{"id":"https://openalex.org/W2089917999","doi":"https://doi.org/10.1109/lsp.2014.2371895","title":"Two Efficient Algorithms for Approximately Orthogonal Nonnegative Matrix Factorization","display_name":"Two Efficient Algorithms for Approximately Orthogonal Nonnegative Matrix Factorization","publication_year":2014,"publication_date":"2014-11-20","ids":{"openalex":"https://openalex.org/W2089917999","doi":"https://doi.org/10.1109/lsp.2014.2371895","mag":"2089917999"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2014.2371895","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2014.2371895","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","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/A5107839929","display_name":"Bo Li","orcid":"https://orcid.org/0009-0001-4607-5329"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo Li","raw_affiliation_strings":["School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090101808","display_name":"Guoxu Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I139024713","display_name":"Guangdong University of Technology","ror":"https://ror.org/04azbjn80","country_code":"CN","type":"education","lineage":["https://openalex.org/I139024713"]},{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]}],"countries":["CN","JP"],"is_corresponding":false,"raw_author_name":"Guoxu Zhou","raw_affiliation_strings":["Department of Automation, Guangdong University of Technology, Guangzhou, China","RIKEN, Brain Science Institute, Wako-shi, Saitama, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]},{"raw_affiliation_string":"RIKEN, Brain Science Institute, Wako-shi, Saitama, Japan","institution_ids":["https://openalex.org/I2800939219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018676117","display_name":"Andrzej Cichocki","orcid":"https://orcid.org/0000-0002-8364-7226"},"institutions":[{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Andrzej Cichocki","raw_affiliation_strings":["RIKEN, Brain Science Institute, Wako-shi, Saitama, Japan"],"affiliations":[{"raw_affiliation_string":"RIKEN, Brain Science Institute, Wako-shi, Saitama, Japan","institution_ids":["https://openalex.org/I2800939219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5107839929"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":2.7178,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.92527193,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"22","issue":"7","first_page":"843","last_page":"846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9929999709129333,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9929999709129333,"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9678000211715698,"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/T13890","display_name":"Remote Sensing and Land Use","score":0.9564999938011169,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"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":0.9087586402893066},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.9077889919281006},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6636101603507996},{"id":"https://openalex.org/keywords/orthogonal-matrix","display_name":"Orthogonal matrix","score":0.6042940020561218},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.601005494594574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5447567105293274},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.49497145414352417},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.49027374386787415},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4806298613548279},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.45640361309051514},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4104975461959839},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23776307702064514},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.1558179259300232},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.1352630853652954}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.9087586402893066},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.9077889919281006},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6636101603507996},{"id":"https://openalex.org/C44292817","wikidata":"https://www.wikidata.org/wiki/Q333871","display_name":"Orthogonal matrix","level":3,"score":0.6042940020561218},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.601005494594574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5447567105293274},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.49497145414352417},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.49027374386787415},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4806298613548279},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.45640361309051514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4104975461959839},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23776307702064514},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1558179259300232},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.1352630853652954},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2014.2371895","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2014.2371895","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1935793623","display_name":null,"funder_award_id":"26730125","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W191001584","https://openalex.org/W1970039276","https://openalex.org/W2043545458","https://openalex.org/W2101139104","https://openalex.org/W2108840817","https://openalex.org/W2113076747","https://openalex.org/W2114475573","https://openalex.org/W2126447985","https://openalex.org/W2149846618","https://openalex.org/W2155151262","https://openalex.org/W2163927692","https://openalex.org/W2404400936","https://openalex.org/W3122703110","https://openalex.org/W4242209908"],"related_works":["https://openalex.org/W2153775038","https://openalex.org/W2152353763","https://openalex.org/W2065762479","https://openalex.org/W2127243424","https://openalex.org/W2302542513","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W2089917999"],"abstract_inverted_index":{"Nonnegative":[0],"matrix":[1],"factorization":[2],"(NMF)":[3],"with":[4,15,37,46],"orthogonality":[5,27],"constraints":[6],"is":[7],"quite":[8],"important":[9],"due":[10],"to":[11,70],"its":[12],"close":[13],"relation":[14],"the":[16,38,53,60],"K-means":[17],"clustering.":[18],"While":[19],"existing":[20],"algorithms":[21,49],"for":[22],"orthogonal":[23,43],"NMF":[24],"impose":[25],"strict":[26],"constraints,":[28],"in":[29],"this":[30],"letter":[31],"we":[32],"propose":[33],"a":[34],"penalty":[35],"method":[36],"aim":[39],"of":[40],"performing":[41],"approximately":[42],"NMF,":[44],"together":[45],"two":[47],"efficient":[48],"respectively":[50],"based":[51],"on":[52],"Hierarchical":[54],"Alternating":[55],"Least":[56],"Squares":[57],"(HALS)":[58],"and":[59,75,80],"Accelerated":[61],"Proximate":[62],"Gradient":[63],"(APG)":[64],"approaches.":[65],"Experimental":[66],"evidence":[67],"was":[68],"provided":[69],"show":[71],"their":[72],"high":[73],"efficiency":[74],"flexibility":[76],"by":[77],"using":[78],"synthetic":[79],"real-world":[81],"data.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
