{"id":"https://openalex.org/W1997120656","doi":"https://doi.org/10.1145/1921632.1921639","title":"Fast Algorithms for Approximating the Singular Value Decomposition","display_name":"Fast Algorithms for Approximating the Singular Value Decomposition","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W1997120656","doi":"https://doi.org/10.1145/1921632.1921639","mag":"1997120656"},"language":"en","primary_location":{"id":"doi:10.1145/1921632.1921639","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1921632.1921639","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Knowledge Discovery from Data","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/A5049656925","display_name":"Aditya Krishna Menon","orcid":"https://orcid.org/0000-0002-1352-7106"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aditya Krishna Menon","raw_affiliation_strings":["University of California, San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038246567","display_name":"Charles Elkan","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles Elkan","raw_affiliation_strings":["University of California, San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":2.3913,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.87540309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"2","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9988999962806702,"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":0.9988999962806702,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9961000084877014,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9922000169754028,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8895593881607056},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.7118898034095764},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6147992610931396},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6053104400634766},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5580983757972717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5558103322982788},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5457096695899963},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5151190161705017},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5038658976554871},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4941146671772003},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.489928662776947},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4742119610309601},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.41142261028289795},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3595955967903137},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18110501766204834},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11902928352355957},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07097411155700684}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8895593881607056},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.7118898034095764},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6147992610931396},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6053104400634766},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5580983757972717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5558103322982788},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5457096695899963},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5151190161705017},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5038658976554871},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4941146671772003},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.489928662776947},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4742119610309601},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.41142261028289795},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3595955967903137},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18110501766204834},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11902928352355957},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07097411155700684},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"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/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1921632.1921639","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1921632.1921639","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Knowledge Discovery from Data","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W174106550","https://openalex.org/W203899762","https://openalex.org/W625640516","https://openalex.org/W1488435683","https://openalex.org/W1547044578","https://openalex.org/W1568377519","https://openalex.org/W1572352401","https://openalex.org/W1576481659","https://openalex.org/W1577871831","https://openalex.org/W1952127226","https://openalex.org/W1968691112","https://openalex.org/W1970576574","https://openalex.org/W1970950689","https://openalex.org/W1981745143","https://openalex.org/W1999935624","https://openalex.org/W2004026774","https://openalex.org/W2007399394","https://openalex.org/W2040387238","https://openalex.org/W2042465463","https://openalex.org/W2044610104","https://openalex.org/W2045390367","https://openalex.org/W2063392856","https://openalex.org/W2064980127","https://openalex.org/W2084439502","https://openalex.org/W2086486316","https://openalex.org/W2090898720","https://openalex.org/W2091352038","https://openalex.org/W2093432797","https://openalex.org/W2117026915","https://openalex.org/W2124659530","https://openalex.org/W2128220624","https://openalex.org/W2138451337","https://openalex.org/W2147927736","https://openalex.org/W2148694408","https://openalex.org/W2242394928","https://openalex.org/W3141273274","https://openalex.org/W4244219114","https://openalex.org/W4245049592","https://openalex.org/W4292023222","https://openalex.org/W4389615663","https://openalex.org/W4394729942"],"related_works":["https://openalex.org/W4366831400","https://openalex.org/W2158044763","https://openalex.org/W4221157149","https://openalex.org/W3206304544","https://openalex.org/W4298234822","https://openalex.org/W2782047334","https://openalex.org/W1970576574","https://openalex.org/W3017414697","https://openalex.org/W2522507432","https://openalex.org/W605362495"],"abstract_inverted_index":{"A":[0,6,15,22],"low-rank":[1,38,65],"approximation":[2],"to":[3,21,24,70,91,99,178,192],"a":[4,8,116,126,167],"matrix":[5,9,66],"is":[7,19,61,134],"with":[10,95,103,147],"significantly":[11],"smaller":[12],"rank":[13,43],"than":[14,152,196],",":[16],"and":[17,120,132,172,188],"which":[18],"close":[20],"according":[23],"some":[25],"norm.":[26],"Many":[27],"practical":[28,82],"applications":[29,83],"involving":[30,84],"the":[31,42,47,51,55,62,101,139],"use":[32],"of":[33,46,53,112,118,129,186],"large":[34,157],"matrices":[35],"focus":[36],"on":[37,115,156],"approximations.":[39],"By":[40],"reducing":[41],"or":[44],"dimensionality":[45],"data,":[48],"we":[49],"reduce":[50],"complexity":[52],"analyzing":[54],"data.":[56,86],"The":[57,182],"singular":[58],"value":[59],"decomposition":[60,102],"most":[63],"popular":[64],"approximation.":[67],"However,":[68],"due":[69],"its":[71],"expensive":[72],"computational":[73],"requirements,":[74],"it":[75],"has":[76],"often":[77],"been":[78],"considered":[79],"intractable":[80],"for":[81],"massive":[85],"Recent":[87],"developments":[88],"have":[89],"tried":[90],"address":[92],"this":[93],"problem,":[94],"several":[96],"methods":[97,185],"proposed":[98],"approximate":[100],"better":[104],"asymptotic":[105],"runtime.":[106],"We":[107,123],"present":[108],"an":[109],"empirical":[110],"study":[111],"these":[113],"techniques":[114],"variety":[117],"dense":[119],"sparse":[121,158],"datasets.":[122],"find":[124],"that":[125],"sampling":[127,184],"approach":[128],"Drineas,":[130],"Kannan":[131],"Mahoney":[133],"often,":[135],"but":[136],"not":[137],"always,":[138],"best":[140],"performing":[141],"method.":[142],"This":[143],"method":[144],"gives":[145],"solutions":[146],"high":[148],"accuracy":[149],"much":[150],"faster":[151],"classical":[153,179,197],"SVD":[154,180],"algorithms,":[155],"datasets":[159],"in":[160],"particular.":[161],"Other":[162],"modern":[163],"methods,":[164],"such":[165],"as":[166],"recent":[168],"algorithm":[169],"by":[170],"Rokhlin":[171],"Tygert,":[173],"also":[174],"offer":[175],"savings":[176],"compared":[177],"algorithms.":[181],"older":[183],"Achlioptas":[187],"McSherry":[189],"are":[190],"shown":[191],"sometimes":[193],"take":[194],"longer":[195],"SVD.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
