{"id":"https://openalex.org/W2903316710","doi":"https://doi.org/10.23919/eusipco.2018.8553569","title":"Jacobi Algorithm for Nonnegative Matrix Factorization with Transform Learning","display_name":"Jacobi Algorithm for Nonnegative Matrix Factorization with Transform Learning","publication_year":2018,"publication_date":"2018-09-01","ids":{"openalex":"https://openalex.org/W2903316710","doi":"https://doi.org/10.23919/eusipco.2018.8553569","mag":"2903316710"},"language":"en","primary_location":{"id":"doi:10.23919/eusipco.2018.8553569","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2018.8553569","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 26th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5008685312","display_name":"Herwig Wendt","orcid":"https://orcid.org/0000-0001-6930-3083"},"institutions":[{"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/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Herwig Wendt","raw_affiliation_strings":["IRIT, Université de Toulouse, CNRS, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT, Université de Toulouse, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4210160189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000651986","display_name":"Dylan Fagot","orcid":null},"institutions":[{"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/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dylan Fagot","raw_affiliation_strings":["IRIT, Université de Toulouse, CNRS, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT, Université de Toulouse, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4210160189"]}]},{"author_position":"last","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/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/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cedric Fevotte","raw_affiliation_strings":["IRIT, Université de Toulouse, CNRS, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT, Université de Toulouse, CNRS, Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4210160189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5412,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64024625,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1062","last_page":"1066"},"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":0.9995999932289124,"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/T11309","display_name":"Music and Audio Processing","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.8826265335083008},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6659784913063049},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5689709186553955},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.5236403942108154},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.485227108001709},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4748975336551666},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.4424116015434265},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.44236406683921814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4409034252166748},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.4171972870826721},{"id":"https://openalex.org/keywords/hartley-transform","display_name":"Hartley transform","score":0.4130132794380188},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4121035933494568},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3450542092323303},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29232102632522583},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.20918366312980652},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.1744566559791565},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.09487348794937134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08578541874885559}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8826265335083008},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6659784913063049},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5689709186553955},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.5236403942108154},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.485227108001709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4748975336551666},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.4424116015434265},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.44236406683921814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4409034252166748},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.4171972870826721},{"id":"https://openalex.org/C67757890","wikidata":"https://www.wikidata.org/wiki/Q1567607","display_name":"Hartley transform","level":5,"score":0.4130132794380188},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4121035933494568},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3450542092323303},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29232102632522583},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.20918366312980652},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.1744566559791565},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.09487348794937134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08578541874885559},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/eusipco.2018.8553569","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco.2018.8553569","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 26th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1981745143","https://openalex.org/W1983821361","https://openalex.org/W2039844283","https://openalex.org/W2113154266","https://openalex.org/W2114508388","https://openalex.org/W2141039087","https://openalex.org/W2156529323","https://openalex.org/W2162514423","https://openalex.org/W2963443859","https://openalex.org/W2963906950"],"related_works":["https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W2146544734","https://openalex.org/W2075222291"],"abstract_inverted_index":{"Nonnegative":[0],"matrix":[1,107],"factorization":[2,17],"(NMF)":[3],"is":[4,47,108],"the":[5,16,44,51,56,62,76,105,127],"state-of-the-art":[6],"approach":[7,102,121],"to":[8,58,126,138],"unsupervised":[9],"audio":[10,145],"source":[11],"separation.":[12],"It":[13],"relies":[14],"on":[15],"of":[18,27,78,115,134],"a":[19,25,85,99,111],"given":[20],"short-time":[21,45],"frequency":[22],"transform":[23,37,46,57],"into":[24],"dictionary":[26],"spectral":[28],"patterns":[29],"and":[30,144],"an":[31,70],"activation":[32],"matrix.":[33],"Recently,":[34],"we":[35,83,97],"introduced":[36],"learning":[38],"for":[39,81],"NMF":[40],"(TL-NMF),":[41],"in":[42,90,103,130,132],"which":[43,82,104],"learnt":[48],"together":[49],"with":[50,136,142],"nonnegative":[52],"factors.":[53],"We":[54],"imposed":[55],"be":[59],"orthogonal":[60,79,106],"likewise":[61],"usual":[63],"Fourier":[64],"or":[65],"Cosine":[66],"transform.":[67],"TL-NMF":[68],"yields":[69],"original":[71],"non-convex":[72],"optimization":[73],"problem":[74],"over":[75],"manifold":[77],"matrices,":[80],"proposed":[84],"projected":[86],"gradient":[87,128],"descent":[88],"algorithm":[89],"our":[91],"previous":[92],"work.":[93],"In":[94],"this":[95],"contribution":[96],"describe":[98],"new":[100,120],"Jacobi":[101],"represented":[109],"as":[110,124,140],"randomly":[112],"chosen":[113],"product":[114],"elementary":[116],"Givens":[117],"matrices.":[118],"The":[119],"performs":[122],"favorably":[123],"compared":[125],"approach,":[129],"particular":[131],"terms":[133],"robustness":[135],"respect":[137],"initialization,":[139],"illustrated":[141],"synthetic":[143],"decomposition":[146],"experiments.":[147]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}