4230	241	5	g.	g.	PROPN
cana-4230	241	6	(	(	PUNCT
cana-4230	241	7	2009	2009	NUM
cana-4230	241	8	)	)	PUNCT
cana-4230	241	9	.	.	PUNCT
cana-4230	242	1	topology	topology	NOUN
cana-4230	242	2	and	and	CCONJ
cana-4230	242	3	data	datum	NOUN
cana-4230	242	4	.	.	PUNCT
cana-4230	243	1	bulletin	bulletin	NOUN
cana-4230	243	2	of	of	ADP
cana-4230	243	3	the	the	DET
cana-4230	243	4	american	american	PROPN
cana-4230	243	5	mathematical	mathematical	PROPN
cana-4230	243	6	society	society	NOUN
cana-4230	243	7	,	,	PUNCT
cana-4230	243	8	46(2	46(2	NOUN
cana-4230	243	9	)	)	PUNCT
cana-4230	243	10	,	,	PUNCT
cana-4230	243	11	255	255	NUM
cana-4230	243	12	-	-	SYM
cana-4230	243	13	308	308	NUM
cana-4230	243	14	.	.	PUNCT
cana-4230	244	1	3	3	X
cana-4230	244	2	.	.	X
cana-4230	244	3	chen	chen	PROPN
cana-4230	244	4	,	,	PUNCT
cana-4230	244	5	c.	c.	PROPN
cana-4230	244	6	,	,	PUNCT
cana-4230	244	7	lian	lian	PROPN
cana-4230	244	8	,	,	PUNCT
cana-4230	244	9	z.	z.	PROPN
cana-4230	244	10	,	,	PUNCT
cana-4230	244	11	huang	huang	PROPN
cana-4230	244	12	,	,	PUNCT
cana-4230	244	13	j.	j.	PROPN
cana-4230	244	14	,	,	PUNCT
cana-4230	244	15	&	&	CCONJ
cana-4230	244	16	luo	luo	PROPN
cana-4230	244	17	,	,	PUNCT
cana-4230	244	18	j.	j.	PROPN
cana-4230	244	19	(	(	PUNCT
cana-4230	244	20	2019	2019	NUM
cana-4230	244	21	)	)	PUNCT
cana-4230	244	22	.	.	PUNCT
cana-4230	245	1	topological	topological	ADJ
cana-4230	245	2	data	datum	NOUN
cana-4230	245	3	analysis	analysis	NOUN
cana-4230	245	4	for	for	ADP
cana-4230	245	5	machine	machine	NOUN
cana-4230	245	6	learning	learning	NOUN
cana-4230	245	7	:	:	PUNCT
cana-4230	245	8	a	a	DET
cana-4230	245	9	survey	survey	NOUN
cana-4230	245	10	.	.	PUNCT
cana-4230	246	1	journal	journal	NOUN
cana-4230	246	2	of	of	ADP
cana-4230	246	3	machine	machine	NOUN
cana-4230	246	4	learning	learn	VERB
cana-4230	246	5	research	research	NOUN
cana-4230	246	6	,	,	PUNCT
cana-4230	246	7	20	20	NUM
cana-4230	246	8	,	,	PUNCT
cana-4230	246	9	1	1	NUM
cana-4230	246	10	-	-	SYM
cana-4230	246	11	57	57	NUM
cana-4230	246	12	.	.	NOUN
cana-4230	247	1	4	4	X
cana-4230	247	2	.	.	X
cana-4230	247	3	edelsbrunner	edelsbrunner	NOUN
cana-4230	247	4	,	,	PUNCT
cana-4230	247	5	h.	h.	PROPN
cana-4230	247	6	,	,	PUNCT
cana-4230	247	7	&	&	CCONJ
cana-4230	247	8	harer	harer	PROPN
cana-4230	247	9	,	,	PUNCT
cana-4230	247	10	j.	j.	PROPN
cana-4230	247	11	(	(	PUNCT
cana-4230	247	12	2010	2010	NUM
cana-4230	247	13	)	)	PUNCT
cana-4230	247	14	.	.	PUNCT
cana-4230	248	1	computational	computational	ADJ
cana-4230	248	2	topology	topology	NOUN
cana-4230	248	3	:	:	PUNCT
cana-4230	248	4	an	an	DET
cana-4230	248	5	introduction	introduction	NOUN
cana-4230	248	6	.	.	PUNCT
cana-4230	249	1	american	american	PROPN
cana-4230	249	2	mathematical	mathematical	PROPN
cana-4230	249	3	society	society	NOUN
cana-4230	249	4	.	.	PUNCT
cana-4230	250	1	5	5	X
cana-4230	250	2	.	.	X
cana-4230	250	3	hofer	hofer	PROPN
cana-4230	250	4	,	,	PUNCT
cana-4230	250	5	c.	c.	PROPN
cana-4230	250	6	,	,	PUNCT
cana-4230	250	7	kwitt	kwitt	PROPN
cana-4230	250	8	,	,	PUNCT
cana-4230	250	9	r.	r.	PROPN
cana-4230	250	10	,	,	PUNCT
cana-4230	250	11	niethammer	niethammer	NOUN
cana-4230	250	12	,	,	PUNCT
cana-4230	250	13	m.	m.	NOUN
cana-4230	250	14	,	,	PUNCT
cana-4230	250	15	&	&	CCONJ
cana-4230	250	16	uhl	uhl	PROPN
cana-4230	250	17	,	,	PUNCT
cana-4230	250	18	a.	a.	NOUN
cana-4230	250	19	(	(	PUNCT
cana-4230	250	20	2020	2020	NUM
cana-4230	250	21	)	)	PUNCT
cana-4230	250	22	.	.	PUNCT
cana-4230	251	1	deep	deep	ADJ
cana-4230	251	2	learning	learn	VERB
cana-4230	251	3	with	with	ADP
cana-4230	251	4	topological	topological	ADJ
cana-4230	251	5	signatures	signature	NOUN
cana-4230	251	6	.	.	PUNCT
cana-4230	252	1	proceedings	proceeding	NOUN
cana-4230	252	2	of	of	ADP
cana-4230	252	3	the	the	DET
cana-4230	252	4	international	international	ADJ
cana-4230	252	5	conference	conference	NOUN
cana-4230	252	6	on	on	ADP
cana-4230	252	7	learning	learn	VERB
cana-4230	252	8	representations	representation	NOUN
cana-4230	252	9	(	(	PUNCT
cana-4230	252	10	iclr	iclr	NOUN
cana-4230	252	11	)	)	PUNCT
cana-4230	252	12	.	.	PUNCT
cana-4230	253	1	6	6	X
cana-4230	253	2	.	.	X
cana-4230	253	3	otter	otter	PROPN
cana-4230	253	4	,	,	PUNCT
cana-4230	253	5	n.	n.	NOUN
cana-4230	253	6	,	,	PUNCT
cana-4230	253	7	porter	porter	NOUN
cana-4230	253	8	,	,	PUNCT
cana-4230	253	9	m.	m.	NOUN
cana-4230	253	10	a.	a.	PROPN
cana-4230	253	11	,	,	PUNCT
cana-4230	253	12	tillmann	tillmann	PROPN
cana-4230	253	13	,	,	PUNCT
cana-4230	253	14	u.	u.	PROPN
cana-4230	253	15	,	,	PUNCT
cana-4230	253	16	grindrod	grindrod	NOUN
cana-4230	253	17	,	,	PUNCT
cana-4230	253	18	p.	p.	PROPN
cana-4230	253	19	,	,	PUNCT
cana-4230	253	20	&	&	CCONJ
cana-4230	253	21	harrington	harrington	PROPN
cana-4230	253	22	,	,	PUNCT
cana-4230	253	23	h.	h.	PROPN
cana-4230	253	24	a.	a.	PROPN
cana-4230	253	25	(	(	PUNCT
cana-4230	253	26	2017	2017	NUM
cana-4230	253	27	)	)	PUNCT
cana-4230	253	28	.	.	PUNCT
cana-4230	254	1	a	a	DET
cana-4230	254	2	roadmap	roadmap	NOUN
cana-4230	254	3	for	for	ADP
cana-4230	254	4	the	the	DET
cana-4230	254	5	computation	computation	NOUN
cana-4230	254	6	of	of	ADP
cana-4230	254	7	persistent	persistent	ADJ
cana-4230	254	8	homology	homology	NOUN
cana-4230	254	9	.	.	PUNCT
cana-4230	255	1	epj	epj	NOUN
cana-4230	255	2	data	data	PROPN
cana-4230	255	3	science	science	NOUN
cana-4230	255	4	,	,	PUNCT
cana-4230	255	5	6(1	6(1	NUM
cana-4230	255	6	)	)	PUNCT
cana-4230	255	7	,	,	PUNCT
cana-4230	255	8	1	1	NUM
cana-4230	255	9	-	-	SYM
cana-4230	255	10	38	38	NUM
cana-4230	255	11	.	.	PUNCT
cana-4230	256	1	7	7	X
cana-4230	256	2	.	.	X
cana-4230	256	3	zomorodian	zomorodian	ADJ
cana-4230	256	4	,	,	PUNCT
cana-4230	256	5	a.	a.	PROPN
cana-4230	256	6	,	,	PUNCT
cana-4230	256	7	&	&	CCONJ
cana-4230	256	8	carlsson	carlsson	PROPN
cana-4230	256	9	,	,	PUNCT
cana-4230	256	10	g.	g.	PROPN
cana-4230	256	11	(	(	PUNCT
cana-4230	256	12	2005	2005	NUM
cana-4230	256	13	)	)	PUNCT
cana-4230	256	14	.	.	PUNCT
cana-4230	257	1	computing	compute	VERB
cana-4230	257	2	persistent	persistent	ADJ
cana-4230	257	3	homology	homology	NOUN
cana-4230	257	4	.	.	PUNCT
cana-4230	258	1	discrete	discrete	VERB
cana-4230	258	2	&	&	CCONJ
cana-4230	258	3	computational	computational	ADJ
cana-4230	258	4	geometry	geometry	NOUN
cana-4230	258	5	,	,	PUNCT
cana-4230	258	6	33(2	33(2	NUM
cana-4230	258	7	)	)	PUNCT
cana-4230	258	8	,	,	PUNCT
cana-4230	258	9	249	249	NUM
cana-4230	258	10	-	-	SYM
cana-4230	258	11	274	274	NUM
cana-4230	258	12	.	.	NOUN
cana-4230	258	13	8	8	NUM
cana-4230	258	14	.	.	PUNCT
cana-4230	259	1	giusti	giusti	PROPN
cana-4230	259	2	,	,	PUNCT
cana-4230	259	3	c.	c.	PROPN
cana-4230	259	4	,	,	PUNCT
cana-4230	259	5	ghrist	ghrist	NOUN
cana-4230	259	6	,	,	PUNCT
cana-4230	259	7	r.	r.	PROPN
cana-4230	259	8	,	,	PUNCT
cana-4230	259	9	&	&	CCONJ
cana-4230	259	10	bassett	bassett	PROPN
cana-4230	259	11	,	,	PUNCT
cana-4230	259	12	d.	d.	PROPN
cana-4230	259	13	s.	s.	PROPN
cana-4230	259	14	(	(	PUNCT
cana-4230	259	15	2016	2016	NUM
cana-4230	259	16	)	)	PUNCT
cana-4230	259	17	.	.	PUNCT
cana-4230	260	1	two	two	NUM
cana-4230	260	2	’s	’s	PART
cana-4230	260	3	company	company	NOUN
cana-4230	260	4	,	,	PUNCT
cana-4230	260	5	three	three	NUM
cana-4230	260	6	(	(	PUNCT
cana-4230	260	7	or	or	CCONJ
cana-4230	260	8	more	more	ADJ
cana-4230	260	9	)	)	PUNCT
cana-4230	260	10	is	be	AUX
cana-4230	260	11	a	a	DET
cana-4230	260	12	simplex	simplex	NOUN
cana-4230	260	13	:	:	PUNCT
cana-4230	260	14	algebraic	algebraic	ADJ
cana-4230	260	15	-	-	PUNCT
cana-4230	260	16	topological	topological	ADJ
cana-4230	260	17	tools	tool	NOUN
cana-4230	260	18	for	for	ADP
cana-4230	260	19	understanding	understand	VERB
cana-4230	260	20	higher	high	ADJ
cana-4230	260	21	-	-	PUNCT
cana-4230	260	22	order	order	NOUN
cana-4230	260	23	structure	structure	NOUN
cana-4230	260	24	in	in	ADP
cana-4230	260	25	neural	neural	ADJ
cana-4230	260	26	data	datum	NOUN
cana-4230	260	27	.	.	PUNCT
cana-4230	261	1	journal	journal	PROPN
cana-4230	261	2	of	of	ADP
cana-4230	261	3	computational	computational	ADJ
cana-4230	261	4	neuroscience	neuroscience	NOUN
cana-4230	261	5	,	,	PUNCT
cana-4230	261	6	41(1	41(1	NUM
cana-4230	261	7	)	)	PUNCT
cana-4230	261	8	,	,	PUNCT
cana-4230	261	9	1	1	NUM
cana-4230	261	10	-	-	SYM
cana-4230	261	11	14	14	NUM
cana-4230	261	12	.	.	PUNCT
cana-4230	262	1	9	9	NUM
cana-4230	262	2	.	.	X
cana-4230	262	3	nicolau	nicolau	PROPN
cana-4230	262	4	,	,	PUNCT
cana-4230	262	5	m.	m.	NOUN
cana-4230	262	6	,	,	PUNCT
cana-4230	262	7	levine	levine	PROPN
cana-4230	262	8	,	,	PUNCT
cana-4230	262	9	a.	a.	PROPN
cana-4230	262	10	j.	j.	PROPN
cana-4230	262	11	,	,	PUNCT
cana-4230	262	12	&	&	CCONJ
cana-4230	262	13	carlsson	carlsson	PROPN
cana-4230	262	14	,	,	PUNCT
cana-4230	262	15	g.	g.	PROPN
cana-4230	262	16	(	(	PUNCT
cana-4230	262	17	2011	2011	NUM
cana-4230	262	18	)	)	PUNCT
cana-4230	262	19	.	.	PUNCT
cana-4230	263	1	topology	topology	NOUN
cana-4230	263	2	based	base	VERB
cana-4230	263	3	data	datum	NOUN
cana-4230	263	4	analysis	analysis	NOUN
cana-4230	263	5	identifies	identify	VERB
cana-4230	263	6	a	a	DET
cana-4230	263	7	subgroup	subgroup	NOUN
cana-4230	263	8	of	of	ADP
cana-4230	263	9	breast	breast	NOUN
cana-4230	263	10	cancers	cancer	NOUN
cana-4230	263	11	with	with	ADP
cana-4230	263	12	a	a	DET
cana-4230	263	13	unique	unique	ADJ
cana-4230	263	14	mutational	mutational	ADJ
cana-4230	263	15	profile	profile	NOUN
cana-4230	263	16	and	and	CCONJ
cana-4230	263	17	excellent	excellent	ADJ
cana-4230	263	18	survival	survival	NOUN
cana-4230	263	19	.	.	PUNCT
cana-4230	264	1	proceedings	proceeding	NOUN
cana-4230	264	2	of	of	ADP
cana-4230	264	3	the	the	DET
cana-4230	264	4	national	national	PROPN
cana-4230	264	5	academy	academy	PROPN
cana-4230	264	6	of	of	ADP
cana-4230	264	7	sciences	sciences	PROPN
cana-4230	264	8	,	,	PUNCT
cana-4230	264	9	108(17	108(17	NUM
cana-4230	264	10	)	)	PUNCT
cana-4230	264	11	,	,	PUNCT
cana-4230	264	12	7265	7265	NUM
cana-4230	264	13	-	-	SYM
cana-4230	264	14	7270	7270	NUM
cana-4230	264	15	.	.	PUNCT
cana-4230	265	1	10	10	NUM
cana-4230	265	2	.	.	X
cana-4230	266	1	petri	petri	ADJ
cana-4230	266	2	,	,	PUNCT
cana-4230	266	3	g.	g.	PROPN
cana-4230	266	4	,	,	PUNCT
cana-4230	266	5	scolamiero	scolamiero	NOUN
cana-4230	266	6	,	,	PUNCT
cana-4230	266	7	m.	m.	NOUN
cana-4230	266	8	,	,	PUNCT
cana-4230	266	9	donato	donato	PROPN
cana-4230	266	10	,	,	PUNCT
cana-4230	266	11	i.	i.	PROPN
cana-4230	266	12	,	,	PUNCT
cana-4230	266	13	&	&	CCONJ
cana-4230	266	14	vaccarino	vaccarino	PROPN
cana-4230	266	15	,	,	PUNCT
cana-4230	266	16	f.	f.	PROPN
cana-4230	266	17	(	(	PUNCT
cana-4230	266	18	2014	2014	NUM
cana-4230	266	19	)	)	PUNCT
cana-4230	266	20	.	.	PUNCT
cana-4230	267	1	topological	topological	ADJ
cana-4230	267	2	strata	strata	NOUN
cana-4230	267	3	of	of	ADP
cana-4230	267	4	weighted	weight	VERB
cana-4230	267	5	complex	complex	ADJ
cana-4230	267	6	networks	network	NOUN
cana-4230	267	7	.	.	PUNCT
cana-4230	268	1	plos	plos	PROPN
cana-4230	268	2	one	one	NUM
cana-4230	268	3	,	,	PUNCT
cana-4230	268	4	8(6	8(6	NUM
cana-4230	268	5	)	)	PUNCT
cana-4230	268	6	,	,	PUNCT
cana-4230	268	7	e66506	e66506	NOUN
cana-4230	268	8	.	.	PROPN
cana-4230	268	9	11	11	NUM
cana-4230	268	10	.	.	X
cana-4230	269	1	sizemore	sizemore	PROPN
cana-4230	269	2	,	,	PUNCT
cana-4230	269	3	a.	a.	PROPN
cana-4230	269	4	e.	e.	PROPN
cana-4230	269	5	,	,	PUNCT
cana-4230	269	6	giusti	giusti	PROPN
cana-4230	269	7	,	,	PUNCT
cana-4230	269	8	c.	c.	PROPN
cana-4230	269	9	,	,	PUNCT
cana-4230	269	10	kahn	kahn	PROPN
cana-4230	269	11	,	,	PUNCT
cana-4230	269	12	a.	a.	PROPN
cana-4230	269	13	,	,	PUNCT
cana-4230	269	14	vettel	vettel	PROPN
cana-4230	269	15	,	,	PUNCT
cana-4230	269	16	j.	j.	PROPN
cana-4230	269	17	m.	m.	PROPN
cana-4230	269	18	,	,	PUNCT
cana-4230	269	19	&	&	CCONJ
cana-4230	269	20	bassett	bassett	PROPN
cana-4230	269	21	,	,	PUNCT
cana-4230	269	22	d.	d.	PROPN
cana-4230	269	23	s.	s.	PROPN
cana-4230	269	24	(	(	PUNCT
cana-4230	269	25	2018	2018	NUM
cana-4230	269	26	)	)	PUNCT
cana-4230	269	27	.	.	PUNCT
cana-4230	270	1	cliques	clique	NOUN
cana-4230	270	2	and	and	CCONJ
cana-4230	270	3	cavities	cavity	NOUN
cana-4230	270	4	in	in	ADP
cana-4230	270	5	the	the	DET
cana-4230	270	6	human	human	ADJ
cana-4230	270	7	connectome	connectome	PROPN
cana-4230	270	8	.	.	PUNCT
cana-4230	271	1	journal	journal	PROPN
cana-4230	271	2	of	of	ADP
cana-4230	271	3	computational	computational	ADJ
cana-4230	271	4	neuroscience	neuroscience	NOUN
cana-4230	271	5	,	,	PUNCT
cana-4230	271	6	44(1	44(1	PROPN
cana-4230	271	7	)	)	PUNCT
cana-4230	271	8	,	,	PUNCT
cana-4230	271	9	115	115	NUM
cana-4230	271	10	-	-	SYM
cana-4230	271	11	145	145	NUM
cana-4230	271	12	.	.	PUNCT
cana-4230	271	13	12	12	NUM
cana-4230	271	14	.	.	PUNCT
cana-4230	272	1	ghrist	ghrist	PROPN
cana-4230	272	2	,	,	PUNCT
cana-4230	272	3	r.	r.	PROPN
cana-4230	272	4	(	(	PUNCT
cana-4230	272	5	2008	2008	NUM
cana-4230	272	6	)	)	PUNCT
cana-4230	272	7	.	.	PUNCT
cana-4230	273	1	barcodes	barcode	NOUN
cana-4230	273	2	:	:	PUNCT
cana-4230	273	3	the	the	DET
cana-4230	273	4	persistent	persistent	ADJ
cana-4230	273	5	topology	topology	NOUN
cana-4230	273	6	of	of	ADP
cana-4230	273	7	data	data	PROPN
cana-4230	273	8	.	.	PUNCT
cana-4230	274	1	bulletin	bulletin	NOUN
cana-4230	274	2	of	of	ADP
cana-4230	274	3	the	the	DET
cana-4230	274	4	american	american	PROPN
cana-4230	274	5	mathematical	mathematical	PROPN
cana-4230	274	6	society	society	NOUN
cana-4230	274	7	,	,	PUNCT
cana-4230	274	8	45(1	45(1	NOUN
cana-4230	274	9	)	)	PUNCT
cana-4230	274	10	,	,	PUNCT
cana-4230	274	11	61	61	NUM
cana-4230	274	12	-	-	SYM
cana-4230	274	13	75	75	NUM
cana-4230	274	14	.	.	PUNCT
cana-4230	275	1	13	13	NUM
cana-4230	275	2	.	.	PUNCT
cana-4230	275	3	milnor	milnor	PROPN
cana-4230	275	4	,	,	PUNCT
cana-4230	275	5	j.	j.	PROPN
cana-4230	275	6	(	(	PUNCT
cana-4230	275	7	1963	1963	NUM
cana-4230	275	8	)	)	PUNCT
cana-4230	275	9	.	.	PUNCT
cana-4230	276	1	morse	morse	PROPN
cana-4230	276	2	theory	theory	NOUN
cana-4230	276	3	.	.	PUNCT
cana-4230	277	1	princeton	princeton	PROPN
cana-4230	277	2	university	university	PROPN
cana-4230	277	3	press	press	NOUN
cana-4230	277	4	.	.	PUNCT
cana-4230	278	1	14	14	NUM
cana-4230	278	2	.	.	X
cana-4230	278	3	patania	patania	PROPN
cana-4230	278	4	,	,	PUNCT
cana-4230	278	5	a.	a.	NOUN
cana-4230	278	6	,	,	PUNCT
cana-4230	278	7	petri	petri	ADJ
cana-4230	278	8	,	,	PUNCT
cana-4230	278	9	g.	g.	PROPN
cana-4230	278	10	,	,	PUNCT
cana-4230	278	11	&	&	CCONJ
cana-4230	278	12	vaccarino	vaccarino	PROPN
cana-4230	278	13	,	,	PUNCT
cana-4230	278	14	f.	f.	PROPN
cana-4230	278	15	(	(	PUNCT
cana-4230	278	16	2017	2017	NUM
cana-4230	278	17	)	)	PUNCT
cana-4230	278	18	.	.	PUNCT
cana-4230	279	1	the	the	DET
cana-4230	279	2	shape	shape	NOUN
cana-4230	279	3	of	of	ADP
cana-4230	279	4	collaborations	collaboration	NOUN
cana-4230	279	5	.	.	PUNCT
cana-4230	280	1	epj	epj	NOUN
cana-4230	280	2	data	datum	NOUN
cana-4230	280	3	science	science	NOUN
cana-4230	280	4	,	,	PUNCT
cana-4230	280	5	6(18	6(18	NUM
cana-4230	280	6	)	)	PUNCT
cana-4230	280	7	.	.	PUNCT
cana-4230	281	1	15	15	NUM
cana-4230	281	2	.	.	PUNCT
cana-4230	282	1	bauer	bauer	PROPN
cana-4230	282	2	,	,	PUNCT
cana-4230	282	3	u.	u.	PROPN
cana-4230	282	4	,	,	PUNCT
cana-4230	282	5	kerber	kerber	PROPN
cana-4230	282	6	,	,	PUNCT
cana-4230	282	7	m.	m.	NOUN
cana-4230	282	8	,	,	PUNCT
cana-4230	282	9	&	&	CCONJ
cana-4230	282	10	reininghaus	reininghaus	PROPN
cana-4230	282	11	,	,	PUNCT
cana-4230	282	12	j.	j.	PROPN
cana-4230	282	13	(	(	PUNCT
cana-4230	282	14	2014	2014	NUM
cana-4230	282	15	)	)	PUNCT
cana-4230	282	16	.	.	PUNCT
cana-4230	283	1	ripser	ripser	NOUN
cana-4230	283	2	:	:	PUNCT
cana-4230	283	3	efficient	efficient	ADJ
cana-4230	283	4	computation	computation	NOUN
cana-4230	283	5	of	of	ADP
cana-4230	283	6	vietoris	vietoris	ADJ
cana-4230	283	7	–	–	PUNCT
cana-4230	283	8	rips	rip	VERB
cana-4230	283	9	persistence	persistence	NOUN
cana-4230	283	10	barcodes	barcode	NOUN
cana-4230	283	11	.	.	PUNCT
cana-4230	284	1	journal	journal	NOUN
cana-4230	284	2	of	of	ADP
cana-4230	284	3	machine	machine	NOUN
cana-4230	284	4	learning	learn	VERB
cana-4230	284	5	research	research	NOUN
cana-4230	284	6	,	,	PUNCT
cana-4230	284	7	16	16	NUM
cana-4230	284	8	,	,	PUNCT
cana-4230	284	9	100	100	NUM
cana-4230	284	10	-	-	SYM
cana-4230	284	11	112	112	NUM
cana-4230	284	12	.	.	PUNCT
cana-4230	285	1	16	16	NUM
cana-4230	285	2	.	.	PUNCT
cana-4230	285	3	bellman	bellman	PROPN
cana-4230	285	4	,	,	PUNCT
cana-4230	285	5	r.	r.	PROPN
cana-4230	285	6	e.	e.	PROPN
cana-4230	285	7	(	(	PUNCT
cana-4230	285	8	1961	1961	NUM
cana-4230	285	9	)	)	PUNCT
cana-4230	285	10	.	.	PUNCT
cana-4230	286	1	adaptive	adaptive	PROPN
cana-4230	286	2	control	control	NOUN
cana-4230	286	3	processes	process	NOUN
cana-4230	286	4	:	:	PUNCT
cana-4230	286	5	a	a	DET
cana-4230	286	6	guided	guide	VERB
cana-4230	286	7	tour	tour	NOUN
cana-4230	286	8	.	.	PUNCT
cana-4230	287	1	princeton	princeton	PROPN
cana-4230	287	2	university	university	PROPN
cana-4230	287	3	press	press	NOUN
cana-4230	287	4	.	.	PUNCT
cana-4230	288	1	17	17	NUM
cana-4230	288	2	.	.	PUNCT
cana-4230	289	1	donoho	donoho	PROPN
cana-4230	289	2	,	,	PUNCT
cana-4230	289	3	d.	d.	PROPN
cana-4230	289	4	l.	l.	PROPN
cana-4230	289	5	(	(	PUNCT
cana-4230	289	6	2000	2000	NUM
cana-4230	289	7	)	)	PUNCT
cana-4230	289	8	.	.	PUNCT
cana-4230	290	1	high	high	ADJ
cana-4230	290	2	-	-	PUNCT
cana-4230	290	3	dimensional	dimensional	ADJ
cana-4230	290	4	data	datum	NOUN
cana-4230	290	5	analysis	analysis	NOUN
cana-4230	290	6	:	:	PUNCT
cana-4230	290	7	the	the	DET
cana-4230	290	8	curses	curse	NOUN
cana-4230	290	9	and	and	CCONJ
cana-4230	290	10	blessings	blessing	NOUN
cana-4230	290	11	of	of	ADP
cana-4230	290	12	dimensionality	dimensionality	NOUN
cana-4230	290	13	.	.	PUNCT
cana-4230	291	1	ams	am	NOUN
cana-4230	291	2	math	math	NOUN
cana-4230	291	3	challenges	challenge	NOUN
cana-4230	291	4	lecture	lecture	VERB
cana-4230	291	5	.	.	PUNCT
cana-4230	292	1	communications	communication	NOUN
cana-4230	292	2	on	on	ADP
cana-4230	292	3	applied	apply	VERB
cana-4230	292	4	nonlinear	nonlinear	ADJ
cana-4230	292	5	analysis	analysis	NOUN
cana-4230	292	6	issn	issn	NOUN
cana-4230	292	7	:	:	PUNCT
cana-4230	292	8	1074	1074	NUM
cana-4230	292	9	-	-	PUNCT
cana-4230	292	10	133x	133x	NUM
cana-4230	292	11	vol	vol	NOUN
cana-4230	292	12	32	32	NUM
cana-4230	292	13	no	no	NOUN
cana-4230	292	14	.	.	PUNCT
cana-4230	293	1	8s	8s	PROPN
cana-4230	293	2	(	(	PUNCT
cana-4230	293	3	2025	2025	NUM
cana-4230	293	4	)	)	PUNCT
cana-4230	293	5	910	910	NUM
cana-4230	293	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-4230	293	7	18	18	NUM
cana-4230	293	8	.	.	PUNCT
cana-4230	294	1	maria	maria	PROPN
cana-4230	294	2	,	,	PUNCT
cana-4230	294	3	c.	c.	PROPN
cana-4230	294	4	,	,	PUNCT
cana-4230	294	5	boissonnat	boissonnat	NOUN
cana-4230	294	6	,	,	PUNCT
cana-4230	294	7	j.	j.	PROPN
cana-4230	294	8	d.	d.	PROPN
cana-4230	294	9	,	,	PUNCT
cana-4230	294	10	glisse	glisse	NOUN
cana-4230	294	11	,	,	PUNCT
cana-4230	294	12	m.	m.	NOUN
cana-4230	294	13	,	,	PUNCT
cana-4230	294	14	&	&	CCONJ
cana-4230	294	15	yvinec	yvinec	NOUN
cana-4230	294	16	,	,	PUNCT
cana-4230	294	17	m.	m.	NOUN
cana-4230	294	18	(	(	PUNCT
cana-4230	294	19	2014	2014	NUM
cana-4230	294	20	)	)	PUNCT
cana-4230	294	21	.	.	PUNCT
cana-4230	295	1	the	the	DET
cana-4230	295	2	gudhi	gudhi	ADJ
cana-4230	295	3	library	library	NOUN
cana-4230	295	4	:	:	PUNCT
cana-4230	295	5	simplicial	simplicial	ADJ
cana-4230	295	6	complexes	complex	NOUN
cana-4230	295	7	and	and	CCONJ
cana-4230	295	8	persistent	persistent	ADJ
cana-4230	295	9	homology	homology	NOUN
cana-4230	295	10	.	.	PUNCT
cana-4230	296	1	proceedings	proceeding	NOUN
cana-4230	296	2	of	of	ADP
cana-4230	296	3	the	the	DET
cana-4230	296	4	4th	4th	ADJ
cana-4230	296	5	international	international	ADJ
cana-4230	296	6	congress	congress	PROPN
cana-4230	296	7	on	on	ADP
cana-4230	296	8	mathematical	mathematical	ADJ
cana-4230	296	9	software	software	NOUN
cana-4230	296	10	.	.	PUNCT
cana-4230	297	1	19	19	NUM
cana-4230	297	2	.	.	X
cana-4230	297	3	van	van	PROPN
cana-4230	297	4	der	der	PROPN
cana-4230	297	5	maaten	maaten	VERB
cana-4230	297	6	,	,	PUNCT
cana-4230	297	7	l.	l.	PROPN
cana-4230	297	8	,	,	PUNCT
cana-4230	297	9	&	&	CCONJ
cana-4230	297	10	hinton	hinton	PROPN
cana-4230	297	11	,	,	PUNCT
cana-4230	297	12	g.	g.	PROPN
cana-4230	297	13	(	(	PUNCT
cana-4230	297	14	2008	2008	NUM
cana-4230	297	15	)	)	PUNCT
cana-4230	297	16	.	.	PUNCT
cana-4230	298	1	visualizing	visualize	VERB
cana-4230	298	2	data	datum	NOUN
cana-4230	298	3	using	use	VERB
cana-4230	298	4	t	t	PROPN
cana-4230	298	5	-	-	PUNCT
cana-4230	298	6	sne	sne	PROPN
cana-4230	298	7	.	.	PROPN
cana-4230	298	8	journal	journal	PROPN
cana-4230	298	9	of	of	ADP
cana-4230	298	10	machine	machine	NOUN
cana-4230	298	11	learning	learn	VERB
cana-4230	298	12	research	research	NOUN
cana-4230	298	13	,	,	PUNCT
cana-4230	298	14	9	9	NUM
cana-4230	298	15	,	,	PUNCT
cana-4230	298	16	2579	2579	NUM
cana-4230	298	17	-	-	SYM
cana-4230	298	18	2605	2605	NUM
cana-4230	298	19	.	.	PUNCT
cana-4230	299	1	20	20	NUM
cana-4230	299	2	.	.	X
cana-4230	299	3	wasserman	wasserman	PROPN
cana-4230	299	4	,	,	PUNCT
cana-4230	299	5	l.	l.	PROPN
cana-4230	299	6	(	(	PUNCT
cana-4230	299	7	2018	2018	NUM
cana-4230	299	8	)	)	PUNCT
cana-4230	299	9	.	.	PUNCT
cana-4230	300	1	topological	topological	ADJ
cana-4230	300	2	data	datum	NOUN
cana-4230	300	3	analysis	analysis	NOUN
cana-4230	300	4	.	.	PUNCT
cana-4230	301	1	annual	annual	ADJ
cana-4230	301	2	review	review	NOUN
cana-4230	301	3	of	of	ADP
cana-4230	301	4	statistics	statistic	NOUN
cana-4230	301	5	and	and	CCONJ
cana-4230	301	6	its	its	PRON
cana-4230	301	7	application	application	NOUN
cana-4230	301	8	,	,	PUNCT
cana-4230	301	9	5	5	NUM
cana-4230	301	10	,	,	PUNCT
cana-4230	301	11	501	501	NUM
cana-4230	301	12	-	-	SYM
cana-4230	301	13	532	532	NUM
cana-4230	301	14	.	.	NUM
cana-4230	301	15	21	21	NUM
cana-4230	301	16	.	.	PUNCT
cana-4230	302	1	zomorodian	zomorodian	ADJ
cana-4230	302	2	,	,	PUNCT
cana-4230	302	3	a.	a.	NOUN
cana-4230	302	4	(	(	PUNCT
cana-4230	302	5	2005	2005	NUM
cana-4230	302	6	)	)	PUNCT
cana-4230	302	7	.	.	PUNCT
cana-4230	303	1	topology	topology	NOUN
cana-4230	303	2	for	for	ADP
cana-4230	303	3	computing	computing	NOUN
cana-4230	303	4	.	.	PUNCT
cana-4230	304	1	cambridge	cambridge	PROPN
cana-4230	304	2	university	university	PROPN
cana-4230	304	3	press	press	NOUN
cana-4230	304	4	.	.	PUNCT
cana-4230	305	1	22	22	NUM
cana-4230	305	2	.	.	PUNCT
cana-4230	305	3	cerri	cerri	PROPN
cana-4230	305	4	,	,	PUNCT
cana-4230	305	5	a.	a.	PROPN
cana-4230	305	6	,	,	PUNCT
cana-4230	305	7	landi	landi	PROPN
cana-4230	305	8	,	,	PUNCT
cana-4230	305	9	c.	c.	PROPN
cana-4230	305	10	,	,	PUNCT
cana-4230	305	11	&	&	CCONJ
cana-4230	305	12	zuddas	zuddas	PROPN
cana-4230	305	13	,	,	PUNCT
cana-4230	305	14	d.	d.	PROPN
cana-4230	305	15	(	(	PUNCT
cana-4230	305	16	2013	2013	NUM
cana-4230	305	17	)	)	PUNCT
cana-4230	305	18	.	.	PUNCT
cana-4230	306	1	multidimensional	multidimensional	ADJ
cana-4230	306	2	persistence	persistence	NOUN
cana-4230	306	3	in	in	ADP
cana-4230	306	4	geometric	geometric	ADJ
cana-4230	306	5	and	and	CCONJ
cana-4230	306	6	topological	topological	ADJ
cana-4230	306	7	data	datum	NOUN
cana-4230	306	8	analysis	analysis	NOUN
cana-4230	306	9	.	.	PUNCT
cana-4230	307	1	computer	computer	NOUN
cana-4230	307	2	graphics	graphics	PROPN
cana-4230	307	3	forum	forum	PROPN
cana-4230	307	4	,	,	PUNCT
cana-4230	307	5	32(5	32(5	NUM
cana-4230	307	6	)	)	PUNCT
cana-4230	307	7	,	,	PUNCT
cana-4230	307	8	49	49	NUM
cana-4230	307	9	-	-	SYM
cana-4230	307	10	62	62	NUM
cana-4230	307	11	.	.	PUNCT
cana-4230	308	1	23	23	NUM
cana-4230	308	2	.	.	PUNCT
cana-4230	309	1	edelsbrunner	edelsbrunner	NOUN
cana-4230	309	2	,	,	PUNCT
cana-4230	309	3	h.	h.	PROPN
cana-4230	309	4	,	,	PUNCT
cana-4230	309	5	letscher	letscher	PROPN
cana-4230	309	6	,	,	PUNCT
cana-4230	309	7	d.	d.	PROPN
cana-4230	309	8	,	,	PUNCT
cana-4230	309	9	&	&	CCONJ
cana-4230	309	10	zomorodian	zomorodian	PROPN
cana-4230	309	11	,	,	PUNCT
cana-4230	309	12	a.	a.	NOUN
cana-4230	309	13	(	(	PUNCT
cana-4230	309	14	2002	2002	NUM
cana-4230	309	15	)	)	PUNCT
cana-4230	309	16	.	.	PUNCT
cana-4230	310	1	topological	topological	ADJ
cana-4230	310	2	persistence	persistence	NOUN
cana-4230	310	3	and	and	CCONJ
cana-4230	310	4	simplification	simplification	NOUN
cana-4230	310	5	.	.	PUNCT
cana-4230	311	1	discrete	discrete	ADJ
cana-4230	311	2	&	&	CCONJ
cana-4230	311	3	computational	computational	ADJ
cana-4230	311	4	geometry	geometry	NOUN
cana-4230	311	5	,	,	PUNCT
cana-4230	311	6	28(4	28(4	NUM
cana-4230	311	7	)	)	PUNCT
cana-4230	311	8	,	,	PUNCT
cana-4230	311	9	511	511	NUM
cana-4230	311	10	-	-	SYM
cana-4230	311	11	533	533	NUM
cana-4230	311	12	.	.	NOUN
cana-4230	311	13	24	24	NUM
cana-4230	311	14	.	.	PUNCT
cana-4230	312	1	hatcher	hatcher	PROPN
cana-4230	312	2	,	,	PUNCT
cana-4230	312	3	a.	a.	PROPN
cana-4230	312	4	(	(	PUNCT
cana-4230	312	5	2002	2002	NUM
cana-4230	312	6	)	)	PUNCT
cana-4230	312	7	.	.	PUNCT
cana-4230	313	1	algebraic	algebraic	ADJ
cana-4230	313	2	topology	topology	PROPN
cana-4230	313	3	.	.	PUNCT
cana-4230	314	1	cambridge	cambridge	PROPN
cana-4230	314	2	university	university	PROPN
cana-4230	314	3	press	press	NOUN
cana-4230	314	4	.	.	PUNCT
cana-4230	315	1	25	25	NUM
cana-4230	315	2	.	.	PUNCT
cana-4230	315	3	munkres	munkre	NOUN
cana-4230	315	4	,	,	PUNCT
cana-4230	315	5	j.	j.	PROPN
cana-4230	315	6	r.	r.	PROPN
cana-4230	315	7	(	(	PUNCT
cana-4230	315	8	2000	2000	NUM
cana-4230	315	9	)	)	PUNCT
cana-4230	315	10	.	.	PUNCT
cana-4230	316	1	topology	topology	NOUN
cana-4230	316	2	.	.	PUNCT
cana-4230	317	1	prentice	prentice	PROPN
cana-4230	317	2	hall	hall	PROPN
cana-4230	317	3	.	.	PUNCT
cana-4230	318	1	26	26	NUM
cana-4230	318	2	.	.	X
cana-4230	318	3	tenenbaum	tenenbaum	PROPN
cana-4230	318	4	,	,	PUNCT
cana-4230	318	5	j.	j.	PROPN
cana-4230	318	6	b.	b.	PROPN
cana-4230	318	7	,	,	PUNCT
cana-4230	318	8	silva	silva	PROPN
cana-4230	318	9	,	,	PUNCT
cana-4230	318	10	v.	v.	PROPN
cana-4230	318	11	d.	d.	PROPN
cana-4230	318	12	,	,	PUNCT
cana-4230	318	13	&	&	CCONJ
cana-4230	318	14	langford	langford	PROPN
cana-4230	318	15	,	,	PUNCT
cana-4230	318	16	j.	j.	PROPN
cana-4230	318	17	c.	c.	PROPN
cana-4230	318	18	(	(	PUNCT
cana-4230	318	19	2000	2000	NUM
cana-4230	318	20	)	)	PUNCT
cana-4230	318	21	.	.	PUNCT
cana-4230	319	1	a	a	DET
cana-4230	319	2	global	global	ADJ
cana-4230	319	3	geometric	geometric	ADJ
cana-4230	319	4	framework	framework	NOUN
cana-4230	319	5	for	for	ADP
cana-4230	319	6	nonlinear	nonlinear	ADJ
cana-4230	319	7	dimensionality	dimensionality	NOUN
cana-4230	319	8	reduction	reduction	NOUN
cana-4230	319	9	.	.	PUNCT
cana-4230	320	1	science	science	NOUN
cana-4230	320	2	,	,	PUNCT
cana-4230	320	3	290(5500	290(5500	NUM
cana-4230	320	4	)	)	PUNCT
cana-4230	320	5	,	,	PUNCT
cana-4230	320	6	2319	2319	NUM
cana-4230	320	7	-	-	SYM
cana-4230	320	8	2323	2323	NUM
cana-4230	320	9	.	.	PUNCT
cana-4230	321	1	27	27	NUM
cana-4230	321	2	.	.	PUNCT
cana-4230	322	1	zomorodian	zomorodian	ADJ
cana-4230	322	2	,	,	PUNCT
cana-4230	322	3	a.	a.	NOUN
cana-4230	322	4	(	(	PUNCT
cana-4230	322	5	2012	2012	NUM
cana-4230	322	6	)	)	PUNCT
cana-4230	322	7	.	.	PUNCT
cana-4230	323	1	fast	fast	ADJ
cana-4230	323	2	construction	construction	NOUN
cana-4230	323	3	of	of	ADP
cana-4230	323	4	the	the	DET
cana-4230	323	5	vietoris	vietoris	ADJ
cana-4230	323	6	–	–	PUNCT
cana-4230	323	7	rips	rip	NOUN
cana-4230	323	8	complex	complex	NOUN
cana-4230	323	9	.	.	PUNCT
cana-4230	324	1	computers	computer	NOUN
cana-4230	324	2	&	&	CCONJ
cana-4230	324	3	graphics	graphic	NOUN
cana-4230	324	4	,	,	PUNCT
cana-4230	324	5	36(2	36(2	NUM
cana-4230	324	6	)	)	PUNCT
cana-4230	324	7	,	,	PUNCT
cana-4230	324	8	156	156	NUM
cana-4230	324	9	-	-	SYM
cana-4230	324	10	164	164	NUM
cana-4230	324	11	.	.	PUNCT