{"id":"https://openalex.org/W2592541154","doi":"https://doi.org/10.1137/140977898","title":"Optimal CUR Matrix Decompositions","display_name":"Optimal CUR Matrix Decompositions","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2592541154","doi":"https://doi.org/10.1137/140977898","mag":"2592541154"},"language":"en","primary_location":{"id":"doi:10.1137/140977898","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140977898","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5010385482","display_name":"Christos Boutsidis","orcid":null},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christos Boutsidis","raw_affiliation_strings":["IBM Research, Almaden, CA"],"affiliations":[{"raw_affiliation_string":"IBM Research, Almaden, CA","institution_ids":["https://openalex.org/I4210085935"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102861589","display_name":"David P. Woodruff","orcid":"https://orcid.org/0000-0002-2158-1380"},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David P. Woodruff","raw_affiliation_strings":["IBM Research, Almaden, CA"],"affiliations":[{"raw_affiliation_string":"IBM Research, Almaden, CA","institution_ids":["https://openalex.org/I4210085935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010385482"],"corresponding_institution_ids":["https://openalex.org/I4210085935"],"apc_list":null,"apc_paid":null,"fwci":8.1485,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.98528251,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"2","first_page":"543","last_page":"589"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9979000091552734,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/combinatorics","display_name":"Combinatorics","score":0.7354624271392822},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.7003873586654663},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6954146027565002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6817007064819336},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.6332583427429199},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.5454552173614502},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4726017117500305},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.4484701454639435},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43185022473335266},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.4116833508014679},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3421463966369629},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2281895875930786},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13911697268486023},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09512639045715332},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08391228318214417},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07087868452072144},{"id":"https://openalex.org/keywords/hankel-matrix","display_name":"Hankel matrix","score":0.06489130854606628},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.0502280592918396}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7354624271392822},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.7003873586654663},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6954146027565002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6817007064819336},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6332583427429199},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.5454552173614502},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4726017117500305},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.4484701454639435},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43185022473335266},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.4116833508014679},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3421463966369629},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2281895875930786},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13911697268486023},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09512639045715332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08391228318214417},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07087868452072144},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.06489130854606628},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0502280592918396},{"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/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140977898","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140977898","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4096326766","display_name":null,"funder_award_id":"FA8750-12-C0323","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4713059963","display_name":null,"funder_award_id":"FA8750","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G7903834952","display_name":null,"funder_award_id":"XDATA","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"}],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1969720662","https://openalex.org/W1970576574","https://openalex.org/W1980191636","https://openalex.org/W1990044052","https://openalex.org/W1998269045","https://openalex.org/W2003690406","https://openalex.org/W2005904620","https://openalex.org/W2013442644","https://openalex.org/W2016527001","https://openalex.org/W2021604182","https://openalex.org/W2037757210","https://openalex.org/W2042465463","https://openalex.org/W2050580360","https://openalex.org/W2052207834","https://openalex.org/W2078465266","https://openalex.org/W2087644270","https://openalex.org/W2107599050","https://openalex.org/W2117756735","https://openalex.org/W2132582398","https://openalex.org/W2141696759","https://openalex.org/W2171810522","https://openalex.org/W2547648546","https://openalex.org/W3112410551"],"related_works":["https://openalex.org/W2782904003","https://openalex.org/W3121932492","https://openalex.org/W2776058083","https://openalex.org/W2118633810","https://openalex.org/W2150953077","https://openalex.org/W4226434912","https://openalex.org/W2002598339","https://openalex.org/W2920738921","https://openalex.org/W2133814741","https://openalex.org/W1995410415"],"abstract_inverted_index":{"The":[0],"CUR":[1,108],"decomposition":[2,109],"of":[3,20,25,38,43,91],"an":[4,11,29],"$m":[5,12,87],"\\times":[6,13,31,50,88],"n$":[7,23,32,89],"matrix":[8,15,33,53,58,62,90],"$A$":[9],"finds":[10],"c$":[14],"$C$":[16],"with":[17,28,35],"a":[18,36,48,107],"subset":[19,37],"$c":[21,49],"<":[22,40],"columns":[24],"$A,$":[26,44,63],"together":[27],"$r":[30,39],"$R$":[34],"m$":[41],"rows":[42],"as":[45,47],"well":[46],"r$":[51],"low-rank":[52],"$U$":[54],"such":[55,106],"that":[56,64],"the":[57,61,79,85,96,128],"$CUR$":[59],"approximates":[60],"is,":[65],"$\\|A":[66],"-":[67,74],"C":[68],"U":[69],"R\\|_{F}^2":[70],"\\leq":[71],"(1+\\varepsilon)":[72],"{}\\|A":[73],"A_k\\|_{F}^2$,":[75],"where":[76,110],"$\\|.\\|_{F}$":[77],"denotes":[78],"Frobenius":[80],"norm":[81],"and":[82,101,112,114,132],"$A_k$":[83],"is":[84],"best":[86],"rank":[92],"$k$":[93],"constructed":[94],"via":[95],"SVD.":[97],"We":[98],"present":[99],"input-sparsity-time":[100],"deterministic":[102],"algorithms":[103,123],"for":[104],"constructing":[105],"$c=O(k/\\varepsilon)$":[111],"$r=O(k/\\varepsilon)$":[113],"rank$(U)":[115],"=":[116],"k$.":[117],"Up":[118],"to":[119],"constant":[120],"factors,":[121],"our":[122],"are":[124],"simultaneously":[125],"optimal":[126],"in":[127],"values":[129],"$c,":[130],"r,$":[131],"rank$(U)$.":[133]},"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":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}