{"id":"https://openalex.org/W4378070712","doi":"https://doi.org/10.1137/21m1462945","title":"Time-Inhomogeneous Diffusion Geometry and Topology","display_name":"Time-Inhomogeneous Diffusion Geometry and Topology","publication_year":2023,"publication_date":"2023-05-22","ids":{"openalex":"https://openalex.org/W4378070712","doi":"https://doi.org/10.1137/21m1462945"},"language":"en","primary_location":{"id":"doi:10.1137/21m1462945","doi":"https://doi.org/10.1137/21m1462945","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1137/21m1462945","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://dx.doi.org/10.1137/21m1462945","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Guillaume Huguet","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210164802","display_name":"Mila - Quebec Artificial Intelligence Institute","ror":"https://ror.org/05c22rx21","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210164802"]},{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Guillaume Huguet","raw_affiliation_strings":["Department of Mathematics and Statistics, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC H3T 1J4, Canada, and Mila - Quebec AI Institute, Montr\u00e9al, QC H2S 3H1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC H3T 1J4, Canada, and Mila - Quebec AI Institute, Montr\u00e9al, QC H2S 3H1, Canada","institution_ids":["https://openalex.org/I4210164802","https://openalex.org/I70931966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053568123","display_name":"Alexander Tong","orcid":"https://orcid.org/0000-0002-2031-4096","observed_orcids":["https://orcid.org/0000-0002-2031-4096"]},"institutions":[{"id":"https://openalex.org/I4210164802","display_name":"Mila - Quebec Artificial Intelligence Institute","ror":"https://ror.org/05c22rx21","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210164802"]},{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alexander Tong","raw_affiliation_strings":["Department of Computer Science and Operations Research, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC H3T 1J4, Canada, and Mila - Quebec AI Institute, Montr\u00e9al, QC H2S 3H1, Canada"],"raw_orcid":"https://orcid.org/0000-0002-2031-4096","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Operations Research, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC H3T 1J4, Canada, and Mila - Quebec AI Institute, Montr\u00e9al, QC H2S 3H1, Canada","institution_ids":["https://openalex.org/I4210164802","https://openalex.org/I70931966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003031729","display_name":"Bastian Rieck","orcid":"https://orcid.org/0000-0003-4335-0302","observed_orcids":["https://orcid.org/0000-0003-4335-0302"]},"institutions":[{"id":"https://openalex.org/I3018134672","display_name":"Helmholtz Munich","ror":"https://ror.org/00cfam450","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I3018134672"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bastian Rieck","raw_affiliation_strings":["Helmholtz Munich, Ingolst\u00e4dter Landstr. 1, 85764 Neuherberg, Germany, and Technical University of Munich, Arcisstr. 21, 80333 Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4335-0302","affiliations":[{"raw_affiliation_string":"Helmholtz Munich, Ingolst\u00e4dter Landstr. 1, 85764 Neuherberg, Germany, and Technical University of Munich, Arcisstr. 21, 80333 Munich, Germany","institution_ids":["https://openalex.org/I3018134672","https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jessie Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jessie Huang","raw_affiliation_strings":["Departments of Computer Science and Genetics, Yale University, New Haven, CT 06520 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Computer Science and Genetics, Yale University, New Haven, CT 06520 USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044308510","display_name":"Manik Razdan Kuchroo","orcid":"https://orcid.org/0000-0001-7512-9739","observed_orcids":["https://orcid.org/0000-0001-7512-9739"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Manik Kuchroo","raw_affiliation_strings":["Department of Neuroscience, Yale University, New Haven, CT 06520 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Neuroscience, Yale University, New Haven, CT 06520 USA","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044875969","display_name":"Matthew Hirn","orcid":"https://orcid.org/0000-0003-0290-4292","observed_orcids":["https://orcid.org/0000-0003-0290-4292"]},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Hirn","raw_affiliation_strings":["Departments of CMSE and Mathematics, Michigan State University, East Lansing, MI 48824 USA"],"raw_orcid":"https://orcid.org/0000-0003-0290-4292","affiliations":[{"raw_affiliation_string":"Departments of CMSE and Mathematics, Michigan State University, East Lansing, MI 48824 USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005117825","display_name":"Guy Wolf","orcid":"https://orcid.org/0000-0002-6740-059X","observed_orcids":["https://orcid.org/0000-0002-6740-059X"]},"institutions":[{"id":"https://openalex.org/I4210164802","display_name":"Mila - Quebec Artificial Intelligence Institute","ror":"https://ror.org/05c22rx21","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210164802"]},{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Guy Wolf","raw_affiliation_strings":["Corresponding coauthor. Department of Mathematics and Statistics, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC H3T 1J4, Canada, and Mila - Quebec AI Institute, Montr\u00e9al, QC H2S 3H1, Canada"],"raw_orcid":"https://orcid.org/0000-0002-6740-059X","affiliations":[{"raw_affiliation_string":"Corresponding coauthor. Department of Mathematics and Statistics, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC H3T 1J4, Canada, and Mila - Quebec AI Institute, Montr\u00e9al, QC H2S 3H1, Canada","institution_ids":["https://openalex.org/I4210164802","https://openalex.org/I70931966"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045475274","display_name":"Smita Krishnaswamy","orcid":"https://orcid.org/0000-0001-5823-1985","observed_orcids":["https://orcid.org/0000-0001-5823-1985"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]},{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Smita Krishnaswamy","raw_affiliation_strings":["Corresponding coauthor. Departments of Computer Science and Genetics, Yale University, New Haven, CT 06520 USA, and Departments of CMSE and Mathematics, Michigan State University, East Lansing, MI 48824 USA"],"raw_orcid":"https://orcid.org/0000-0001-5823-1985","affiliations":[{"raw_affiliation_string":"Corresponding coauthor. Departments of Computer Science and Genetics, Yale University, New Haven, CT 06520 USA, and Departments of CMSE and Mathematics, Michigan State University, East Lansing, MI 48824 USA","institution_ids":["https://openalex.org/I32971472","https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5005117825","https://openalex.org/A5045475274"],"corresponding_institution_ids":["https://openalex.org/I32971472","https://openalex.org/I4210164802","https://openalex.org/I70931966","https://openalex.org/I87216513"],"apc_list":null,"apc_paid":null,"fwci":0.5429,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61409812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":95},"biblio":{"volume":"5","issue":"2","first_page":"346","last_page":"372"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/time-inhomogeneous-diffusion","display_name":"time-inhomogeneous diffusion","score":0.9070000052452087},{"id":"https://openalex.org/keywords/convergence-bounds","display_name":"convergence bounds","score":0.6660000085830688},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"topological data analysis","score":0.7459999918937683},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"persistent homology","score":0.8840000033378601},{"id":"https://openalex.org/keywords/hierarchical-clustering","display_name":"hierarchical clustering","score":0.7919999957084656},{"id":"https://openalex.org/keywords/manifold-learning","display_name":"manifold learning","score":0.7440000176429749},{"id":"https://openalex.org/keywords/data-geometry","display_name":"data geometry","score":0.4399999976158142}],"concepts":[{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.5985500812530518},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5839927196502686},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.5075644254684448},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.4812988340854645},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.4668505787849426},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.455243319272995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4266880750656128},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3670854866504669},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3331061005592346},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3202100396156311},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3024486303329468},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2149658501148224},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.1388009488582611},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12458747625350952},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11109089851379395},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/21m1462945","doi":"https://doi.org/10.1137/21m1462945","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1137/21m1462945","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2203.14860","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2203.14860","pdf_url":"https://arxiv.org/pdf/2203.14860","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:push-zb.helmholtz-munich.de:69392","doi":null,"is_oa":false,"landing_page_url":"https://push-zb.helmholtz-munich.de/frontdoor.php?source_opus=69392","pdf_url":null,"source":{"id":"https://openalex.org/S7407055352","display_name":"PuSH - Publication Server of Helmholtz Zentrum M\u00fcnchen","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J. Math. Data Sci. 5, 346-372 (2023)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2203.14860","doi":"https://doi.org/10.48550/arxiv.2203.14860","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2203.14860","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1137/21m1462945","doi":"https://doi.org/10.1137/21m1462945","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1137/21m1462945","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2864574505","display_name":null,"funder_award_id":"03267","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7599175891","display_name":"CAREER: Understanding Invariant Convolutional Neural Networks through Many Particle Physics","funder_award_id":"1845856","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8633301738","display_name":"Finding emergent structure in multi-sample biological data with the dual geometry of cells and features   ","funder_award_id":"R01GM135929","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309949","display_name":"Canadian Institute for Advanced Research","ror":"https://ror.org/01sdtdd95"},{"id":"https://openalex.org/F4320330273","display_name":"Institut de Valorisation des Donn\u00e9es","ror":"https://ror.org/05a3srq89"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4378070712.pdf","grobid_xml":"https://content.openalex.org/works/W4378070712.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1565546618","https://openalex.org/W2022686119","https://openalex.org/W2026882380","https://openalex.org/W2036780368","https://openalex.org/W2037613900","https://openalex.org/W2060702495","https://openalex.org/W2071391326","https://openalex.org/W2127774996","https://openalex.org/W2132914434","https://openalex.org/W2164500538","https://openalex.org/W2514213613","https://openalex.org/W2805619986","https://openalex.org/W2993894543","https://openalex.org/W3013843370","https://openalex.org/W3128654710","https://openalex.org/W3129538072","https://openalex.org/W3165474212","https://openalex.org/W4213367101","https://openalex.org/W4214544930","https://openalex.org/W4245668478"],"related_works":["https://openalex.org/W2959830301","https://openalex.org/W6922137155","https://openalex.org/W3161908143","https://openalex.org/W4398157636","https://openalex.org/W2129730857","https://openalex.org/W4385385733","https://openalex.org/W2100117429","https://openalex.org/W3006527408","https://openalex.org/W2559081705","https://openalex.org/W2006554089"],"abstract_inverted_index":{"Abstract.":[0],"Diffusion":[1,35],"condensation":[2,36,138,181,187,203,235],"is":[3,37,125],"a":[4,9,40,48,75,96,131,149,241],"dynamic":[5],"process":[6,42,67,182,204],"that":[7,15,136,179,238],"yields":[8],"sequence":[10],"of":[11,32,65,91,106,114,119,155,159,166,201,218,233],"multiscale":[12],"data":[13,123,156,168,175,209,247],"representations":[14],"aim":[16],"to":[17,55,147,205],"encode":[18],"meaningful":[19],"abstractions.":[20],"It":[21],"has":[22],"proven":[23],"effective":[24],"for":[25],"manifold":[26],"learning,":[27],"denoising,":[28],"clustering,":[29],"and":[30,51,63,71,88,236,245],"visualization":[31],"high-dimensional":[33],"data.":[34,57],"constructed":[38],"as":[39,194,196],"time-inhomogeneous":[41],"where":[43],"each":[44],"step":[45],"first":[46],"computes":[47],"diffusion":[49,108,124,137,212,234],"operator":[50],"then":[52],"applies":[53],"it":[54,239],"the":[56,61,84,89,92,104,107,120,153,164,167,180,197,202,208,231],"We":[58,143,177,189,214],"theoretically":[59],"analyze":[60],"convergence":[62,80,232],"evolution":[64,165],"this":[66,145,191],"from":[68,95],"geometric,":[69],"spectral,":[70],"topological":[72,132,174,219,244],"perspectives.":[73],"From":[74,130],"geometric":[76,246],"perspective,":[77,98,133],"we":[78,134,172],"obtain":[79,148],"bounds":[81,100],"based":[82,102,151],"on":[83,103,122,127,152],"smallest":[85],"transition":[86],"probability":[87],"radius":[90],"data,":[93],"whereas":[94],"spectral":[97,111],"our":[99],"are":[101,113],"eigenspectrum":[105],"kernel.":[109],"Our":[110,225],"results":[112],"particular":[115],"interest":[116],"since":[117],"most":[118],"literature":[121],"focused":[126],"homogeneous":[128],"processes.":[129],"show":[135,178],"generalizes":[139],"centroid-based":[140],"hierarchical":[141],"clustering.":[142],"use":[144,173,190],"perspective":[146],"bound":[150],"number":[154],"points,":[157],"independent":[158],"their":[160],"location.":[161],"To":[162],"understand":[163],"geometry":[169],"beyond":[170],"convergence,":[171],"analysis.":[176,248],"itself":[183],"defines":[184],"an":[185],"intrinsic":[186,192],"homology.":[188],"topology,":[193],"well":[195],"ambient":[198],"persistent":[199],"homology,":[200],"study":[206],"how":[207],"changes":[210],"over":[211],"time.":[213],"demonstrate":[215],"both":[216],"types":[217],"information":[220],"in":[221],"well-understood":[222],"toy":[223],"examples.":[224],"work":[226],"gives":[227],"theoretical":[228],"insight":[229],"into":[230],"shows":[237],"provides":[240],"link":[242],"between":[243]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2023-05-25T00:00:00"}