{"id":"https://openalex.org/W7131825936","doi":"https://doi.org/10.48550/arxiv.2602.22536","title":"Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization","display_name":"Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization","publication_year":2026,"publication_date":"2026-02-26","ids":{"openalex":"https://openalex.org/W7131825936","doi":"https://doi.org/10.48550/arxiv.2602.22536"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.22536","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127394624","display_name":"Jichao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Jichao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127445546","display_name":"Ran Miao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miao, Ran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127450064","display_name":"Limin Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Limin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24346909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.37549999356269836,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.37549999356269836,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.3111000061035156,"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/T11289","display_name":"Single-cell and spatial transcriptomics","score":0.05000000074505806,"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":0.7084000110626221},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6693999767303467},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5924999713897705},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.538100004196167},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5216000080108643},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.48080000281333923},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4309000074863434},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4113999903202057}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.7084000110626221},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6693999767303467},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6225000023841858},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5924999713897705},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.538100004196167},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5216000080108643},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4713999927043915},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4309000074863434},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3441999852657318},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3255000114440918},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.30720001459121704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.302700012922287},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2973000109195709},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27720001339912415},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.259799987077713}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.22536","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.22536","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.22536","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":"pmh:doi:10.48550/arxiv.2602.22536","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"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":{"Matrix":[0,5],"factorization":[1,45],"techniques,":[2],"especially":[3],"Nonnegative":[4],"Factorization":[6],"(NMF),":[7],"have":[8],"been":[9],"widely":[10],"used":[11],"for":[12],"dimensionality":[13],"reduction":[14],"and":[15,26,104,121,164],"interpretable":[16],"data":[17],"representation.":[18],"However,":[19],"existing":[20],"NMF-based":[21],"methods":[22],"are":[23],"inherently":[24],"single-scale":[25],"fail":[27],"to":[28,95],"capture":[29],"the":[30,79,111,115,118,170,173],"evolution":[31],"of":[32,50,57,91,114,172],"connectivity":[33,81],"structures":[34],"across":[35,138],"resolutions.":[36],"In":[37],"this":[38],"work,":[39],"we":[40,69],"propose":[41],"persistent":[42,67],"nonnegative":[43],"matrix":[44],"(pNMF),":[46],"a":[47,55,62,71,89,96,134,142,152],"scale-parameterized":[48],"family":[49],"NMF":[51,98],"problems,":[52],"that":[53],"produces":[54],"sequence":[56,90],"persistence-aligned":[58],"embeddings":[59,116],"rather":[60,140],"than":[61,141],"single":[63,143],"one.":[64],"By":[65],"leveraging":[66],"homology,":[68],"identify":[70],"canonical":[72,86],"minimal":[73],"sufficient":[74],"scale":[75,119],"set":[76],"at":[77],"which":[78,145],"underlying":[80],"undergoes":[82],"qualitative":[83],"changes.":[84],"These":[85],"scales":[87],"induce":[88],"graph":[92],"Laplacians,":[93],"leading":[94],"coupled":[97],"formulation":[99],"with":[100,157],"scale-wise":[101],"geometric":[102],"regularization":[103],"explicit":[105],"cross-scale":[106],"consistency":[107],"constraint.":[108],"We":[109,150],"analyze":[110],"structural":[112],"properties":[113],"along":[117],"parameter":[120],"establish":[122],"bounds":[123],"on":[124,162],"their":[125],"increments":[126],"between":[127],"consecutive":[128],"scales.":[129],"The":[130],"resulting":[131],"model":[132],"defines":[133],"nontrivial":[135],"solution":[136],"path":[137],"scales,":[139],"factorization,":[144],"poses":[146],"new":[147],"computational":[148],"challenges.":[149],"develop":[151],"sequential":[153],"alternating":[154],"optimization":[155],"algorithm":[156],"guaranteed":[158],"convergence.":[159],"Numerical":[160],"experiments":[161],"synthetic":[163],"single-cell":[165],"RNA":[166],"sequencing":[167],"datasets":[168],"demonstrate":[169],"effectiveness":[171],"proposed":[174],"approach":[175],"in":[176],"multi-scale":[177],"low-rank":[178],"embeddings.":[179]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-02-28T00:00:00"}