{"id":"https://openalex.org/W3210186461","doi":"https://doi.org/10.1109/tmm.2021.3124087","title":"Efficient and Differentiable Low-Rank Matrix Completion With Back Propagation","display_name":"Efficient and Differentiable Low-Rank Matrix Completion With Back Propagation","publication_year":2021,"publication_date":"2021-11-02","ids":{"openalex":"https://openalex.org/W3210186461","doi":"https://doi.org/10.1109/tmm.2021.3124087","mag":"3210186461"},"language":"en","primary_location":{"id":"doi:10.1109/tmm.2021.3124087","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmm.2021.3124087","pdf_url":null,"source":{"id":"https://openalex.org/S137030581","display_name":"IEEE Transactions on Multimedia","issn_l":"1520-9210","issn":["1520-9210","1941-0077"],"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 Multimedia","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/A5084849129","display_name":"Zhaoliang Chen","orcid":"https://orcid.org/0000-0002-7832-908X"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaoliang Chen","raw_affiliation_strings":["College of Computer and Data Science, Fuzhou University, Fuzhou, China","Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-7832-908X","affiliations":[{"raw_affiliation_string":"College of Computer and Data Science, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]},{"raw_affiliation_string":"Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079063216","display_name":"Jie Yao","orcid":"https://orcid.org/0000-0002-5863-3586"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Yao","raw_affiliation_strings":["College of Computer and Data Science, Fuzhou University, Fuzhou, China","Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Data Science, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]},{"raw_affiliation_string":"Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050524397","display_name":"Guobao Xiao","orcid":"https://orcid.org/0000-0003-2928-8100"},"institutions":[{"id":"https://openalex.org/I354108","display_name":"Minjiang University","ror":"https://ror.org/00s7tkw17","country_code":"CN","type":"education","lineage":["https://openalex.org/I354108"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guobao Xiao","raw_affiliation_strings":["College of Computer and Control Engineering, Minjiang University, Fuzhou, China","Fujian Provincial Key Laboratory of Information Processing and Intelligent Control, Minjiang University, Fuzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-2928-8100","affiliations":[{"raw_affiliation_string":"College of Computer and Control Engineering, Minjiang University, Fuzhou, China","institution_ids":["https://openalex.org/I354108"]},{"raw_affiliation_string":"Fujian Provincial Key Laboratory of Information Processing and Intelligent Control, Minjiang University, Fuzhou, China","institution_ids":["https://openalex.org/I354108"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100604225","display_name":"Shiping Wang","orcid":"https://orcid.org/0000-0001-5195-9682"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shiping Wang","raw_affiliation_strings":["College of Computer and Data Science, Fuzhou University, Fuzhou, China","Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-5195-9682","affiliations":[{"raw_affiliation_string":"College of Computer and Data Science, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]},{"raw_affiliation_string":"Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, China","institution_ids":["https://openalex.org/I80947539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8255,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.83524958,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":null,"first_page":"228","last_page":"242"},"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":0.9955999851226807,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.992900013923645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.714580774307251},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.680200457572937},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6151756644248962},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.51333087682724},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.505746603012085},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.46822023391723633},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.46053341031074524},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4554550051689148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4316655993461609},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4285505414009094},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.41366612911224365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.402580201625824},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3947540521621704},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38116490840911865},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20887872576713562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20603623986244202},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12190660834312439}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.714580774307251},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.680200457572937},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6151756644248962},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.51333087682724},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.505746603012085},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.46822023391723633},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.46053341031074524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4554550051689148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4316655993461609},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4285505414009094},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.41366612911224365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.402580201625824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3947540521621704},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38116490840911865},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20887872576713562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20603623986244202},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12190660834312439},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tmm.2021.3124087","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmm.2021.3124087","pdf_url":null,"source":{"id":"https://openalex.org/S137030581","display_name":"IEEE Transactions on Multimedia","issn_l":"1520-9210","issn":["1520-9210","1941-0077"],"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 Multimedia","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1353530241","display_name":null,"funder_award_id":"U1705262","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W195665135","https://openalex.org/W1482071412","https://openalex.org/W1860736741","https://openalex.org/W1965125844","https://openalex.org/W1969698720","https://openalex.org/W1980500788","https://openalex.org/W2022451443","https://openalex.org/W2027982384","https://openalex.org/W2074682976","https://openalex.org/W2075547019","https://openalex.org/W2113802117","https://openalex.org/W2118550318","https://openalex.org/W2187214659","https://openalex.org/W2339666411","https://openalex.org/W2505029951","https://openalex.org/W2561455088","https://openalex.org/W2752077201","https://openalex.org/W2752190933","https://openalex.org/W2768166594","https://openalex.org/W2780100774","https://openalex.org/W2798559986","https://openalex.org/W2883367876","https://openalex.org/W2884847196","https://openalex.org/W2903665338","https://openalex.org/W2921396149","https://openalex.org/W2940460948","https://openalex.org/W2962791795","https://openalex.org/W2963218026","https://openalex.org/W2963315679","https://openalex.org/W2963885538","https://openalex.org/W2964258799","https://openalex.org/W2970522139","https://openalex.org/W2987271886","https://openalex.org/W2995650332","https://openalex.org/W2998673651","https://openalex.org/W3003365835","https://openalex.org/W3009518004","https://openalex.org/W3035115225","https://openalex.org/W3036906866","https://openalex.org/W3038662035","https://openalex.org/W3041435406","https://openalex.org/W3094373624","https://openalex.org/W3098306969","https://openalex.org/W3100203369","https://openalex.org/W3102415113","https://openalex.org/W3114863340","https://openalex.org/W3133501200","https://openalex.org/W3160988939","https://openalex.org/W3195106575","https://openalex.org/W4295021216","https://openalex.org/W6676611517","https://openalex.org/W6680012447","https://openalex.org/W6682042988","https://openalex.org/W6703697878","https://openalex.org/W6710575211","https://openalex.org/W6729455701","https://openalex.org/W6737558694","https://openalex.org/W6762973898","https://openalex.org/W6763624801"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W4382583540","https://openalex.org/W2148568324","https://openalex.org/W1990844505","https://openalex.org/W1607100495","https://openalex.org/W4378770618","https://openalex.org/W4386721910","https://openalex.org/W2038393145","https://openalex.org/W2059545631","https://openalex.org/W2010100052"],"abstract_inverted_index":{"The":[0,234],"low-rank":[1,34,40,153,256],"matrix":[2,20,41,125],"completion":[3],"has":[4],"gained":[5],"rapidly":[6],"increasing":[7],"attention":[8],"from":[9,169],"researchers":[10],"in":[11,21,142,210,226,244],"recent":[12],"years":[13],"for":[14],"its":[15],"efficient":[16,148],"recovery":[17,230],"of":[18,39,50,69,76,109,114,136,173,198,228,240,246],"the":[19,28,37,46,59,77,85,107,123,134,163,170,177,186,204,211,238,241],"various":[22],"fields.":[23],"Numerous":[24],"studies":[25,70],"have":[26,71],"exploited":[27],"popular":[29],"neural":[30],"networks":[31],"to":[32,45,56,73,105,161,184,195,216],"yield":[33],"outputs":[35],"under":[36],"framework":[38,156,179,213,243],"factorization.":[42],"However,":[43],"due":[44],"discontinuity":[47],"and":[48,132,189,206,231,249],"nonconvexity":[49],"rank":[51,60,78],"function,":[52,79,176],"it":[53,201],"is":[54,130],"difficult":[55],"directly":[57],"optimize":[58,162],"function":[61],"via":[62,91],"back":[63,92,159],"propagation.":[64],"Although":[65],"a":[66,191,217],"large":[67],"number":[68],"attempted":[72],"find":[74],"relaxations":[75],"e.g.,":[80],"Schatten-$p$norm,":[81],"they":[82],"still":[83,101],"face":[84],"following":[86],"issues":[87],"when":[88],"updating":[89],"parameters":[90,209],"propagation:":[93],"1)":[94],"These":[95],"methods":[96],"or":[97],"surrogate":[98,116,175],"functions":[99,117],"are":[100,261],"non-differentiable,":[102],"bringing":[103],"obstacles":[104],"deriving":[106],"gradients":[108],"trainable":[110],"variables.":[111],"2)":[112],"Most":[113],"these":[115,140],"perform":[118],"singular":[119,181],"value":[120,182],"decomposition":[121,183],"upon":[122],"original":[124,171],"at":[126],"each":[127],"iteration,":[128],"which":[129],"time-consuming":[131],"blocks":[133],"propagation":[135,160,188],"gradients.":[137],"To":[138],"address":[139],"problems,":[141],"this":[143,174],"paper,":[144],"we":[145,222],"develop":[146],"an":[147],"block-wise":[149,192],"model":[150],"dubbed":[151],"differentiable":[152],"learning":[154,193,250],"(DLRL)":[155],"that":[157],"adopts":[158],"Multi-Schatten-$p$norm":[164],"Surrogate":[165],"(MSS)":[166],"function.":[167,220],"Distinct":[168],"optimization":[172,257],"proposed":[178,212,242],"avoids":[180],"admit":[185],"gradient":[187],"builds":[190],"scheme":[194],"minimize":[196],"values":[197],"Schatten-$p$norms.":[199],"Accordingly,":[200],"speeds":[202],"up":[203],"computation":[205],"makes":[207],"all":[208],"learnable":[214],"according":[215],"predefined":[218],"loss":[219],"Finally,":[221],"conduct":[223],"substantial":[224],"experiments":[225],"terms":[227,245],"image":[229],"collaborative":[232],"filtering.":[233],"experimental":[235],"results":[236],"verify":[237],"superiority":[239],"both":[247],"runtimes":[248],"performance":[251],"compared":[252],"with":[253],"other":[254],"state-of-the-art":[255],"methods.":[258],"Our":[259],"codes":[260],"available":[262],"athttps://github.com/chenzl23/DLRL.":[263]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}