{"id":"https://openalex.org/W2126447985","doi":"https://doi.org/10.1109/tsp.2012.2190410","title":"Fast Nonnegative Matrix/Tensor Factorization Based on Low-Rank Approximation","display_name":"Fast Nonnegative Matrix/Tensor Factorization Based on Low-Rank Approximation","publication_year":2012,"publication_date":"2012-03-08","ids":{"openalex":"https://openalex.org/W2126447985","doi":"https://doi.org/10.1109/tsp.2012.2190410","mag":"2126447985"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2190410","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2190410","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/A5090101808","display_name":"Guoxu Zhou","orcid":"https://orcid.org/0000-0003-1187-577X"},"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"]},{"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":true,"raw_author_name":"Guoxu Zhou","raw_affiliation_strings":["Laboratory for Advanced Brain Signal Processing, RIKEN, Brain Science Institute, RIKEN, Wako, Saitama, Japan","School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"Laboratory for Advanced Brain Signal Processing, RIKEN, Brain Science Institute, RIKEN, Wako, Saitama, Japan","institution_ids":["https://openalex.org/I2800939219"]},{"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/A5018676117","display_name":"Andrzej Cichocki","orcid":"https://orcid.org/0000-0002-8364-7226"},"institutions":[{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"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","PL"],"is_corresponding":false,"raw_author_name":"Andrzej Cichocki","raw_affiliation_strings":["RIKEN Brain Science Institute, Saitama, Japan","Systems Research Institute, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"RIKEN Brain Science Institute, Saitama, Japan","institution_ids":["https://openalex.org/I2800939219"]},{"raw_affiliation_string":"Systems Research Institute, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043262479","display_name":"Shengli Xie","orcid":"https://orcid.org/0000-0003-2041-5214"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengli Xie","raw_affiliation_strings":["Faculty of Automation, Guangdong University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"Faculty of Automation, Guangdong University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I139024713"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090101808"],"corresponding_institution_ids":["https://openalex.org/I2800939219","https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":6.8065,"has_fulltext":false,"cited_by_count":160,"citation_normalized_percentile":{"value":0.97770701,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"60","issue":"6","first_page":"2928","last_page":"2940"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10575","display_name":"Wireless Communication Networks Research","score":0.9739999771118164,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9412000179290771,"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":0.8988561630249023},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6927037239074707},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.6359027624130249},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5873383283615112},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5625264644622803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4739546775817871},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.47121113538742065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.463284432888031},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46299538016319275},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.46035096049308777},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.41893020272254944},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4167563021183014},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4163857102394104},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3633146286010742},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.297079861164093},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07432618737220764},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.07011458277702332}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8988561630249023},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6927037239074707},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.6359027624130249},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5873383283615112},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5625264644622803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4739546775817871},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.47121113538742065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.463284432888031},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46299538016319275},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.46035096049308777},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.41893020272254944},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4167563021183014},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4163857102394104},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3633146286010742},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.297079861164093},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07432618737220764},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.07011458277702332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2012.2190410","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2190410","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W191001584","https://openalex.org/W1246381107","https://openalex.org/W1530028809","https://openalex.org/W1600936177","https://openalex.org/W1902027874","https://openalex.org/W1963826206","https://openalex.org/W1970576574","https://openalex.org/W1973246170","https://openalex.org/W1999352252","https://openalex.org/W2000215628","https://openalex.org/W2001141328","https://openalex.org/W2013912476","https://openalex.org/W2017288758","https://openalex.org/W2018282388","https://openalex.org/W2024165284","https://openalex.org/W2026034143","https://openalex.org/W2057261601","https://openalex.org/W2059745395","https://openalex.org/W2076566842","https://openalex.org/W2103056111","https://openalex.org/W2108119513","https://openalex.org/W2108837778","https://openalex.org/W2110096996","https://openalex.org/W2114475573","https://openalex.org/W2117756735","https://openalex.org/W2118718620","https://openalex.org/W2120565458","https://openalex.org/W2120816706","https://openalex.org/W2121739212","https://openalex.org/W2125779688","https://openalex.org/W2126337883","https://openalex.org/W2132538571","https://openalex.org/W2135029798","https://openalex.org/W2144719328","https://openalex.org/W2145962650","https://openalex.org/W2150102617","https://openalex.org/W2161077892","https://openalex.org/W2168103112","https://openalex.org/W2403545325","https://openalex.org/W2404400936","https://openalex.org/W2492794003","https://openalex.org/W2522330017","https://openalex.org/W2950256799","https://openalex.org/W2951443864","https://openalex.org/W3118552534","https://openalex.org/W4230985103","https://openalex.org/W4253284464","https://openalex.org/W6677759377","https://openalex.org/W6681875376","https://openalex.org/W6713487064"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W2037504162","https://openalex.org/W4390394189","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2539013788","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W2075222291"],"abstract_inverted_index":{"Nonnegative":[0],"matrix":[1,33],"factorization":[2],"(NMF)":[3],"algorithms":[4,85,151],"often":[5],"suffer":[6],"from":[7],"slow":[8],"convergence":[9],"speed":[10],"due":[11],"to":[12,35,49,69,78,169,173],"the":[13,80,94,110,116,128,134,163,170,184,187,201,206],"nonnegativity":[14],"constraints,":[15],"especially":[16],"for":[17],"large-scale":[18],"problems.":[19],"Low-rank":[20],"approximation":[21,66],"methods":[22],"such":[23],"as":[24,54,153,155],"principle":[25],"component":[26],"analysis":[27],"(PCA)":[28],"are":[29,98,157],"widely":[30],"used":[31],"in":[32,57,127,137],"factorizations":[34],"suppress":[36,89],"noise,":[37],"reduce":[38,79],"computational":[39,81],"complexity":[40,82],"and":[41,114,197,203],"memory":[42],"requirements.":[43],"However,":[44],"they":[45,55,156],"cannot":[46],"be":[47,145],"applied":[48],"NMF":[50,70,84,150],"directly":[51],"so":[52],"far":[53],"result":[56],"factors":[58],"with":[59],"mixed":[60],"signs.":[61],"In":[62,92],"this":[63],"paper,":[64],"low-rank":[65],"is":[67,74,109,115,124,133,167,191],"introduced":[68],"(named":[71],"lraNMF),":[72],"which":[73,132],"not":[75],"only":[76],"able":[77],"of":[83,106,112,119,165,189,205],"significantly,":[86],"but":[87],"also":[88,144],"bipolar":[90],"noise.":[91],"fact,":[93],"new":[95],"update":[96,141],"rules":[97,142],"typically":[99],"about":[100],"times":[101],"faster":[102],"than":[103],"traditional":[104],"ones":[105],"NMF,":[107],"here":[108],"number":[111],"observations":[113],"low":[117],"rank":[118],"latent":[120],"factors.":[121],"Therefore":[122],"lraNMF":[123,166],"particularly":[125],"efficient":[126],"case":[129,136],"where":[130],",":[131],"general":[135],"NMF.":[138],"The":[139],"proposed":[140,185,207],"can":[143],"incorporated":[146],"into":[147],"most":[148],"existing":[149],"straightforwardly":[152],"long":[154],"based":[158],"on":[159,195],"Euclidean":[160],"distance.":[161],"Then":[162],"concept":[164],"generalized":[168],"tensor":[171],"field":[172],"perform":[174],"a":[175],"fast":[176],"sequential":[177],"nonnegative":[178],"Tucker":[179],"decomposition":[180],"(NTD).":[181],"By":[182],"applying":[183],"methods,":[186],"practicability":[188],"NMF/NTD":[190],"significantly":[192],"improved.":[193],"Simulations":[194],"synthetic":[196],"real":[198],"data":[199],"show":[200],"validity":[202],"efficiency":[204],"approaches.":[208]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":18},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-03-02T08:37:19.008085","created_date":"2025-10-10T00:00:00"}