{"id":"https://openalex.org/W7114781948","doi":"https://doi.org/10.48550/arxiv.2512.07879","title":"Nonnegative Matrix Factorization through Cone Collapse","display_name":"Nonnegative Matrix Factorization through Cone Collapse","publication_year":2025,"publication_date":"2025-11-27","ids":{"openalex":"https://openalex.org/W7114781948","doi":"https://doi.org/10.48550/arxiv.2512.07879"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2512.07879","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.07879","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2512.07879","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Nguyen, Manh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen, Manh","raw_affiliation_strings":["Department of Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Pimentel-Alarc\u00f3n, Daniel","orcid":null},"institutions":[{"id":"https://openalex.org/I2802999273","display_name":"Wisconsin Institutes for Discovery","ror":"https://ror.org/05gbven85","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2802999273"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pimentel-Alarc\u00f3n, Daniel","raw_affiliation_strings":["Department of Biostatistics and Medical Informatics, Wisconsin Institute of Discovery, University of Wisconsin-Madison"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biostatistics and Medical Informatics, Wisconsin Institute of Discovery, University of Wisconsin-Madison","institution_ids":["https://openalex.org/I2802999273"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.24950000643730164,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.24950000643730164,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.22509999573230743,"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/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.03440000116825104,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.7261999845504761},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5953999757766724},{"id":"https://openalex.org/keywords/convex-cone","display_name":"Convex cone","score":0.5866000056266785},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5464000105857849},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.47429999709129333},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.4659000039100647},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.429500013589859},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4187000095844269},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.41519999504089355},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.39489999413490295}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.7261999845504761},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7111999988555908},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5953999757766724},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.5866000056266785},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5464000105857849},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.47429999709129333},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.4659000039100647},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4278999865055084},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.41519999504089355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40139999985694885},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.39489999413490295},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.349700003862381},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C23379248","wikidata":"https://www.wikidata.org/wiki/Q200904","display_name":"Epipolar geometry","level":3,"score":0.33899998664855957},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.33219999074935913},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3303000032901764},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.28940001130104065},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28450000286102295},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C24484764","wikidata":"https://www.wikidata.org/wiki/Q2687694","display_name":"Dual cone and polar cone","level":3,"score":0.2676999866962433},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25450000166893005}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2512.07879","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.07879","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2512.07879","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.07879","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Nonnegative":[0],"matrix":[1,38],"factorization":[2],"(NMF)":[3],"is":[4],"a":[5,72,150],"widely":[6],"used":[7],"tool":[8],"for":[9],"learning":[10],"parts-based,":[11],"low-dimensional":[12],"representations":[13],"of":[14,140,191],"nonnegative":[15,104],"data,":[16,126],"with":[17],"applications":[18],"in":[19,71,130],"vision,":[20],"text,":[21,169],"and":[22,57,93,106,134,170,187,208],"bioinformatics.":[23],"In":[24,83],"clustering":[25,192,212],"applications,":[26],"orthogonal":[27,152],"NMF":[28,88,153,159,179],"(ONMF)":[29],"variants":[30],"further":[31],"impose":[32],"(approximate)":[33],"orthogonality":[34],"on":[35,124,144],"the":[36,62,102,111,116,125,136,161,200],"representation":[37],"so":[39],"that":[40,99,197],"its":[41],"rows":[42],"behave":[43],"like":[44],"soft":[45],"cluster":[46],"indicators.":[47],"Existing":[48],"algorithms,":[49],"however,":[50],"are":[51],"typically":[52],"derived":[53],"from":[54,89,101],"optimization":[55],"viewpoints":[56],"do":[58],"not":[59],"explicitly":[60,198],"exploit":[61],"conic":[63],"geometry":[64],"induced":[65],"by":[66,115,156],"NMF:":[67],"data":[68,201],"points":[69],"lie":[70],"convex":[73],"cone":[74,113,139,202],"whose":[75],"extreme":[76,163],"rays":[77],"encode":[78],"fundamental":[79],"directions":[80],"or":[81,176],"\"topics\".":[82],"this":[84,90,145],"work":[85],"we":[86,147],"revisit":[87],"geometric":[91],"perspective":[92],"propose":[94],"Cone":[95,127],"Collapse,":[96],"an":[97],"algorithm":[98],"starts":[100],"full":[103],"orthant":[105],"iteratively":[107],"shrinks":[108],"it":[109],"toward":[110],"minimal":[112,137],"generated":[114],"data.":[117],"We":[118],"prove":[119],"that,":[120],"under":[121],"mild":[122],"assumptions":[123],"Collapse":[128],"terminates":[129],"finitely":[131],"many":[132],"steps":[133],"recovers":[135],"generating":[138],"$\\mathbf{X}^\\top$":[141],".":[142],"Building":[143],"basis,":[146],"then":[148],"derive":[149],"cone-aware":[151],"model":[154],"(CC-NMF)":[155],"applying":[157],"uni-orthogonal":[158],"to":[160],"recovered":[162],"rays.":[164],"Across":[165],"16":[166],"benchmark":[167],"gene-expression,":[168],"image":[171],"datasets,":[172],"CC-NMF":[173],"consistently":[174],"matches":[175],"outperforms":[177],"strong":[178,210],"baselines-including":[180],"multiplicative":[181],"updates,":[182],"ANLS,":[183],"projective":[184],"NMF,":[185],"ONMF,":[186],"sparse":[188],"NMF-in":[189],"terms":[190],"purity.":[193],"These":[194],"results":[195],"demonstrate":[196],"recovering":[199],"can":[203],"yield":[204],"both":[205],"theoretically":[206],"grounded":[207],"empirically":[209],"NMF-based":[211],"methods.":[213]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-12-11T00:00:00"}