{"id":"https://openalex.org/W4387869778","doi":"https://doi.org/10.1109/mlsp55844.2023.10285984","title":"Accelerated Algorithms For Nonlinear Matrix Decomposition With The Relu Function","display_name":"Accelerated Algorithms For Nonlinear Matrix Decomposition With The Relu Function","publication_year":2023,"publication_date":"2023-09-17","ids":{"openalex":"https://openalex.org/W4387869778","doi":"https://doi.org/10.1109/mlsp55844.2023.10285984"},"language":"en","primary_location":{"id":"doi:10.1109/mlsp55844.2023.10285984","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp55844.2023.10285984","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://orbi.umons.ac.be/bitstream/20.500.12907/46211/1/34%20Accelerated%20Algorithms%20for%20Nonlinear%20Matrix%20Decomposition%20with%20the%20ReLU%20function.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091957476","display_name":"Giovanni Seraghiti","orcid":null},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giovanni Seraghiti","raw_affiliation_strings":["University of Bologna, Piazza di Porta San Donato 5,Bologna,Italy,40126"],"affiliations":[{"raw_affiliation_string":"University of Bologna, Piazza di Porta San Donato 5,Bologna,Italy,40126","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091957477","display_name":"Atharva Awari","orcid":null},"institutions":[{"id":"https://openalex.org/I130929987","display_name":"University of Mons","ror":"https://ror.org/02qnnz951","country_code":"BE","type":"education","lineage":["https://openalex.org/I130929987"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Atharva Awari","raw_affiliation_strings":["University of Mons, Rue de Houdain 9, 7000 Mons,Belgium","University of Mons, Rue de Houdain 9, 7000 Mons, Belgium"],"affiliations":[{"raw_affiliation_string":"University of Mons, Rue de Houdain 9, 7000 Mons,Belgium","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"University of Mons, Rue de Houdain 9, 7000 Mons, Belgium","institution_ids":["https://openalex.org/I130929987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011982474","display_name":"Arnaud Vandaele","orcid":"https://orcid.org/0000-0001-8181-3043"},"institutions":[{"id":"https://openalex.org/I130929987","display_name":"University of Mons","ror":"https://ror.org/02qnnz951","country_code":"BE","type":"education","lineage":["https://openalex.org/I130929987"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Arnaud Vandaele","raw_affiliation_strings":["University of Mons, Rue de Houdain 9, 7000 Mons,Belgium","University of Mons, Rue de Houdain 9, 7000 Mons, Belgium"],"affiliations":[{"raw_affiliation_string":"University of Mons, Rue de Houdain 9, 7000 Mons,Belgium","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"University of Mons, Rue de Houdain 9, 7000 Mons, Belgium","institution_ids":["https://openalex.org/I130929987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044580481","display_name":"Margherita Porcelli","orcid":"https://orcid.org/0000-0003-0183-1204"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Margherita Porcelli","raw_affiliation_strings":["University of Bologna, Piazza di Porta San Donato 5,Bologna,Italy,40126"],"affiliations":[{"raw_affiliation_string":"University of Bologna, Piazza di Porta San Donato 5,Bologna,Italy,40126","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040368041","display_name":"Nicolas Gillis","orcid":"https://orcid.org/0000-0001-6423-6897"},"institutions":[{"id":"https://openalex.org/I130929987","display_name":"University of Mons","ror":"https://ror.org/02qnnz951","country_code":"BE","type":"education","lineage":["https://openalex.org/I130929987"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Nicolas Gillis","raw_affiliation_strings":["University of Mons, Rue de Houdain 9, 7000 Mons,Belgium","University of Mons, Rue de Houdain 9, 7000 Mons, Belgium"],"affiliations":[{"raw_affiliation_string":"University of Mons, Rue de Houdain 9, 7000 Mons,Belgium","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"University of Mons, Rue de Houdain 9, 7000 Mons, Belgium","institution_ids":["https://openalex.org/I130929987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5091957476"],"corresponding_institution_ids":["https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":0.6367,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63444995,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9993000030517578,"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/T10057","display_name":"Face and Expression Recognition","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6523547172546387},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.6462855935096741},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5105353593826294},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5042365789413452},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.48997870087623596},{"id":"https://openalex.org/keywords/approx","display_name":"Approx","score":0.4899217486381531},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.47873827815055847},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4504738748073578},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4473348557949066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41051509976387024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.308879554271698},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08201783895492554},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0780717134475708}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6523547172546387},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6462855935096741},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5105353593826294},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5042365789413452},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.48997870087623596},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.4899217486381531},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.47873827815055847},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4504738748073578},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4473348557949066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41051509976387024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.308879554271698},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08201783895492554},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0780717134475708},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/mlsp55844.2023.10285984","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mlsp55844.2023.10285984","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:orbi.umons.ac.be:20.500.12907/46211","is_oa":true,"landing_page_url":"https://orbi.umons.ac.be/handle/20.500.12907/46211","pdf_url":"https://orbi.umons.ac.be/bitstream/20.500.12907/46211/1/34%20Accelerated%20Algorithms%20for%20Nonlinear%20Matrix%20Decomposition%20with%20the%20ReLU%20function.pdf","source":{"id":"https://openalex.org/S7407055454","display_name":"ORBi UMONS","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE International Workshop on Machine Learning for Signal Processing (2023-09-17); IEEE International Workshop on Machine Learning for Signal Processing, 17-20 Septembre 2023","raw_type":"peer reviewed"},{"id":"pmh:oai:cris.unibo.it:11585/954248","is_oa":false,"landing_page_url":"https://hdl.handle.net/11585/954248","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:flore.unifi.it:2158/1351292","is_oa":false,"landing_page_url":"https://hdl.handle.net/2158/1351292","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"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":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:orbi.umons.ac.be:20.500.12907/46211","is_oa":true,"landing_page_url":"https://orbi.umons.ac.be/handle/20.500.12907/46211","pdf_url":"https://orbi.umons.ac.be/bitstream/20.500.12907/46211/1/34%20Accelerated%20Algorithms%20for%20Nonlinear%20Matrix%20Decomposition%20with%20the%20ReLU%20function.pdf","source":{"id":"https://openalex.org/S7407055454","display_name":"ORBi UMONS","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE International Workshop on Machine Learning for Signal Processing (2023-09-17); IEEE International Workshop on Machine Learning for Signal Processing, 17-20 Septembre 2023","raw_type":"peer reviewed"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387869778.pdf","grobid_xml":"https://content.openalex.org/works/W4387869778.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1902027874","https://openalex.org/W1988720110","https://openalex.org/W2004026774","https://openalex.org/W2007339694","https://openalex.org/W2029213856","https://openalex.org/W2118550318","https://openalex.org/W2804176448","https://openalex.org/W3114089334","https://openalex.org/W4225834014","https://openalex.org/W6735923916"],"related_works":["https://openalex.org/W1968270095","https://openalex.org/W4296478327","https://openalex.org/W1960072520","https://openalex.org/W2042397106","https://openalex.org/W4361730764","https://openalex.org/W3204184292","https://openalex.org/W1965029248","https://openalex.org/W2220129715","https://openalex.org/W2300902614","https://openalex.org/W183366865"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,73],"study":[4],"the":[5,37,41,51,63,109,121,128,133,136],"following":[6],"nonlinear":[7,32,46],"matrix":[8,16,21],"decomposition":[9],"(NMD)":[10],"problem:":[11],"given":[12],"a":[13,19,59,105,125],"sparse":[14],"nonnegative":[15],"X,":[17],"find":[18],"low-rank":[20],"$\\Theta$":[22],"such":[23],"that":[24,66],"$X\\approx":[25],"f(\\Theta)$,":[26],"where":[27,39],"f":[28],"is":[29],"an":[30,85,91,115],"element-wise":[31],"function.":[33,130],"We":[34,48,56,112,131],"focus":[35],"on":[36,120,139],"case":[38],"$f(\\cdot)=\\max(0,\\cdot)$,":[40],"rectified":[42],"linear":[43],"unit":[44],"(ReLU)":[45],"activation.":[47],"refer":[49],"to":[50,69,89,104],"corresponding":[52],"problem":[53],"as":[54,124],"ReLU-NMD.":[55,71],"first":[57],"provide":[58],"brief":[60],"overview":[61],"of":[62,135],"existing":[64,92],"approaches":[65],"were":[67],"developed":[68],"tackle":[70],"Then":[72],"introduce":[74],"two":[75],"new":[76],"algorithms:":[77],"(1)":[78],"aggressive":[79],"accelerated":[80],"NMD":[81,97],"(A-NMD)":[82],"which":[83,99],"uses":[84],"adaptive":[86],"Nesterov":[87],"extrapolation":[88],"accelerate":[90],"algorithm,":[93],"and":[94,102,141],"(2)":[95],"three-block":[96],"(3B-NMD)":[98],"parametrizes":[100],"$\\Theta=WH$":[101],"leads":[103],"significant":[106],"reduction":[107],"in":[108],"computational":[110],"cost.":[111],"also":[113],"propose":[114],"effective":[116],"initialization":[117],"strategy":[118],"based":[119],"nuclear":[122],"norm":[123],"proxy":[126],"for":[127],"rank":[129],"illustrate":[132],"effectiveness":[134],"proposed":[137],"algorithms":[138],"synthetic":[140],"real-world":[142],"data":[143],"sets.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}
