{"id":"https://openalex.org/W3041674974","doi":"https://doi.org/10.1137/20m1352193","title":"A Performance Guarantee for Spectral Clustering","display_name":"A Performance Guarantee for Spectral Clustering","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3041674974","doi":"https://doi.org/10.1137/20m1352193","mag":"3041674974"},"language":"en","primary_location":{"id":"doi:10.1137/20m1352193","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1352193","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/20m1352193","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034076533","display_name":"March T. Boedihardjo","orcid":"https://orcid.org/0000-0003-4969-0586"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"March Boedihardjo","raw_affiliation_strings":["University of California-Los Angeles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California-Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055672444","display_name":"Shaofeng Deng","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shaofeng Deng","raw_affiliation_strings":["Univ. of California Davis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of California Davis","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080565728","display_name":"Thomas Strohmer","orcid":"https://orcid.org/0000-0003-2029-3317"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Strohmer","raw_affiliation_strings":["Univ. of California Davis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of California Davis","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4163,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54973822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"3","issue":"1","first_page":"369","last_page":"387"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9789999723434448,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.944599986076355,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spectral-clustering","display_name":"Spectral clustering","score":0.7772994041442871},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.7525177001953125},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7232524156570435},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.6668875813484192},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6097399592399597},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.593779981136322},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5423948764801025},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5088536739349365},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4897727966308594},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46454620361328125},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4602692425251007},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4494268596172333},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.4340524673461914},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43319639563560486},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39664795994758606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32077187299728394},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09607052803039551},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08856958150863647},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08003279566764832},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.07638430595397949}],"concepts":[{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.7772994041442871},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.7525177001953125},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7232524156570435},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.6668875813484192},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6097399592399597},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.593779981136322},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5423948764801025},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5088536739349365},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4897727966308594},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46454620361328125},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4602692425251007},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4494268596172333},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.4340524673461914},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43319639563560486},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39664795994758606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32077187299728394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09607052803039551},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08856958150863647},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08003279566764832},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.07638430595397949},{"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/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1352193","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1352193","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2007.05627","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.05627","pdf_url":"https://arxiv.org/pdf/2007.05627","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:3041674974","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2007.05627","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2007.05627","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.05627","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1137/20m1352193","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1352193","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2624195884","display_name":null,"funder_award_id":"CCF 1934568","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3114566917","display_name":null,"funder_award_id":"DMS 1737943","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5652851020","display_name":null,"funder_award_id":"DMS 1620455","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G651271590","display_name":null,"funder_award_id":"DMS 1856221","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1483985387","https://openalex.org/W1520260139","https://openalex.org/W1967184357","https://openalex.org/W1970377488","https://openalex.org/W2039592987","https://openalex.org/W2059971059","https://openalex.org/W2086959852","https://openalex.org/W2103718624","https://openalex.org/W2132914434","https://openalex.org/W2142408004","https://openalex.org/W2150593711","https://openalex.org/W2963037546","https://openalex.org/W2963057284","https://openalex.org/W2963814147","https://openalex.org/W2966291568","https://openalex.org/W2968890898","https://openalex.org/W3017750840","https://openalex.org/W3043617248","https://openalex.org/W3080407530","https://openalex.org/W3100144903","https://openalex.org/W3104227803"],"related_works":["https://openalex.org/W2101737005","https://openalex.org/W2059971059","https://openalex.org/W3016253806","https://openalex.org/W2762594064","https://openalex.org/W2786537543","https://openalex.org/W2989721195","https://openalex.org/W2158804804","https://openalex.org/W3204864912","https://openalex.org/W3114784257","https://openalex.org/W2893274952","https://openalex.org/W2964179623","https://openalex.org/W2588638503","https://openalex.org/W2396585661","https://openalex.org/W3113827893","https://openalex.org/W2952769483","https://openalex.org/W2920024376","https://openalex.org/W2890639290","https://openalex.org/W3094857862","https://openalex.org/W2099163034","https://openalex.org/W2259577537"],"abstract_inverted_index":{"The":[0],"two-step":[1],"spectral":[2,49,134,156],"clustering":[3,50,135],"method,":[4],"which":[5,82,133,149],"consists":[6],"of":[7,77,111],"the":[8,32,43,54,58,72,90,93,108,112,118,140,144],"Laplacian":[9,114],"eigenmap":[10],"and":[11,74],"a":[12,16,28,66,78,101,130,152],"rounding":[13],"step,":[14],"is":[15,48,89,136],"widely":[17],"used":[18],"method":[19],"for":[20,107,155],"graph":[21,113],"partitioning.":[22],"It":[23],"can":[24],"be":[25],"seen":[26],"as":[27,151],"natural":[29],"relaxation":[30],"to":[31,52,57,92,117,138,143],"NP-hard":[33],"minimum":[34,59,94,145],"ratio":[35,60,95,146],"cut":[36,61,96,147],"problem.":[37,97],"In":[38],"this":[39,87],"paper,":[40],"we":[41,64,83,99,128],"study":[42],"following":[44],"central":[45],"question:":[46],"When":[47],"able":[51],"find":[53],"global":[55,141],"solution":[56,91,142],"problem?":[62],"First,":[63],"provide":[65],"condition":[67,131],"that":[68,86,115],"naturally":[69],"depends":[70],"on":[71],"intra-":[73],"intercluster":[75],"connectivities":[76],"given":[79],"partition":[80,88],"under":[81,132],"may":[84],"certify":[85],"Then,":[98],"develop":[100],"deterministic":[102],"two-to-infinity":[103],"norm":[104],"perturbation":[105],"bound":[106],"invariant":[109],"subspace":[110],"corresponds":[116],"$k$":[119],"smallest":[120],"eigenvalues.":[121],"Finally,":[122],"by":[123],"combining":[124],"these":[125],"two":[126],"results":[127],"give":[129],"guaranteed":[137],"output":[139],"problem,":[148],"serves":[150],"performance":[153],"guarantee":[154],"clustering.":[157]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}