{"id":"https://openalex.org/W2983384503","doi":"https://doi.org/10.1137/17m1152255","title":"On Approximating Matrix Norms in Data Streams","display_name":"On Approximating Matrix Norms in Data Streams","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2983384503","doi":"https://doi.org/10.1137/17m1152255","mag":"2983384503"},"language":"en","primary_location":{"id":"doi:10.1137/17m1152255","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1152255","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":true,"oa_status":"green","oa_url":"https://dr.ntu.edu.sg/bitstream/10356/146275/2/M115225.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090676285","display_name":"Yi Li","orcid":"https://orcid.org/0000-0002-6420-653X"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yi Li","raw_affiliation_strings":["Division of Mathematics, Nanyang Technological University, Singapore, 637371"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematics, Nanyang Technological University, Singapore, 637371","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102936404","display_name":"Huy L. Nguy\u00ean","orcid":"https://orcid.org/0000-0001-5128-6545"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Huy L. Nguy\u1ec5n","raw_affiliation_strings":["Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115","institution_ids":["https://openalex.org/I12912129"]}]},{"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/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David P. Woodruff","raw_affiliation_strings":["Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7923,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.80468148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"6","first_page":"1643","last_page":"1697"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9983999729156494,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9983999729156494,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.7771632671356201},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6945608854293823},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6098425388336182},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5597913861274719},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5320457220077515},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5147843360900879},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.48684972524642944},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44905003905296326},{"id":"https://openalex.org/keywords/streaming-algorithm","display_name":"Streaming algorithm","score":0.43944522738456726},{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.43478959798812866},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43120265007019043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13460314273834229},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10277783870697021}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7771632671356201},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6945608854293823},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6098425388336182},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5597913861274719},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5320457220077515},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5147843360900879},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.48684972524642944},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44905003905296326},{"id":"https://openalex.org/C187166803","wikidata":"https://www.wikidata.org/wiki/Q2835831","display_name":"Streaming algorithm","level":3,"score":0.43944522738456726},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.43478959798812866},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43120265007019043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13460314273834229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10277783870697021},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":2,"locations":[{"id":"doi:10.1137/17m1152255","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1152255","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"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/146275","is_oa":true,"landing_page_url":"https://hdl.handle.net/10356/146275","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/146275/2/M115225.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:dr.ntu.edu.sg:10356/146275","is_oa":true,"landing_page_url":"https://hdl.handle.net/10356/146275","pdf_url":"https://dr.ntu.edu.sg/bitstream/10356/146275/2/M115225.pdf","source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"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":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1678081061","display_name":"CAREER: Faster and Smaller Sketches for Bigger Data","funder_award_id":"1750716","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2451892224","display_name":"AF: Small: Data Stream Algorithms with Application to Linear Algebra","funder_award_id":"1815840","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4072675397","display_name":null,"funder_award_id":"CCF-1815840","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G549042368","display_name":null,"funder_award_id":"MOE2018-T2-1-013","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2983384503.pdf","grobid_xml":"https://content.openalex.org/works/W2983384503.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1493892051","https://openalex.org/W1497701622","https://openalex.org/W1560153690","https://openalex.org/W1991127564","https://openalex.org/W1995895837","https://openalex.org/W2025051251","https://openalex.org/W2045533739","https://openalex.org/W2058009001","https://openalex.org/W2080234606","https://openalex.org/W2080745194","https://openalex.org/W2081131431","https://openalex.org/W2107917944","https://openalex.org/W2114203129","https://openalex.org/W2124608575","https://openalex.org/W2146232410","https://openalex.org/W2148541040","https://openalex.org/W2580753685","https://openalex.org/W2963211500","https://openalex.org/W4293404332"],"related_works":["https://openalex.org/W772650738","https://openalex.org/W2044221060","https://openalex.org/W2112958926","https://openalex.org/W2067698461","https://openalex.org/W3037833187","https://openalex.org/W4293414471","https://openalex.org/W2950768703","https://openalex.org/W832725505","https://openalex.org/W2400272108","https://openalex.org/W819457920"],"abstract_inverted_index":{"This":[0,73],"paper":[1],"presents":[2],"a":[3,192,203],"systematic":[4],"study":[5],"of":[6,10,15,27,71,120,156,181,205],"the":[7,12,21,113,117,178,185,215,224,227,235],"space":[8,28,68,164],"complexity":[9,31,180],"estimating":[11,116],"Schatten":[13,182,236],"$p$-norms":[14,183],"an":[16,53,96,104,121],"$n\\times":[17],"n$":[18],"matrix":[19],"in":[20,69,130,162,177],"turnstile":[22],"streaming":[23],"model.":[24],"Both":[25],"kinds":[26],"complexities,":[29],"bit":[30],"and":[32,44,89,153,189,218],"sketching":[33,39,43,179,234],"dimension,":[34],"are":[35,47,143,212],"considered.":[36,48],"Furthermore,":[37],"two":[38],"models,":[40],"general":[41,172,229],"linear":[42,173],"bilinear":[45,210],"sketching,":[46],"When":[49],"$p$":[50,94],"is":[51,95,112,226],"not":[52],"even":[54,77,97],"integer,":[55,98],"we":[56,99],"show":[57],"that":[58],"any":[59],"one-pass":[60],"algorithm":[61],"with":[62,83,184],"constant":[63],"success":[64],"probability":[65],"requires":[66],"near-linear":[67,140],"terms":[70],"bits.":[72],"lower":[74,128,141],"bound":[75,106,232],"holds":[76],"for":[78,101,133,145,171,196,209,214,221,233],"sparse":[79,102],"matrices,":[80],"i.e.,":[81],"matrices":[82,103],"$O(1)$":[84],"nonzero":[85],"entries":[86],"per":[87,90],"row":[88],"column.":[91],"However,":[92],"when":[93],"give":[100,175],"upper":[105,231],"which,":[107],"up":[108],"to":[109,166],"logarithmic":[110,163],"factors,":[111],"same":[114],"as":[115],"$p$th":[118],"moment":[119],"$n$-dimensional":[122],"vector.":[123],"These":[124],"results":[125,170,208],"considerably":[126],"strengthen":[127],"bounds":[129,142],"previous":[131],"work":[132],"arbitrary":[134],"(not":[135],"necessarily":[136],"sparse)":[137],"matrices.":[138],"Similar":[139],"obtained":[144],"Ky":[146],"Fan":[147],"norms,":[148],"SVD":[149],"entropy,":[150],"eigenvalue":[151],"shrinkers,":[152],"M-estimators,":[154],"many":[155],"which":[157],"could":[158],"have":[159],"been":[160],"solvable":[161],"prior":[165],"this":[167],"work.":[168],"The":[169,207],"sketches":[174,211],"separations":[176],"corresponding":[186],"vector":[187],"$p$-norms,":[188],"rule":[190],"out":[191],"table-lookup":[193],"nearest-neighbor":[194],"search":[195],"$p":[197],"=":[198],"1$,":[199],"making":[200],"progress":[201],"on":[202],"question":[204],"Andoni.":[206],"tight":[213,220],"rank":[216],"problem":[217],"nearly":[219],"$p\\geq":[222],"2$;":[223],"latter":[225],"first":[228],"subquadratic":[230],"norms.":[237]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}