{"id":"https://openalex.org/W4214500875","doi":"https://doi.org/10.1137/20m1348601","title":"The Ratio-Cut Polytope and K-Means Clustering","display_name":"The Ratio-Cut Polytope and K-Means Clustering","publication_year":2022,"publication_date":"2022-02-24","ids":{"openalex":"https://openalex.org/W4214500875","doi":"https://doi.org/10.1137/20m1348601"},"language":"en","primary_location":{"id":"doi:10.1137/20m1348601","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1348601","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-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/A5043926638","display_name":"Antonio De Rosa","orcid":"https://orcid.org/0000-0002-1392-4881"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Antonio De Rosa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059503583","display_name":"Aida Khajavirad","orcid":"https://orcid.org/0000-0002-7097-1676"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aida Khajavirad","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043926638"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7882,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8154445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"32","issue":"1","first_page":"173","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10057","display_name":"Face and Expression Recognition","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/polytope","display_name":"Polytope","score":0.8341942429542542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7800109386444092},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7540225982666016},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.687902569770813},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.6727672815322876},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6452207565307617},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5602077841758728},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5093392133712769},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.490667462348938},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.39793887734413147},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35873886942863464},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12041336297988892},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08571785688400269}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8341942429542542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7800109386444092},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7540225982666016},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.687902569770813},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.6727672815322876},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6452207565307617},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5602077841758728},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5093392133712769},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.490667462348938},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.39793887734413147},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35873886942863464},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12041336297988892},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08571785688400269},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1348601","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1348601","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8399504094","display_name":null,"funder_award_id":"DMS-1906451 - 2112311","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1975552235","https://openalex.org/W1986219860","https://openalex.org/W2043471141","https://openalex.org/W2106292145","https://openalex.org/W2150593711","https://openalex.org/W2567866584","https://openalex.org/W2767194928","https://openalex.org/W2899810529","https://openalex.org/W2913439212","https://openalex.org/W2942858066","https://openalex.org/W2963057284","https://openalex.org/W2963264680","https://openalex.org/W2963301123","https://openalex.org/W2963496884","https://openalex.org/W2963814147","https://openalex.org/W2963919656","https://openalex.org/W3102657012"],"related_works":["https://openalex.org/W2386048074","https://openalex.org/W2952452737","https://openalex.org/W4300637737","https://openalex.org/W2109445739","https://openalex.org/W2055782437","https://openalex.org/W2107689258","https://openalex.org/W4205854323","https://openalex.org/W2115855742","https://openalex.org/W3149578574","https://openalex.org/W2059496069"],"abstract_inverted_index":{"We":[0,53,69],"introduce":[1,78],"the":[2,7,33,37,55,59,72,91,102,107,114,130,142,146,158,190,203],"ratio-cut":[3,11,60],"polytope":[4,28,61],"defined":[5],"as":[6,47],"convex":[8,34],"hull":[9,35],"of":[10,17,36,40,43,58,66,74,93,167],"vectors":[12],"corresponding":[13],"to":[14,32],"all":[15],"partitions":[16],"$n$":[18],"points":[19],"in":[20,201],"$\\mathbb{R}^m$":[21],"into":[22],"at":[23],"most":[24],"$K$":[25],"clusters.":[26,205],"This":[27,152],"is":[29,153,173],"closely":[30],"related":[31],"feasible":[38],"region":[39],"a":[41,79,118,154,196],"number":[42],"clustering":[44,49,76,169],"problems":[45],"such":[46],"K-means":[48,75,123,168],"and":[50,62,77,96,125,179],"spectral":[51],"clustering.":[52],"study":[54],"facial":[56],"structure":[57],"derive":[63,97],"several":[64],"types":[65],"facet-defining":[67],"inequalities.":[68],"then":[70,141],"consider":[71,113],"problem":[73],"novel":[80],"linear":[81],"programming":[82,199],"(LP)":[83],"relaxation":[84,105,144,166,193,200],"for":[85,122,163],"it.":[86],"Subsequently,":[87],"we":[88,112,126],"focus":[89],"on":[90],"case":[92],"two":[94],"clusters":[95,109,148],"sufficient":[98],"condition":[99],"under":[100],"which":[101],"proposed":[103,191],"LP":[104,143,165,192],"recovers":[106,145],"underlying":[108],"exactly.":[110],"Namely,":[111],"stochastic":[115],"ball":[116],"model,":[117],"popular":[119,197],"generative":[120],"model":[121],"clustering,":[124],"show":[127],"that":[128,171,189],"if":[129,178,181],"separation":[131],"distance":[132],"between":[133],"cluster":[134],"centers":[135],"satisfies":[136],"$\\Delta":[137,182],">":[138,183],"1+\\sqrt":[139],"3$,":[140],"planted":[147,204],"with":[149,175],"high":[150,176],"probability.":[151],"major":[155],"improvement":[156],"over":[157],"only":[159,180],"existing":[160],"recovery":[161,172],"guarantee":[162],"an":[164],"stating":[170],"possible":[174],"probability":[177],"4$.":[184],"Our":[185],"numerical":[186],"experiments":[187],"indicate":[188],"significantly":[194],"outperforms":[195],"semidefinite":[198],"recovering":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
