{"id":"https://openalex.org/W2000157792","doi":"https://doi.org/10.1109/isit.2009.5205567","title":"Matrix completion from a few entries","display_name":"Matrix completion from a few entries","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2000157792","doi":"https://doi.org/10.1109/isit.2009.5205567","mag":"2000157792"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2009.5205567","doi":"https://doi.org/10.1109/isit.2009.5205567","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205567","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","is_traditional":true,"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/A5007082744","display_name":"Raghunandan Hulikal Keshavan","orcid":"https://orcid.org/0009-0001-7292-9965","observed_orcids":["https://orcid.org/0009-0001-7292-9965"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raghunandan H. Keshavan","raw_affiliation_strings":["EE Department, University of Stanford, Stanford, CA, USA","EE Department, Stanford University, CA 94304, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EE Department, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"EE Department, Stanford University, CA 94304, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028243041","display_name":"Sewoong Oh","orcid":"https://orcid.org/0000-0002-8975-8306","observed_orcids":["https://orcid.org/0000-0002-8975-8306"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sewoong Oh","raw_affiliation_strings":["EE Department, University of Stanford, Stanford, CA, USA","EE Department, Stanford University, CA 94304, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EE Department, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"EE Department, Stanford University, CA 94304, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011999109","display_name":"Andrea Montanari A","orcid":"https://orcid.org/0000-0002-0267-8574","observed_orcids":["https://orcid.org/0000-0002-0267-8574"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea Montanari","raw_affiliation_strings":["EE and Statistics Departments, University of Stanford, Stanford, CA, USA","EE and Statistics Departments, Stanford University, CA 94304, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EE and Statistics Departments, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"EE and Statistics Departments, Stanford University, CA 94304, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":39.0265,"has_fulltext":false,"cited_by_count":697,"citation_normalized_percentile":{"value":0.99969221,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"324","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.00019999999494757503,"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/T10136","display_name":"Statistical Methods and Inference","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/matrix-completion","display_name":"matrix completion","score":0.9879999756813049},{"id":"https://openalex.org/keywords/low-rank-matrix","display_name":"low-rank matrices","score":0.8009999990463257},{"id":"https://openalex.org/keywords/exact-reconstruction","display_name":"exact reconstruction","score":0.6079999804496765},{"id":"https://openalex.org/keywords/sparse-random-matrices","display_name":"sparse random matrices","score":0.7450000047683716},{"id":"https://openalex.org/keywords/matrix-spectrum","display_name":"matrix spectra","score":0.47699999809265137},{"id":"https://openalex.org/keywords/reconstruction-algorithms","display_name":"reconstruction algorithms","score":0.34200000762939453},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"compressed sensing","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7664495706558228},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6344858407974243},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5934572219848633},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5778669118881226},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5634936094284058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5259761214256287},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4676349461078644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.420405775308609},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3479907512664795},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/isit.2009.5205567","doi":"https://doi.org/10.1109/isit.2009.5205567","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205567","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8624150147","display_name":"CAREER:  New Information Processing Techniques from Statistical Physics and Probability Theory","funder_award_id":"0743978","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1573301526","https://openalex.org/W1918870341","https://openalex.org/W1969811075","https://openalex.org/W1970950689","https://openalex.org/W1979750072","https://openalex.org/W1982114217","https://openalex.org/W2011359124","https://openalex.org/W2021145763","https://openalex.org/W2021680564","https://openalex.org/W2026709222","https://openalex.org/W2031327377","https://openalex.org/W2045512849","https://openalex.org/W2047071281","https://openalex.org/W2047537297","https://openalex.org/W2057531168","https://openalex.org/W2065569293","https://openalex.org/W2103972604","https://openalex.org/W2118550318","https://openalex.org/W2119367754","https://openalex.org/W2120316325","https://openalex.org/W2124608575","https://openalex.org/W2134332047","https://openalex.org/W2145096794","https://openalex.org/W2146130798","https://openalex.org/W2158923808","https://openalex.org/W2296616510","https://openalex.org/W2339666411","https://openalex.org/W2611328865","https://openalex.org/W2949834189","https://openalex.org/W2951927428","https://openalex.org/W2952066970","https://openalex.org/W4210731599","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W1621177609","https://openalex.org/W7099676438","https://openalex.org/W2069652865","https://openalex.org/W7098286444","https://openalex.org/W2810415161","https://openalex.org/W2586408739","https://openalex.org/W3010434925","https://openalex.org/W2169978421","https://openalex.org/W2124608575","https://openalex.org/W7099692086"],"abstract_inverted_index":{"Let":[0],"M":[1,33,57],"be":[2,64],"an":[3,28],"n\u00bf":[4],"\u00d7":[5],"n":[6],"matrix":[7],"of":[8,21,79,101,122,130,141],"rank":[9],"r":[10,53],"\u00bf":[11,48],"n,":[12],"and":[13,56,88,90,136],"assume":[14],"that":[15,31],"a":[16,82,128,131],"uniformly":[17],"random":[18,143],"subset":[19],"E":[20],"its":[22,113],"entries":[23,40],"is":[24,58,104],"observed.":[25],"We":[26],"describe":[27],"efficient":[29],"algorithm":[30,103],"reconstructs":[32],"from":[34,67],"|E|":[35,68],"=":[36,54,69],"O(r":[37],"n)":[38,72],"observed":[39],"with":[41],"relative":[42],"root":[43],"mean":[44],"square":[45],"error":[46],"RMSE":[47],"C(\u00bf)":[49],"(nr/|E|)1/2.":[50],"Further,":[51],"if":[52],"O(1)":[55],"sufficiently":[59],"unstructured,":[60],"then":[61],"it":[62],"can":[63],"reconstructed":[65],"exactly":[66],"O(n":[70],"log":[71,106],"entries.":[73],"This":[74],"settles":[75],"(in":[76],"the":[77,93,110,120,139],"case":[78],"bounded":[80],"rank)":[81],"question":[83],"left":[84],"open":[85],"by":[86,134],"Candes":[87],"Recht":[89],"improves":[91],"over":[92],"guarantees":[94],"for":[95,115],"their":[96],"reconstruction":[97],"algorithm.":[98],"The":[99],"complexity":[100],"our":[102],"O(|E|r":[105],"n),":[107],"which":[108],"opens":[109],"way":[111],"to":[112],"use":[114],"massive":[116],"data":[117],"sets.":[118],"In":[119],"process":[121],"proving":[123],"these":[124],"statements,":[125],"we":[126],"obtain":[127],"generalization":[129],"celebrated":[132],"result":[133],"Friedman-Kahn-Szemeredi":[135],"Feige-Ofek":[137],"on":[138],"spectrum":[140],"sparse":[142],"matrices.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":46},{"year":2020,"cited_by_count":50},{"year":2019,"cited_by_count":85},{"year":2018,"cited_by_count":76},{"year":2017,"cited_by_count":64},{"year":2016,"cited_by_count":71},{"year":2015,"cited_by_count":62},{"year":2014,"cited_by_count":47},{"year":2013,"cited_by_count":38},{"year":2012,"cited_by_count":40}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}