{"id":"https://openalex.org/W2990876778","doi":"https://doi.org/10.1109/smc.2019.8913926","title":"Convergence Analysis of an SLF-NMU Algorithm for Non-negative Latent Factor Analysis on a High-Dimensional and Sparse Matrix","display_name":"Convergence Analysis of an SLF-NMU Algorithm for Non-negative Latent Factor Analysis on a High-Dimensional and Sparse Matrix","publication_year":2019,"publication_date":"2019-10-01","ids":{"openalex":"https://openalex.org/W2990876778","doi":"https://doi.org/10.1109/smc.2019.8913926","mag":"2990876778"},"language":"en","primary_location":{"id":"doi:10.1109/smc.2019.8913926","is_oa":false,"landing_page_url":"https://doi.org/10.1109/smc.2019.8913926","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Systems, Man and Cybernetics (SMC)","raw_type":"proceedings-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/A5010873564","display_name":"Zhigang Liu","orcid":"https://orcid.org/0000-0002-3669-3764"},"institutions":[{"id":"https://openalex.org/I4210123021","display_name":"Chongqing Institute of Green and Intelligent Technology","ror":"https://ror.org/031npqv35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210123021"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhigang Liu","raw_affiliation_strings":["Chongqing Engineering Research Center of Big Data Application for Smart Cities, and Chongqing Key Laboratory of Big Data and Intelligent Computing, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chongqing Engineering Research Center of Big Data Application for Smart Cities, and Chongqing Key Laboratory of Big Data and Intelligent Computing, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, China","institution_ids":["https://openalex.org/I4210123021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088955392","display_name":"Xin Luo","orcid":"https://orcid.org/0000-0002-1348-5305"},"institutions":[{"id":"https://openalex.org/I4210123021","display_name":"Chongqing Institute of Green and Intelligent Technology","ror":"https://ror.org/031npqv35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210123021"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Luo","raw_affiliation_strings":["Chongqing Engineering Research Center of Big Data Application for Smart Cities, and Chongqing Key Laboratory of Big Data and Intelligent Computing, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chongqing Engineering Research Center of Big Data Application for Smart Cities, and Chongqing Key Laboratory of Big Data and Intelligent Computing, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, China","institution_ids":["https://openalex.org/I4210123021"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210123021"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19091683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":null,"first_page":"1750","last_page":"1756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9771999716758728,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.974399983882904,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.7431731224060059},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7102946043014526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6096898317337036},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5832415819168091},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5630689859390259},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5091027617454529},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5089185237884521},{"id":"https://openalex.org/keywords/factor-analysis","display_name":"Factor analysis","score":0.41762447357177734},{"id":"https://openalex.org/keywords/factor","display_name":"Factor (programming language)","score":0.41049039363861084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27314382791519165},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2523585259914398},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.21371319890022278}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.7431731224060059},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7102946043014526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6096898317337036},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5832415819168091},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5630689859390259},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5091027617454529},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5089185237884521},{"id":"https://openalex.org/C10879293","wikidata":"https://www.wikidata.org/wiki/Q726474","display_name":"Factor analysis","level":2,"score":0.41762447357177734},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.41049039363861084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27314382791519165},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2523585259914398},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.21371319890022278},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/smc.2019.8913926","is_oa":false,"landing_page_url":"https://doi.org/10.1109/smc.2019.8913926","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Systems, Man and Cybernetics (SMC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1479822238","https://openalex.org/W1846534543","https://openalex.org/W1902027874","https://openalex.org/W1966286510","https://openalex.org/W1989529706","https://openalex.org/W1994292689","https://openalex.org/W1999047234","https://openalex.org/W2049633694","https://openalex.org/W2054141820","https://openalex.org/W2056398894","https://openalex.org/W2059745395","https://openalex.org/W2084327978","https://openalex.org/W2099779699","https://openalex.org/W2108119513","https://openalex.org/W2110096996","https://openalex.org/W2112284959","https://openalex.org/W2119523409","https://openalex.org/W2135029798","https://openalex.org/W2278138779","https://openalex.org/W2390938437","https://openalex.org/W2470039937","https://openalex.org/W2606637053","https://openalex.org/W2765820394","https://openalex.org/W2795974822","https://openalex.org/W2805046565","https://openalex.org/W2807151223","https://openalex.org/W2907017794","https://openalex.org/W2919538836","https://openalex.org/W2928382658","https://openalex.org/W3101457173","https://openalex.org/W6680012447"],"related_works":["https://openalex.org/W4238302630","https://openalex.org/W2089458918","https://openalex.org/W2604765381","https://openalex.org/W4320002724","https://openalex.org/W76439796","https://openalex.org/W2897827065","https://openalex.org/W2089386776","https://openalex.org/W2387708436","https://openalex.org/W3025509461","https://openalex.org/W3123146305"],"abstract_inverted_index":{"Non-negative":[0],"latent":[1,41],"factor":[2],"(NLF)":[3],"models":[4],"have":[5],"been":[6],"frequently":[7],"applied":[8],"to":[9,52,88,112],"information":[10],"extraction,":[11],"pattern":[12],"recognition,":[13],"and":[14,25,32,44],"community":[15],"detection.":[16],"An":[17],"NLF":[18,54,110],"model":[19,111],"can":[20,84],"well":[21],"represent":[22],"a":[23,62,89,115],"high-dimensional":[24],"sparse":[26],"(HiDS)":[27],"matrix":[28,63],"of":[29,75],"non-negative":[30,43],"data":[31],"efficiently":[33],"acquire":[34],"useful":[35],"knowledge":[36],"from":[37,100],"it.":[38],"A":[39],"single":[40],"factor-dependent,":[42],"multiplicative":[45],"update":[46],"(SLF-NMU)":[47],"algorithm":[48,107],"is":[49,64],"highly":[50],"efficient":[51],"build":[53],"model.":[55],"However,":[56],"its":[57,86],"convergence":[58,73,87],"ability":[59],"on":[60,96],"such":[61],"still":[65],"unveiled":[66],"in":[67],"theory.":[68],"This":[69],"paper":[70],"presents":[71],"the":[72],"property":[74],"an":[76,105,109],"SLF-NMU":[77,106],"algorithm.":[78],"We":[79],"theoretically":[80],"prove":[81],"that":[82,104],"it":[83],"guarantee":[85],"Karush-Kuhn-Tucher":[90],"(KKT)":[91],"stationary":[92],"point.":[93],"Empirical":[94],"studies":[95],"two":[97],"HiDS":[98],"matrices":[99],"practical":[101],"applications":[102],"indicate":[103],"make":[108],"converge":[113],"at":[114],"relatively":[116],"steady":[117],"state.":[118]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
