{"id":"https://openalex.org/W1572395709","doi":"https://doi.org/10.1109/tip.2015.2458176","title":"A Random Algorithm for Low-Rank Decomposition of Large-Scale Matrices With Missing Entries","display_name":"A Random Algorithm for Low-Rank Decomposition of Large-Scale Matrices With Missing Entries","publication_year":2015,"publication_date":"2015-07-17","ids":{"openalex":"https://openalex.org/W1572395709","doi":"https://doi.org/10.1109/tip.2015.2458176","mag":"1572395709","pmid":"https://pubmed.ncbi.nlm.nih.gov/26208344"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2015.2458176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2015.2458176","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1411.0814","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yiguang Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiguang Liu","raw_affiliation_strings":["Vision and Image Processing Laboratory, College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vision and Image Processing Laboratory, College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yinjie Lei","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinjie Lei","raw_affiliation_strings":["College of Electronics and Information Engineering, Sichuan University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Electronics and Information Engineering, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I24201400"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Chunguang Li","orcid":null},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunguang Li","raw_affiliation_strings":["Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Wenzheng Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenzheng Xu","raw_affiliation_strings":["Vision and Image Processing Laboratory, College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vision and Image Processing Laboratory, College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yifei Pu","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yifei Pu","raw_affiliation_strings":["Vision and Image Processing Laboratory, College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vision and Image Processing Laboratory, College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0028,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.774175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":"11","first_page":"4502","last_page":"4511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.38830000162124634,"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":0.38830000162124634,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.37630000710487366,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.09430000185966492,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7793999910354614},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6626999974250793},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6480000019073486},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.5922999978065491},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5049999952316284},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4959000051021576},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.4392000138759613},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.399399995803833},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.388700008392334}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7793999910354614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7332000136375427},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6626999974250793},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6480000019073486},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.5922999978065491},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5386999845504761},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5049999952316284},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4997999966144562},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4959000051021576},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.4392000138759613},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4334999918937683},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.365200012922287},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.3587000072002411},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.350600004196167},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3431999981403351},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.33959999680519104},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C41431624","wikidata":"https://www.wikidata.org/wiki/Q1053357","display_name":"Block size","level":3,"score":0.3131999969482422},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C2780985081","wikidata":"https://www.wikidata.org/wiki/Q676502","display_name":"Data Matrix","level":5,"score":0.2558000087738037},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2531999945640564}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2015.2458176","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2015.2458176","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:26208344","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26208344","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:arXiv.org:1411.0814","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1411.0814","pdf_url":"https://arxiv.org/pdf/1411.0814","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1411.0814","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1411.0814","pdf_url":"https://arxiv.org/pdf/1411.0814","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G125885159","display_name":null,"funder_award_id":"61411130133","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7002694999","display_name":null,"funder_award_id":"61179071","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7495127705","display_name":"\u57fa\u4e8e\u52a8\u529b\u7cfb\u7edf\u7684L1\u8303\u6570\u77e9\u9635\u4f4e\u79e9\u5206\u89e3\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"61173182","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1572395709.pdf","grobid_xml":"https://content.openalex.org/works/W1572395709.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1968691112","https://openalex.org/W1995273075","https://openalex.org/W1997201895","https://openalex.org/W1999844561","https://openalex.org/W2026057672","https://openalex.org/W2057590040","https://openalex.org/W2065476260","https://openalex.org/W2074125290","https://openalex.org/W2103305137","https://openalex.org/W2110531331","https://openalex.org/W2117756735","https://openalex.org/W2128438692","https://openalex.org/W2144730813","https://openalex.org/W2166163936","https://openalex.org/W2611015177","https://openalex.org/W6679973066","https://openalex.org/W6684754188","https://openalex.org/W6929385289"],"related_works":[],"abstract_inverted_index":{"A":[0],"random":[1,120,216],"submatrix":[2,184],"method":[3],"(RSM)":[4],"is":[5,36,147,237],"proposed":[6],"to":[7,75,139,177,256],"calculate":[8],"the":[9,18,56,62,79,122,125,136,142,151,153,158,165,179,183,187,194,244,257],"low-rank":[10],"decomposition":[11],"U(m\u00d7r)V(n\u00d7r)(T)":[12],"(r":[13],"<":[14,31],"m,":[15],"n)":[16],"of":[17,64,141,182,193,197],"matrix":[19],"Y\u2208R(m\u00d7n)":[20],"(assuming":[21],"m":[22],">":[23],"n":[24],"generally)":[25],"with":[26,51,99,128,164,219],"known":[27,82,92],"entry":[28],"percentage":[29],"0":[30],"\u03c1":[32],"\u2264":[33],"1.":[34],"RSM":[35,60,236],"very":[37],"fast":[38],"as":[39,69,222,232],"only":[40,70],"O(mr(2)\u03c1(r))":[41],"or":[42,103,108,157,190,254],"O(n(3)\u03c1(3r))":[43],"floating-point":[44],"operations":[45],"(flops)":[46],"are":[47,84,94,169,202],"required,":[48],"compared":[49],"favorably":[50],"O(mnr+r(2)(m+n))":[52],"flops":[53],"required":[54],"by":[55,91,186],"state-of-the-art":[57,245],"algorithms.":[58,246],"Meanwhile,":[59],"has":[61,249],"advantage":[63],"a":[65,117,129],"small":[66],"memory":[67],"requirement":[68],"max(n(2),mr+nr)":[71],"real":[72,228],"values":[73,146,168],"need":[74],"be":[76,178,209],"saved.":[77],"With":[78],"assumption":[80],"that":[81,124,235],"entries":[83,93],"uniformly":[85],"distributed":[86],"in":[87],"Y,":[88],"submatrices":[89,201],"formed":[90,185],"randomly":[95,203],"selected":[96],"from":[97],"Y":[98],"statistical":[100],"size":[101],"k\u00d7n\u03c1(k)":[102],"m\u03c1(l)\u00d7l":[104],",":[105],"where":[106],"k":[107],"l":[109,191],"takes":[110],"r+1":[111],"usually.":[112],"We":[113],"propose":[114],"and":[115,206,226],"prove":[116],"theorem,":[118,152],"under":[119],"noises":[121],"probability":[123],"subspace":[126],"associated":[127,138,163],"smaller":[130],"singular":[131,145,161,167],"value":[132],"will":[133],"turn":[134],"into":[135],"space":[137],"anyone":[140],"r":[143],"largest":[144],"smaller.":[148],"Based":[149],"on":[150,215,227],"n\u03c1(k)-k":[154],"null":[155,180],"vectors":[156,162,175,181],"l-r":[159],"right":[160],"minor":[166],"calculated":[170],"for":[171],"each":[172],"submatrix.":[173],"The":[174,212],"ought":[176],"chosen":[188],"n\u03c1(k)":[189],"columns":[192],"ground":[195],"truth":[196],"V(T).":[198],"If":[199],"enough":[200],"chosen,":[204],"V":[205],"U":[207],"can":[208],"estimated":[210],"accordingly.":[211],"experimental":[213],"results":[214],"synthetic":[217],"matrices":[218],"sizes":[220],"such":[221,231],"13":[223],"1072":[224],"\u00d710(24)":[225],"data":[229],"sets":[230],"dinosaur":[233],"indicate":[234],"4.30":[238],"\u223c":[239],"197.95":[240],"times":[241],"faster":[242],"than":[243],"It,":[247],"meanwhile,":[248],"considerable":[250],"high":[251],"precision":[252],"achieving":[253],"approximating":[255],"best.":[258]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2016-06-24T00:00:00"}
