{"id":"https://openalex.org/W1973733387","doi":"https://doi.org/10.1109/tsp.2014.2360141","title":"Soft Nonnegative Matrix Co-Factorization","display_name":"Soft Nonnegative Matrix Co-Factorization","publication_year":2014,"publication_date":"2014-09-23","ids":{"openalex":"https://openalex.org/W1973733387","doi":"https://doi.org/10.1109/tsp.2014.2360141","mag":"1973733387"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2014.2360141","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2014.2360141","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068887439","display_name":"Nicolas Seichepine","orcid":null},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I205703379","display_name":"Institut Mines-T\u00e9l\u00e9com","ror":"https://ror.org/025vp2923","country_code":"FR","type":"facility","lineage":["https://openalex.org/I205703379"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Seichepine","raw_affiliation_strings":["T\u00e9l\u00e9com ParisTech, Institut Mines-T\u00e9l\u00e9com","S2A - Signal, Statistique et Apprentissage (T\u00e9l\u00e9com Paris 19 Place Marguerite Perey 91120 Palaiseau - France)","TSI - D\u00e9partement Traitement du Signal et des Images (T\u00e9l\u00e9com ParisTech / TSI 46, rue Barrault 75634 PARIS Cedex 13 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"T\u00e9l\u00e9com ParisTech, Institut Mines-T\u00e9l\u00e9com","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I205703379"]},{"raw_affiliation_string":"S2A - Signal, Statistique et Apprentissage (T\u00e9l\u00e9com Paris 19 Place Marguerite Perey 91120 Palaiseau - France)","institution_ids":["https://openalex.org/I12356871"]},{"raw_affiliation_string":"TSI - D\u00e9partement Traitement du Signal et des Images (T\u00e9l\u00e9com ParisTech / TSI 46, rue Barrault 75634 PARIS Cedex 13 - France)","institution_ids":["https://openalex.org/I12356871"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060031161","display_name":"Slim Essid","orcid":"https://orcid.org/0000-0002-0028-327X"},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I205703379","display_name":"Institut Mines-T\u00e9l\u00e9com","ror":"https://ror.org/025vp2923","country_code":"FR","type":"facility","lineage":["https://openalex.org/I205703379"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Slim Essid","raw_affiliation_strings":["T\u00e9l\u00e9com ParisTech, Institut Mines-T\u00e9l\u00e9com","S2A - Signal, Statistique et Apprentissage (T\u00e9l\u00e9com Paris 19 Place Marguerite Perey 91120 Palaiseau - France)","TSI - D\u00e9partement Traitement du Signal et des Images (T\u00e9l\u00e9com ParisTech / TSI 46, rue Barrault 75634 PARIS Cedex 13 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"T\u00e9l\u00e9com ParisTech, Institut Mines-T\u00e9l\u00e9com","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I205703379"]},{"raw_affiliation_string":"S2A - Signal, Statistique et Apprentissage (T\u00e9l\u00e9com Paris 19 Place Marguerite Perey 91120 Palaiseau - France)","institution_ids":["https://openalex.org/I12356871"]},{"raw_affiliation_string":"TSI - D\u00e9partement Traitement du Signal et des Images (T\u00e9l\u00e9com ParisTech / TSI 46, rue Barrault 75634 PARIS Cedex 13 - France)","institution_ids":["https://openalex.org/I12356871"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022368934","display_name":"C\u00e9dric F\u00e9votte","orcid":"https://orcid.org/0000-0003-3801-5534"},"institutions":[{"id":"https://openalex.org/I4210113427","display_name":"Lagrange Laboratory","ror":"https://ror.org/02fdv8735","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I201841394","https://openalex.org/I4210113427","https://openalex.org/I4210126779","https://openalex.org/I4210148025"]},{"id":"https://openalex.org/I59769168","display_name":"LaGrange College","ror":"https://ror.org/04w4aze46","country_code":"US","type":"education","lineage":["https://openalex.org/I59769168"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Cedric Fevotte","raw_affiliation_strings":["CNRS, Laboratoire Lagrange","LAGRANGE - Joseph Louis LAGRANGE (Boulevard de l'Observatoire B.P. 4229 06304 Nice Cedex 04 - France - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, Laboratoire Lagrange","institution_ids":["https://openalex.org/I59769168"]},{"raw_affiliation_string":"LAGRANGE - Joseph Louis LAGRANGE (Boulevard de l'Observatoire B.P. 4229 06304 Nice Cedex 04 - France - France)","institution_ids":["https://openalex.org/I4210113427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105628617","display_name":"Olivier Capp\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210165912","display_name":"Laboratoire Traitement et Communication de l\u2019Information","ror":"https://ror.org/057er4c39","country_code":"FR","type":"facility","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102","https://openalex.org/I4210165912"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Cappe","raw_affiliation_strings":["T\u00e9l\u00e9com ParisTech, CNRS LTCI","S2A - Signal, Statistique et Apprentissage (T\u00e9l\u00e9com Paris 19 Place Marguerite Perey 91120 Palaiseau - France)","TSI - D\u00e9partement Traitement du Signal et des Images (T\u00e9l\u00e9com ParisTech / TSI 46, rue Barrault 75634 PARIS Cedex 13 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"T\u00e9l\u00e9com ParisTech, CNRS LTCI","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590","https://openalex.org/I4210165912"]},{"raw_affiliation_string":"S2A - Signal, Statistique et Apprentissage (T\u00e9l\u00e9com Paris 19 Place Marguerite Perey 91120 Palaiseau - France)","institution_ids":["https://openalex.org/I12356871"]},{"raw_affiliation_string":"TSI - D\u00e9partement Traitement du Signal et des Images (T\u00e9l\u00e9com ParisTech / TSI 46, rue Barrault 75634 PARIS Cedex 13 - France)","institution_ids":["https://openalex.org/I12356871"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.6245,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.95842676,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"62","issue":"22","first_page":"5940","last_page":"5949"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10860","display_name":"Speech and Audio Processing","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.6062776446342468},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5604742169380188},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5409600734710693},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5368365049362183},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5340669751167297},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5020532608032227},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.49677544832229614},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4764719009399414},{"id":"https://openalex.org/keywords/majorization","display_name":"Majorization","score":0.47041967511177063},{"id":"https://openalex.org/keywords/modalities","display_name":"Modalities","score":0.42360612750053406},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.41770148277282715},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3519679307937622},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3481287956237793},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3435882031917572},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.18766406178474426},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08915817737579346}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.6062776446342468},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5604742169380188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5409600734710693},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5368365049362183},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5340669751167297},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5020532608032227},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.49677544832229614},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4764719009399414},{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.47041967511177063},{"id":"https://openalex.org/C2779903281","wikidata":"https://www.wikidata.org/wiki/Q6888026","display_name":"Modalities","level":2,"score":0.42360612750053406},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.41770148277282715},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3519679307937622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3481287956237793},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3435882031917572},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18766406178474426},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08915817737579346},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2014.2360141","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2014.2360141","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01116863v1","is_oa":false,"landing_page_url":"https://imt.hal.science/hal-01116863","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, 2014, 62 (22), pp.5940-5949. ⟨10.1109/TSP.2014.2360141⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W59193195","https://openalex.org/W87112183","https://openalex.org/W1479822238","https://openalex.org/W1632866817","https://openalex.org/W1902027874","https://openalex.org/W1971791733","https://openalex.org/W1979301943","https://openalex.org/W1990231296","https://openalex.org/W1999031685","https://openalex.org/W2003020982","https://openalex.org/W2006031689","https://openalex.org/W2034298135","https://openalex.org/W2039844283","https://openalex.org/W2054553473","https://openalex.org/W2069214509","https://openalex.org/W2081074144","https://openalex.org/W2083667973","https://openalex.org/W2106153115","https://openalex.org/W2112039577","https://openalex.org/W2113990625","https://openalex.org/W2114508388","https://openalex.org/W2117420919","https://openalex.org/W2120575676","https://openalex.org/W2127851351","https://openalex.org/W2148596671","https://openalex.org/W2149414429","https://openalex.org/W2150415460","https://openalex.org/W2159094433","https://openalex.org/W2161077892","https://openalex.org/W2404400936","https://openalex.org/W2530593441","https://openalex.org/W2620757702","https://openalex.org/W6602402129","https://openalex.org/W6603655804","https://openalex.org/W6628651604","https://openalex.org/W6636705969","https://openalex.org/W6675737803","https://openalex.org/W6682063170","https://openalex.org/W6728390481","https://openalex.org/W6738902873"],"related_works":["https://openalex.org/W371413493","https://openalex.org/W1988514170","https://openalex.org/W4320039931","https://openalex.org/W4313303878","https://openalex.org/W4214702501","https://openalex.org/W1970837389","https://openalex.org/W3160314930","https://openalex.org/W2474792379","https://openalex.org/W1999959286","https://openalex.org/W1990140521"],"abstract_inverted_index":{"This":[0,73],"work":[1],"introduces":[2],"a":[3,59,91],"new":[4],"framework":[5],"for":[6,65,111],"nonnegative":[7],"matrix":[8],"factorization":[9],"(NMF)":[10],"in":[11,151],"multisensor":[12],"or":[13,71],"multimodal":[14,155],"data":[15,32,160],"configurations,":[16],"where":[17,81],"taking":[18],"into":[19],"account":[20],"the":[21,27,54,98,121,125,137],"mutual":[22],"dependence":[23],"that":[24,43,94],"exists":[25],"between":[26,97],"related":[28,99],"parallel":[29],"streams":[30],"of":[31,115,141],"is":[33,75,145],"expected":[34],"to":[35,147],"improve":[36],"performance.":[37],"In":[38],"contrast":[39],"with":[40,103],"previous":[41],"works":[42],"focused":[44],"on":[45],"co-factorization":[46,61],"methods":[47],"\u2014where":[48],"some":[49],"factors":[50],"are":[51,84],"shared":[52],"by":[53,90],"different":[55,104],"modalities\u2014":[56],"we":[57],"propose":[58],"soft":[60],"scheme":[62],"which":[63],"accounts":[64],"possible":[66,130],"local":[67],"discrepancies":[68],"across":[69],"modalities":[70],"channels.":[72],"objective":[74],"formalized":[76],"as":[77],"an":[78],"optimization":[79],"problem":[80],"concurrent":[82],"factorizations":[83],"jointly":[85],"performed":[86],"while":[87],"being":[88],"tied":[89],"coupling":[92,131],"term":[93],"penalizes":[95],"differences":[96],"factor":[100],"matrices":[101],"associated":[102],"modalities.":[105],"We":[106],"provide":[107],"majorization-minimization":[108],"(MM)":[109],"algorithms":[110],"three":[112],"common":[113],"measures":[114],"fit":[116],"\u2014the":[117],"squared":[118,138],"Euclidean":[119,139],"norm,":[120],"Kullback-Leibler":[122],"divergence":[123],"and":[124,128,161],"Itakura-Saito":[126],"divergence\u2014":[127],"two":[129,152],"variants,":[132],"using":[133,158,165],"either":[134],"the$\\ell":[135],"_{1}$or":[136],"norm":[140],"differences.":[142],"The":[143],"approach":[144],"shown":[146],"achieve":[148],"promising":[149],"performance":[150],"audio-related":[153],"tasks:":[154],"speaker":[156],"diarization":[157],"audiovisual":[159],"audio":[162],"source":[163],"separation":[164],"stereo":[166],"data.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}