{"id":"https://openalex.org/W3214295422","doi":"https://doi.org/10.1109/tkde.2021.3125947","title":"A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization","display_name":"A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3214295422","doi":"https://doi.org/10.1109/tkde.2021.3125947","mag":"3214295422"},"language":"en","primary_location":{"id":"doi:10.1109/tkde.2021.3125947","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2021.3125947","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Knowledge and Data Engineering","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/A5100785848","display_name":"Li Xiao","orcid":"https://orcid.org/0000-0001-8513-6334"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiao Li","raw_affiliation_strings":["School of Data Science, The Chinese University of Hong Kong - Shenzhen, 407605 Shenzhen, Guangdong, China, (e-mail: lixiao0982@gmail.com)"],"affiliations":[{"raw_affiliation_string":"School of Data Science, The Chinese University of Hong Kong - Shenzhen, 407605 Shenzhen, Guangdong, China, (e-mail: lixiao0982@gmail.com)","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011989964","display_name":"Zhihui Zhu","orcid":"https://orcid.org/0000-0002-3856-0375"},"institutions":[{"id":"https://openalex.org/I131651094","display_name":"University of Denver","ror":"https://ror.org/04w7skc03","country_code":"US","type":"education","lineage":["https://openalex.org/I131651094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhihui Zhu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Denver, 2927 Denver, Colorado, United States, (e-mail: zhihui.zhu@du.edu)"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Denver, 2927 Denver, Colorado, United States, (e-mail: zhihui.zhu@du.edu)","institution_ids":["https://openalex.org/I131651094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033881291","display_name":"Qiuwei Li","orcid":"https://orcid.org/0000-0002-2306-6649"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiuwei Li","raw_affiliation_strings":["Department of Mathematics, UCLA, 8783 Los Angeles, California, United States, (e-mail: liqiuweiss@gmail.com)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, 8783 Los Angeles, California, United States, (e-mail: liqiuweiss@gmail.com)","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100399791","display_name":"Kai Liu","orcid":"https://orcid.org/0000-0001-5336-7939"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kai Liu","raw_affiliation_strings":["Computer Science Division, Clemson University, 2545 Clemson, South Carolina, United States, (e-mail: liukaizhijia@gmail.com)"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, Clemson University, 2545 Clemson, South Carolina, United States, (e-mail: liukaizhijia@gmail.com)","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100785848"],"corresponding_institution_ids":["https://openalex.org/I4210116924"],"apc_list":null,"apc_paid":null,"fwci":0.9607,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.77882353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9986000061035156,"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":0.9986000061035156,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9940999746322632,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9890000224113464,"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/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.8738614320755005},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5847485065460205},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5755547285079956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5547050833702087},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.5292263031005859},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5261746644973755},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5211625099182129},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4816819131374359},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4777989983558655},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4741344451904297},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46853795647621155},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4175769090652466},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36661654710769653},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2205745279788971},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07290002703666687}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8738614320755005},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5847485065460205},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5755547285079956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5547050833702087},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.5292263031005859},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5261746644973755},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5211625099182129},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4816819131374359},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4777989983558655},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4741344451904297},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46853795647621155},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4175769090652466},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36661654710769653},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2205745279788971},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07290002703666687},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tkde.2021.3125947","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2021.3125947","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Knowledge and Data Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1489499640","https://openalex.org/W1594523130","https://openalex.org/W1850275953","https://openalex.org/W1854811422","https://openalex.org/W1902027874","https://openalex.org/W1967138577","https://openalex.org/W2013029404","https://openalex.org/W2021361347","https://openalex.org/W2026034143","https://openalex.org/W2027982384","https://openalex.org/W2039844283","https://openalex.org/W2050968963","https://openalex.org/W2063790512","https://openalex.org/W2067931421","https://openalex.org/W2070135644","https://openalex.org/W2078853581","https://openalex.org/W2097521761","https://openalex.org/W2099779699","https://openalex.org/W2104819583","https://openalex.org/W2108119513","https://openalex.org/W2108840817","https://openalex.org/W2110096996","https://openalex.org/W2113359929","https://openalex.org/W2120816706","https://openalex.org/W2129732816","https://openalex.org/W2229285313","https://openalex.org/W2521548303","https://openalex.org/W2571268788","https://openalex.org/W2595304583","https://openalex.org/W2741901159","https://openalex.org/W2962881408","https://openalex.org/W2969761511","https://openalex.org/W3041063529","https://openalex.org/W4301014524","https://openalex.org/W6680012447","https://openalex.org/W6726669034","https://openalex.org/W6755058994"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","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":{"The":[0],"symmetric":[1,33,69,99,137],"Nonnegative":[2],"Matrix":[3],"Factorization":[4],"(NMF),":[5],"a":[6,72,94,104,131],"special":[7],"but":[8],"important":[9],"class":[10],"of":[11,106,121,134,160],"the":[12,32,45,48,63,68,77,89,97,118,135,158,161],"general":[13],"NMF,":[14],"has":[15],"found":[16],"numerous":[17],"applications":[18],"in":[19],"data":[20,146],"analysis":[21],"such":[22],"as":[23,37,39],"various":[24],"clustering":[25,150],"tasks.":[26],"Unfortunately,":[27],"designing":[28,80],"fast":[29],"algorithms":[30,108],"for":[31,40,79],"NMF":[34,70],"is":[35,123],"not":[36],"easy":[38],"its":[41],"nonsymmetric":[42,74,91],"counterpart,":[43],"since":[44],"latter":[46],"admits":[47],"splitting":[49],"property":[50],"that":[51,87,111],"allows":[52],"state-of-the-art":[53],"alternating-type":[54,82,107,162],"algorithms.":[55,83,163],"To":[56],"overcome":[57],"this":[58],"issue,":[59],"we":[60,102,140],"first":[61],"split":[62],"decision":[64],"variable":[65],"and":[66,109,125,147,156],"transform":[67],"to":[71,96,130,151],"penalized":[73,90],"one,":[75],"paving":[76],"way":[78],"efficient":[81],"We":[84],"then":[85],"show":[86,110],"solving":[88],"reformulation":[92],"returns":[93],"solution":[95],"original":[98,136],"NMF.":[100,138],"Moreover,":[101],"design":[103],"family":[105],"they":[112],"all":[113],"admit":[114],"strong":[115],"convergence":[116],"guarantee:":[117],"generated":[119],"sequence":[120],"iterates":[122],"convergent":[124],"converges":[126],"at":[127],"least":[128],"sublinearly":[129],"critical":[132],"point":[133],"Finally,":[139],"conduct":[141],"experiments":[142],"on":[143],"both":[144],"synthetic":[145],"real":[148],"image":[149],"support":[152],"our":[153],"theoretical":[154],"results":[155],"demonstrate":[157],"performance":[159]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
