{"id":"https://openalex.org/W2154034263","doi":"https://doi.org/10.1145/1553374.1553446","title":"On sampling-based approximate spectral decomposition","display_name":"On sampling-based approximate spectral decomposition","publication_year":2009,"publication_date":"2009-06-14","ids":{"openalex":"https://openalex.org/W2154034263","doi":"https://doi.org/10.1145/1553374.1553446","mag":"2154034263"},"language":"en","primary_location":{"id":"doi:10.1145/1553374.1553446","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1553374.1553446","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th Annual International Conference on Machine Learning","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/A5018301052","display_name":"Sanjiv Kumar","orcid":"https://orcid.org/0000-0002-4080-1414"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sanjiv Kumar","raw_affiliation_strings":["Google Research, New York, NY"],"affiliations":[{"raw_affiliation_string":"Google Research, New York, NY","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058849006","display_name":"Mehryar Mohri","orcid":"https://orcid.org/0000-0002-3987-9847"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mehryar Mohri","raw_affiliation_strings":["Courant Institute and Google Research, New York, NY"],"affiliations":[{"raw_affiliation_string":"Courant Institute and Google Research, New York, NY","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I1291425158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029768722","display_name":"Ameet Talwalkar","orcid":"https://orcid.org/0000-0001-6650-1893"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ameet Talwalkar","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York, NY"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York, NY","institution_ids":["https://openalex.org/I36672615"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018301052"],"corresponding_institution_ids":["https://openalex.org/I1291425158"],"apc_list":null,"apc_paid":null,"fwci":8.9199,"has_fulltext":false,"cited_by_count":87,"citation_normalized_percentile":{"value":0.98461436,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"553","last_page":"560"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9993000030517578,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9993000030517578,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"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/T10320","display_name":"Neural Networks and Applications","score":0.9969000220298767,"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":0.8176137208938599},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.7166770100593567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6889359951019287},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5945287346839905},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5940529704093933},{"id":"https://openalex.org/keywords/adaptive-sampling","display_name":"Adaptive sampling","score":0.5616379380226135},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47074398398399353},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43175944685935974},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3377380967140198},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3201448917388916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.274189829826355},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09651800990104675},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.07864075899124146}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8176137208938599},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.7166770100593567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6889359951019287},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5945287346839905},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5940529704093933},{"id":"https://openalex.org/C2781395549","wikidata":"https://www.wikidata.org/wiki/Q4680762","display_name":"Adaptive sampling","level":3,"score":0.5616379380226135},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47074398398399353},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43175944685935974},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3377380967140198},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3201448917388916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.274189829826355},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09651800990104675},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.07864075899124146},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1553374.1553446","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1553374.1553446","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th Annual International Conference on Machine Learning","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.6427","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.6427","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.mcgill.ca/~icml2009/papers/256.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.8224","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.8224","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/~skumar/nys_col_ICML.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.367.7346","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.367.7346","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.nyu.edu/~mohri/pub/nys_col.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":17,"referenced_works":["https://openalex.org/W1558808826","https://openalex.org/W1952127226","https://openalex.org/W1967934524","https://openalex.org/W1979750072","https://openalex.org/W2099262739","https://openalex.org/W2103318769","https://openalex.org/W2112545207","https://openalex.org/W2116810533","https://openalex.org/W2145713404","https://openalex.org/W2150738795","https://openalex.org/W2155759509","https://openalex.org/W2156287497","https://openalex.org/W2160840682","https://openalex.org/W2165874743","https://openalex.org/W3004219628","https://openalex.org/W6681279965","https://openalex.org/W6684578312"],"related_works":["https://openalex.org/W2782904003","https://openalex.org/W2038693912","https://openalex.org/W1991602789","https://openalex.org/W4226434912","https://openalex.org/W2118633810","https://openalex.org/W2150953077","https://openalex.org/W1582396021","https://openalex.org/W2002598339","https://openalex.org/W2920931670","https://openalex.org/W1988359706"],"abstract_inverted_index":{"This":[0,81],"paper":[1],"addresses":[2],"the":[3,31,34,43,78],"problem":[4],"of":[5,10,91],"approximate":[6],"singular":[7],"value":[8],"decomposition":[9,29],"large":[11],"dense":[12],"matrices":[13],"that":[14],"arises":[15],"naturally":[16],"in":[17],"many":[18],"machine":[19],"learning":[20],"applications.":[21,55],"We":[22,37,56],"discuss":[23],"two":[24,44],"recently":[25],"introduced":[26],"sampling-based":[27],"spectral":[28],"techniques:":[30],"Nystr\u00f6m":[32],"and":[33,46],"Column-sampling":[35],"methods.":[36],"present":[38],"a":[39,89],"theoretical":[40],"comparison":[41],"between":[42],"methods":[45,87],"provide":[47,58],"novel":[48,82],"insights":[49],"regarding":[50],"their":[51],"suitability":[52],"for":[53],"various":[54],"then":[57],"experimental":[59],"results":[60],"motivated":[61],"by":[62],"this":[63],"theory.":[64],"Finally,":[65],"we":[66],"propose":[67],"an":[68],"efficient":[69],"adaptive":[70],"sampling":[71,86],"technique":[72,83],"to":[73],"select":[74],"informative":[75],"columns":[76],"from":[77],"original":[79],"matrix.":[80],"outperforms":[84],"standard":[85],"on":[88],"variety":[90],"datasets.":[92]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}