{"id":"https://openalex.org/W2133045322","doi":"https://doi.org/10.1109/sysose.2006.1652299","title":"Fast Monte-Carlo Low Rank Approximations for Matrices","display_name":"Fast Monte-Carlo Low Rank Approximations for Matrices","publication_year":2006,"publication_date":"2006-07-21","ids":{"openalex":"https://openalex.org/W2133045322","doi":"https://doi.org/10.1109/sysose.2006.1652299","mag":"2133045322"},"language":"en","primary_location":{"id":"doi:10.1109/sysose.2006.1652299","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sysose.2006.1652299","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE/SMC International Conference on System of Systems Engineering","raw_type":"proceedings-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/A5002855648","display_name":"Shmuel Friedland","orcid":"https://orcid.org/0000-0002-0423-5005"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. Friedland","raw_affiliation_strings":["Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Chicago, IL, USA","Dept. of Math., Stat. & Comput. Sci., Illinois Univ., Chicago, IL"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"Dept. of Math., Stat. & Comput. Sci., Illinois Univ., Chicago, IL","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027422333","display_name":"Amir Niknejad","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Niknejad","raw_affiliation_strings":["Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Chicago, IL, USA","Dept. of Math., Stat. & Comput. Sci., Illinois Univ., Chicago, IL"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"Dept. of Math., Stat. & Comput. Sci., Illinois Univ., Chicago, IL","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057694750","display_name":"M. Kaveh","orcid":"https://orcid.org/0009-0006-3006-6125"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Kaveh","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Administration (CSENG)"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Administration (CSENG)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090051911","display_name":"Hossein Zare","orcid":"https://orcid.org/0000-0003-1496-0785"},"institutions":[{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]},{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Zare","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","University of Minnesota Twin Cities"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"University of Minnesota Twin Cities","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002855648"],"corresponding_institution_ids":["https://openalex.org/I157725225","https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":1.6978,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84586121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"204","last_page":"209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9979000091552734,"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":0.9979000091552734,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/T12303","display_name":"Tensor decomposition and applications","score":0.9957000017166138,"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":0.6564604043960571},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.6174004673957825},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5985493659973145},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5841513872146606},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5483591556549072},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5274914503097534},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5064011812210083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46895402669906616},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.440130352973938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39524656534194946},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.29939061403274536},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23473182320594788},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06474584341049194},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.06419780850410461}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.6564604043960571},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.6174004673957825},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5985493659973145},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5841513872146606},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5483591556549072},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5274914503097534},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5064011812210083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46895402669906616},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.440130352973938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39524656534194946},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.29939061403274536},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23473182320594788},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06474584341049194},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06419780850410461},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/sysose.2006.1652299","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sysose.2006.1652299","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE/SMC International Conference on System of Systems Engineering","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.2206","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.2206","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.math.uic.edu/~friedlan/PID203087.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1952127226","https://openalex.org/W1977496278","https://openalex.org/W1994157509","https://openalex.org/W1995433152","https://openalex.org/W2004791924","https://openalex.org/W2065811242","https://openalex.org/W2066624117","https://openalex.org/W2103318769","https://openalex.org/W2130283017","https://openalex.org/W2139328257","https://openalex.org/W2148541040","https://openalex.org/W2162302435","https://openalex.org/W2798909945","https://openalex.org/W4254311734"],"related_works":["https://openalex.org/W2964108162","https://openalex.org/W2772729003","https://openalex.org/W2618985210","https://openalex.org/W2155332744","https://openalex.org/W2002598080","https://openalex.org/W1997120656","https://openalex.org/W2721481757","https://openalex.org/W2962894463","https://openalex.org/W2962895005","https://openalex.org/W2938523900"],"abstract_inverted_index":{"In":[0],"many":[1,120],"applications,":[2],"it":[3],"is":[4,25,35,42,91,104],"of":[5,19,69,78,80,84,88],"interest":[6],"to":[7,65],"approximate":[8],"data,":[9],"given":[10,36],"by":[11,15,37],"mtimesn":[12,70],"matrix":[13,17,71],"A,":[14],"a":[16,55,62,105],"B":[18],"at":[20],"most":[21],"rank":[22],"k,":[23],"which":[24,41],"much":[26],"smaller":[27],"than":[28,109],"m":[29,49],"and":[30,50,127],"n.":[31,51],"The":[32,86],"best":[33],"approximation":[34,64,108],"singular":[38],"value":[39],"decomposition,":[40],"too":[43],"time":[44],"consuming":[45],"for":[46,59],"very":[47],"large":[48],"We":[52,113],"present":[53],"here":[54],"Monte":[56],"Carlo":[57],"algorithm":[58,90,117],"iteratively":[60],"computing":[61],"k-rank":[63,107],"the":[66,76,110],"data":[67,123,125,128],"consisting":[68],"A.":[72,85],"Each":[73],"iteration":[74,103],"involves":[75],"reading":[77],"O(k)":[79],"columns":[81],"or":[82],"rows":[83],"complexity":[87],"our":[89],"O(kmn).":[92],"Our":[93],"algorithm,":[94],"distinguished":[95],"from":[96],"other":[97],"known":[98],"algorithms,":[99],"guarantees":[100],"that":[101,115],"each":[102],"better":[106],"previous":[111],"iteration.":[112],"believe":[114],"this":[116],"will":[118],"have":[119],"applications":[121],"in":[122],"mining,":[124],"storage":[126],"analysis":[129]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
