{"id":"https://openalex.org/W2467768057","doi":"https://doi.org/10.48550/arxiv.1606.07315","title":"Nearly-optimal Robust Matrix Completion","display_name":"Nearly-optimal Robust Matrix Completion","publication_year":2016,"publication_date":"2016-06-23","ids":{"openalex":"https://openalex.org/W2467768057","doi":"https://doi.org/10.48550/arxiv.1606.07315","mag":"2467768057"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1606.07315","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1606.07315","pdf_url":"https://arxiv.org/pdf/1606.07315","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1606.07315","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055532477","display_name":"Yeshwanth Cherapanamjeri","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cherapanamjeri, Yeshwanth","raw_affiliation_strings":["University of California, Berkeley, Berkeley, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Berkeley, Berkeley, United States","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023098408","display_name":"Kartik Gupta","orcid":"https://orcid.org/0000-0002-2969-6828","observed_orcids":["https://orcid.org/0000-0002-2969-6828"]},"institutions":[{"id":"https://openalex.org/I4210124949","display_name":"Microsoft Research (India)","ror":"https://ror.org/02w7f3w92","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210124949"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gupta, Kartik","raw_affiliation_strings":["Microsoft Research India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research India","institution_ids":["https://openalex.org/I4210124949"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034432097","display_name":"Prateek Jain","orcid":"https://orcid.org/0000-0002-8191-9785","observed_orcids":["https://orcid.org/0000-0002-8191-9785","https://orcid.org/0000-0002-6410-9713"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I4210124949","display_name":"Microsoft Research (India)","ror":"https://ror.org/02w7f3w92","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210124949"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Jain, Prateek","raw_affiliation_strings":["Microsoft Research India","Microsoft (United States), Redmond, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research India","institution_ids":["https://openalex.org/I4210124949"]},{"raw_affiliation_string":"Microsoft (United States), Redmond, United States","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":73,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"797","last_page":"805"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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/T12303","display_name":"Tensor decomposition and applications","score":0.0,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robust-matrix-completion","display_name":"robust matrix completion","score":1.0},{"id":"https://openalex.org/keywords/low-rank-matrix-recovery","display_name":"low-rank matrix recovery","score":0.984000027179718},{"id":"https://openalex.org/keywords/projected-gradient-descent","display_name":"projected gradient descent","score":0.9160000085830688},{"id":"https://openalex.org/keywords/hard-thresholding","display_name":"hard thresholding","score":0.9800000190734863},{"id":"https://openalex.org/keywords/robust-pca","display_name":"robust principal component analysis","score":0.9259999990463257},{"id":"https://openalex.org/keywords/nearly-linear-time-algorithms","display_name":"near-linear time algorithms","score":0.7689999938011169},{"id":"https://openalex.org/keywords/time-complexity-bounds","display_name":"time complexity bounds","score":0.8830000162124634}],"concepts":[{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.9161866903305054},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6352712512016296},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5857112407684326},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.561514675617218},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.545667827129364},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5435985326766968},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.5000207424163818},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49911069869995117},{"id":"https://openalex.org/C2777749129","wikidata":"https://www.wikidata.org/wiki/Q17148469","display_name":"Robust principal component analysis","level":3,"score":0.4956115484237671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4872797727584839},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4655535817146301},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4467763900756836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41277170181274414},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17618480324745178},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16463473439216614},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.09078741073608398},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.06521886587142944},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.05564087629318237},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:1606.07315","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1606.07315","pdf_url":"https://arxiv.org/pdf/1606.07315","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,"listed_in":[],"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"},{"id":"mag:2467768057","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1606.07315.pdf","pdf_url":null,"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,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1606.07315","doi":"https://doi.org/10.48550/arxiv.1606.07315","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1606.07315","pdf_url":null,"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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2963739640","doi":null,"is_oa":false,"landing_page_url":"http://proceedings.mlr.press/v70/cherapanamjeri17a/cherapanamjeri17a.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306419644","display_name":"International Conference on Machine Learning","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":null,"is_accepted":false,"is_published":false,"raw_source_name":"International Conference on Machine Learning","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1606.07315","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1606.07315","pdf_url":"https://arxiv.org/pdf/1606.07315","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,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2467768057.pdf","grobid_xml":"https://content.openalex.org/works/W2467768057.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W152374499","https://openalex.org/W1573301526","https://openalex.org/W1712752320","https://openalex.org/W2003753589","https://openalex.org/W2110451175","https://openalex.org/W2120872934","https://openalex.org/W2415208755","https://openalex.org/W2611328865","https://openalex.org/W2798707604"],"related_works":["https://openalex.org/W6929385289","https://openalex.org/W2403076655","https://openalex.org/W1985488339","https://openalex.org/W2937195548","https://openalex.org/W4417302370","https://openalex.org/W176313890","https://openalex.org/W7100341077","https://openalex.org/W2479577152","https://openalex.org/W1920371452","https://openalex.org/W7095869873"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"consider":[4],"the":[5,13,48,65,95,101,113,130,166],"problem":[6,116],"of":[7,26,30,64,78,86,109,162],"Robust":[8],"Matrix":[9],"Completion":[10],"(RMC)":[11],"where":[12],"goal":[14],"is":[15,158],"to":[16,46,112,121],"recover":[17],"a":[18,23,32,40,54,62],"low-rank":[19,49,102],"matrix":[20,50,103,118,126],"by":[21],"observing":[22],"small":[24],"number":[25,77,85],"its":[27],"entries":[28,67],"out":[29],"which":[31],"few":[33,63],"can":[34],"be":[35],"arbitrarily":[36],"corrupted.":[37],"We":[38],"propose":[39],"simple":[41],"projected":[42,55],"gradient":[43,56],"descent":[44,57],"method":[45,154],"estimate":[47],"that":[51,147],"alternately":[52],"performs":[53],"step":[58],"and":[59,145],"cleans":[60],"up":[61],"corrupted":[66],"using":[68,74],"hard-thresholding.":[69],"Our":[70,88,138],"algorithm":[71,128],"solves":[72],"RMC":[73],"nearly":[75,83,122],"optimal":[76,84],"observations":[79],"as":[80,82],"well":[81],"corruptions.":[87],"result":[89,111],"also":[90],"implies":[91],"significant":[92],"improvement":[93],"over":[94],"existing":[96,132,167],"time":[97,124],"complexity":[98],"bounds":[99],"for":[100,129,149,155],"completion":[104],"problem.":[105],"Finally,":[106],"an":[107,159,160],"application":[108],"our":[110,142,153],"robust":[114,156],"PCA":[115,157],"(low-rank+sparse":[117],"separation)":[119],"leads":[120],"linear":[123],"(in":[125],"dimensions)":[127],"same;":[131],"state-of-the-art":[133],"methods":[134],"require":[135],"quadratic":[136],"time.":[137],"empirical":[139],"results":[140,144],"corroborate":[141],"theoretical":[143],"show":[146],"even":[148],"moderate":[150],"sized":[151],"problems,":[152],"order":[161],"magnitude":[163],"faster":[164],"than":[165],"methods.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-07-22T00:00:00"}
