{"id":"https://openalex.org/W2117909080","doi":"https://doi.org/10.1137/15m1047209","title":"Partitioning Well-Clustered Graphs: Spectral Clustering Works!","display_name":"Partitioning Well-Clustered Graphs: Spectral Clustering Works!","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2117909080","doi":"https://doi.org/10.1137/15m1047209","mag":"2117909080"},"language":"en","primary_location":{"id":"doi:10.1137/15m1047209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1047209","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":"http://proceedings.mlr.press/v40/Peng15.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112534230","display_name":"Richard Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard Peng","raw_affiliation_strings":["[Georgia Institute of Technology.]"],"affiliations":[{"raw_affiliation_string":"[Georgia Institute of Technology.]","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062035495","display_name":"He Sun","orcid":"https://orcid.org/0000-0002-5852-3125"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He Sun","raw_affiliation_strings":["School of Informatics"],"affiliations":[{"raw_affiliation_string":"School of Informatics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061476201","display_name":"Luca Zanetti","orcid":"https://orcid.org/0000-0002-4667-2764"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Zanetti","raw_affiliation_strings":["Department of Mathematical Sciences"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112534230"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":3.9873,"has_fulltext":true,"cited_by_count":45,"citation_normalized_percentile":{"value":0.93933576,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"2","first_page":"710","last_page":"743"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9973999857902527,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9940999746322632,"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/cluster-analysis","display_name":"Cluster analysis","score":0.7273442149162292},{"id":"https://openalex.org/keywords/spectral-clustering","display_name":"Spectral clustering","score":0.7015810608863831},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5285683274269104},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.522001326084137},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5103170275688171},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.48334094882011414},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43537116050720215},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.42714163661003113},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4251721203327179},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3807382881641388},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34109750390052795},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3409789800643921},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1477052867412567}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7273442149162292},{"id":"https://openalex.org/C105611402","wikidata":"https://www.wikidata.org/wiki/Q2976589","display_name":"Spectral clustering","level":3,"score":0.7015810608863831},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5285683274269104},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.522001326084137},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5103170275688171},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.48334094882011414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43537116050720215},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.42714163661003113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4251721203327179},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3807382881641388},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34109750390052795},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3409789800643921},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1477052867412567},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1047209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1047209","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:research-information.bris.ac.uk:publications/499f7ee5-878e-4899-9384-19d84ce5d241","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/499f7ee5-878e-4899-9384-19d84ce5d241","pdf_url":"http://proceedings.mlr.press/v40/Peng15.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.698.9756","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.698.9756","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://seis.bris.ac.uk/%7Ehs15417/colt15.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:publications/499f7ee5-878e-4899-9384-19d84ce5d241","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/499f7ee5-878e-4899-9384-19d84ce5d241","pdf_url":"http://proceedings.mlr.press/v40/Peng15.pdf","source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2117909080.pdf","grobid_xml":"https://content.openalex.org/works/W2117909080.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W163149739","https://openalex.org/W340925356","https://openalex.org/W1510081914","https://openalex.org/W1558625102","https://openalex.org/W1605711022","https://openalex.org/W1698842591","https://openalex.org/W1832961665","https://openalex.org/W1965562201","https://openalex.org/W1967184357","https://openalex.org/W1970377488","https://openalex.org/W1978627835","https://openalex.org/W1983193888","https://openalex.org/W1989720410","https://openalex.org/W1995547833","https://openalex.org/W2004879152","https://openalex.org/W2029698681","https://openalex.org/W2034331023","https://openalex.org/W2073459066","https://openalex.org/W2078013954","https://openalex.org/W2085849439","https://openalex.org/W2088658556","https://openalex.org/W2089703809","https://openalex.org/W2121947440","https://openalex.org/W2127048411","https://openalex.org/W2129575457","https://openalex.org/W2132914434","https://openalex.org/W2147717514","https://openalex.org/W2148025043","https://openalex.org/W2150148016","https://openalex.org/W2150865801","https://openalex.org/W2163925208","https://openalex.org/W2165755074","https://openalex.org/W2165874743","https://openalex.org/W2278710066","https://openalex.org/W2339338500","https://openalex.org/W2397770138","https://openalex.org/W2605800612","https://openalex.org/W2610857016","https://openalex.org/W2949896029","https://openalex.org/W2962751222","https://openalex.org/W3031108707","https://openalex.org/W3098071389","https://openalex.org/W3102641634","https://openalex.org/W3104227803"],"related_works":["https://openalex.org/W4286829927","https://openalex.org/W51907474","https://openalex.org/W2366795653","https://openalex.org/W3124727659","https://openalex.org/W2765311429","https://openalex.org/W3165971014","https://openalex.org/W3008542237","https://openalex.org/W4321483917","https://openalex.org/W2365247705","https://openalex.org/W2583316250"],"abstract_inverted_index":{"In":[0],"this":[1,71],"paper":[2],"we":[3],"study":[4],"variants":[5],"of":[6,24,35,58,66],"the":[7,22,32,36,42,67,76],"widely":[8],"used":[9],"spectral":[10,60],"clustering":[11,61],"that":[12],"partitions":[13],"a":[14,25,28,55,63,101,113],"graph":[15,26],"into":[16,27,45],"$k$":[17,46],"clusters":[18,47],"by":[19],"(1)":[20],"embedding":[21],"vertices":[23],"low-dimensional":[29],"space":[30],"using":[31],"bottom":[33],"eigenvectors":[34],"Laplacian":[37],"matrix":[38,114],"and":[39,79,116],"(2)":[40],"grouping":[41],"embedded":[43],"points":[44],"via":[48],"$k$-means":[49],"algorithms.":[50],"We":[51,98],"show":[52],"that,":[53],"for":[54,92,106],"wide":[56],"class":[57],"graphs,":[59],"gives":[62],"good":[64],"approximation":[65],"optimal":[68],"clustering.":[69],"While":[70],"approach":[72],"was":[73],"proposed":[74],"in":[75],"early":[77],"1990s":[78],"has":[80],"comprehensive":[81],"applications,":[82],"prior":[83],"to":[84],"our":[85],"work":[86],"similar":[87],"results":[88],"were":[89],"known":[90],"only":[91],"graphs":[93,109],"generated":[94],"from":[95],"stochastic":[96],"models.":[97],"also":[99],"give":[100],"nearly":[102],"linear":[103],"time":[104],"algorithm":[105],"partitioning":[107],"well-clustered":[108],"based":[110],"on":[111],"computing":[112],"exponential":[115],"approximate":[117],"nearest":[118],"neighbor":[119],"data":[120],"structures.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}
