{"id":"https://openalex.org/W2295225727","doi":"https://doi.org/10.1145/2840728.2840751","title":"Spectral Embedding of k-Cliques, Graph Partitioning and k-Means","display_name":"Spectral Embedding of k-Cliques, Graph Partitioning and k-Means","publication_year":2016,"publication_date":"2016-01-05","ids":{"openalex":"https://openalex.org/W2295225727","doi":"https://doi.org/10.1145/2840728.2840751","mag":"2295225727"},"language":"en","primary_location":{"id":"doi:10.1145/2840728.2840751","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2840728.2840751","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2840728.2840751","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/2840728.2840751","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056617357","display_name":"Pranjal Awasthi","orcid":null},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pranjal Awasthi","raw_affiliation_strings":["Rutgers University, New Brunswick, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rutgers University, New Brunswick, NJ, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071016611","display_name":"Moses Charikar","orcid":"https://orcid.org/0000-0003-0807-3389"},"institutions":[{"id":"https://openalex.org/I1743320","display_name":"Palo Alto University","ror":"https://ror.org/04f812k67","country_code":"US","type":"education","lineage":["https://openalex.org/I1743320"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Moses Charikar","raw_affiliation_strings":["Stanford University, Palo Alto, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University, Palo Alto, USA","institution_ids":["https://openalex.org/I1743320","https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060555975","display_name":"Ravishankar Krishnaswamy","orcid":"https://orcid.org/0000-0002-5765-0843"},"institutions":[{"id":"https://openalex.org/I4210124949","display_name":"Microsoft Research (India)","ror":"https://ror.org/02w7f3w92","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210124949"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ravishankar Krishnaswamy","raw_affiliation_strings":["Microsoft Research, Bangalore, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, Bangalore, India","institution_ids":["https://openalex.org/I4210124949"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086919065","display_name":"Ali Kemal Sinop","orcid":"https://orcid.org/0000-0001-6550-6027"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Kemal Sinop","raw_affiliation_strings":["Simons Institute, Berkeley, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simons Institute, Berkeley, USA","institution_ids":["https://openalex.org/I4210107338"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"301","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9958000183105469,"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":0.9958000183105469,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9789999723434448,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9581999778747559,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7556644678115845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.563220739364624},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.515245258808136},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.503546416759491},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.49689725041389465},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.46687954664230347},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46509233117103577},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4319410026073456},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.41696658730506897},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4148849844932556},{"id":"https://openalex.org/keywords/strength-of-a-graph","display_name":"Strength of a graph","score":0.4127804934978485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3101568818092346},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.26399335265159607},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07264870405197144},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.052853792905807495}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7556644678115845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.563220739364624},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.515245258808136},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.503546416759491},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.49689725041389465},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.46687954664230347},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46509233117103577},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4319410026073456},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.41696658730506897},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4148849844932556},{"id":"https://openalex.org/C19332903","wikidata":"https://www.wikidata.org/wiki/Q7623247","display_name":"Strength of a graph","level":5,"score":0.4127804934978485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3101568818092346},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.26399335265159607},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07264870405197144},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.052853792905807495}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2840728.2840751","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2840728.2840751","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2840728.2840751","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science","raw_type":"proceedings-article"},{"id":"pmh:oai:alma.01RUT_INST:11663531000004646","is_oa":false,"landing_page_url":"https://scholarship.libraries.rutgers.edu/esploro/outputs/conferenceProceeding/Spectral-Embedding-of-k-Cliques-Graph-Partitioning/991031654695004646","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference Proceedings"}],"best_oa_location":{"id":"doi:10.1145/2840728.2840751","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2840728.2840751","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/2840728.2840751","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1312587160","display_name":"AF:  Small:  Approximation Techniques for Combinatorial Optimization","funder_award_id":"1565581","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3415264451","display_name":"AF: Medium: Towards Provable Bounds for Machine Learning","funder_award_id":"1302518","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8485875341","display_name":null,"funder_award_id":"CCF-1565581","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2295225727.pdf","grobid_xml":"https://content.openalex.org/works/W2295225727.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W100944330","https://openalex.org/W200434350","https://openalex.org/W1497169204","https://openalex.org/W1585655309","https://openalex.org/W1605711022","https://openalex.org/W1631603072","https://openalex.org/W1659092632","https://openalex.org/W1832961665","https://openalex.org/W1884716544","https://openalex.org/W1981276685","https://openalex.org/W1983193888","https://openalex.org/W1986007546","https://openalex.org/W1993111701","https://openalex.org/W1995547833","https://openalex.org/W2034331023","https://openalex.org/W2034534236","https://openalex.org/W2044343300","https://openalex.org/W2059971059","https://openalex.org/W2064027395","https://openalex.org/W2066052393","https://openalex.org/W2067081844","https://openalex.org/W2086565575","https://openalex.org/W2088844265","https://openalex.org/W2117154949","https://openalex.org/W2121947440","https://openalex.org/W2128550154","https://openalex.org/W2129575457","https://openalex.org/W2130470622","https://openalex.org/W2134370969","https://openalex.org/W2139841919","https://openalex.org/W2150148016","https://openalex.org/W2152986618","https://openalex.org/W2154876245","https://openalex.org/W2160167256","https://openalex.org/W2165755074","https://openalex.org/W2200304227","https://openalex.org/W2295224288","https://openalex.org/W2304387544","https://openalex.org/W2999905431","https://openalex.org/W3022762247","https://openalex.org/W3098071389","https://openalex.org/W3105471108","https://openalex.org/W3120740533","https://openalex.org/W6604134081","https://openalex.org/W6608197349","https://openalex.org/W6638526118","https://openalex.org/W6684031994","https://openalex.org/W6922501783"],"related_works":["https://openalex.org/W2767587315","https://openalex.org/W2546705119","https://openalex.org/W2950385387","https://openalex.org/W2152478214","https://openalex.org/W2130209831","https://openalex.org/W2053279533","https://openalex.org/W2170810426","https://openalex.org/W2002373719","https://openalex.org/W2106688078","https://openalex.org/W2962951681"],"abstract_inverted_index":{"We":[0,87],"introduce":[1],"and":[2,15,52,62,96,221,241],"study":[3],"a":[4,20,30,77,81,101,114,154,227],"new":[5,129,238],"notion":[6],"of":[7,37,58,76,84,116,146,195,231,246],"graph":[8,21,31,67,79,167,247],"partitioning,":[9],"intimately":[10],"connected":[11],"to":[12,28,113,127,156,192,209,237],"spectral":[13,74,104,136,160,222],"clustering":[14,105,137,161,216],"k-means":[16,205,220],"clustering.":[17],"Formally,":[18],"given":[19,78],"G":[22,61],"on":[23,40,139],"n":[24,41],"vertices,":[25,42],"we":[26,98,121,142,150,176,224],"ask":[27],"find":[29],"H":[32,63],"that":[33,44,100,158,179,226],"is":[34,48],"the":[35,55,59,72,135,189,193,197,203,244],"union":[36,83],"k":[38,85],"cliques":[39],"such":[43],"LG":[45,51],"LH":[46,53],"where":[47],"maximized.":[49],"Here":[50],"are":[54],"(normalized)":[56],"Laplacians":[57],"graphs":[60],"respectively.":[64],"Informally,":[65],"our":[66,128,147],"partitioning":[68,168,172],"objective":[69,90,110,130,148],"asks":[70],"for":[71,202,243],"optimal":[73],"simplification":[75],"as":[80,153,171,188,219],"disjoint":[82],"cliques.":[86],"justify":[88],"this":[89,109,119,183,232],"function":[91,131],"in":[92],"several":[93],"ways.":[94],"First":[95],"foremost,":[97],"show":[99,178],"commonly":[102],"used":[103],"algorithm":[106,126,138],"implicitly":[107],"optimizes":[108],"function,":[111],"up":[112],"factor":[115],"O(k).":[117],"Using":[118],"connection,":[120],"immediately":[122],"get":[123],"an":[124],"O(k)-approximation":[125],"by":[132],"simply":[133],"using":[134],"G.":[140],"Next,":[141],"demonstrate":[143],"another":[144],"application":[145],"function:":[149],"use":[151],"it":[152],"means":[155],"proving":[157],"simple":[159],"algorithms":[162],"can":[163],"solve":[164],"some":[165,214],"well-studied":[166],"problems":[169],"(such":[170,218],"into":[173],"expanders).":[174],"Additionally,":[175],"also":[177],"(a":[180],"relaxation":[181],"of)":[182],"optimization":[184,233],"problem":[185,191,234],"naturally":[186],"arises":[187],"dual":[190],"question":[194],"finding":[196],"worst-case":[198],"integrality":[199],"gap":[200],"instance":[201],"classical":[204,215],"SDP.":[206],"Finally,":[207],"owing":[208],"these":[210],"close":[211],"connection":[212],"between":[213],"techniques":[217,242],"clustering),":[223],"argue":[225],"more":[228],"complete":[229],"understanding":[230],"could":[235],"lead":[236],"algorithmic":[239],"insights":[240],"area":[245],"partitioning.":[248]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
