{"id":"https://openalex.org/W7118796868","doi":"https://doi.org/10.48550/arxiv.2601.00447","title":"Unifying Proportional Fairness in Centroid and Non-Centroid Clustering","display_name":"Unifying Proportional Fairness in Centroid and Non-Centroid Clustering","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7118796868","doi":"https://doi.org/10.48550/arxiv.2601.00447"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.00447","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00447","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2601.00447","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122047072","display_name":"Benjamin Cookson","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cookson, Benjamin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103285429","display_name":"Nisarg Shah","orcid":"https://orcid.org/0000-0002-0946-3402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shah, Nisarg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122181043","display_name":"Ziqi Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Ziqi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5122047072"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.12160000205039978,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.12160000205039978,"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/T10883","display_name":"Ethics and Social Impacts of AI","score":0.10320000350475311,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11719","display_name":"Data Quality and Management","score":0.08739999681711197,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.7530999779701233},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6692000031471252},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5672000050544739},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5012999773025513},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4729999899864197},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4415999948978424},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4172999858856201},{"id":"https://openalex.org/keywords/data-point","display_name":"Data point","score":0.413100004196167}],"concepts":[{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.7530999779701233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.671999990940094},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6692000031471252},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5672000050544739},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4729999899864197},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4415999948978424},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4178999960422516},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.413100004196167},{"id":"https://openalex.org/C115328559","wikidata":"https://www.wikidata.org/wiki/Q4041956","display_name":"k-medians clustering","level":5,"score":0.4074999988079071},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C207968372","wikidata":"https://www.wikidata.org/wiki/Q310401","display_name":"k-means clustering","level":3,"score":0.3758000135421753},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3172999918460846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30329999327659607},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29899999499320984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29840001463890076},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2921000123023987},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.00447","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00447","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2601.00447","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00447","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.43436199426651,"id":"https://metadata.un.org/sdg/10"},{"display_name":"Peace, Justice and strong institutions","score":0.41554009914398193,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Proportional":[0],"fairness":[1,110],"criteria":[2,111],"inspired":[3],"by":[4,43,71],"democratic":[5],"ideals":[6],"of":[7,100],"proportional":[8,109],"representation":[9,120],"have":[10],"received":[11],"growing":[12],"attention":[13],"in":[14,23,35,52,63,80,91,137,173],"the":[15,113,135,142,165],"clustering":[16],"literature.":[17],"Prior":[18],"work":[19],"has":[20],"investigated":[21],"them":[22],"two":[24,108],"separate":[25],"paradigms.":[26],"Chen":[27],"et":[28,56],"al.":[29,57],"[ICML":[30],"2019]":[31],"study":[32,60,107],"centroid":[33,102,147],"clustering,":[34,62,90],"which":[36,64,92,129],"each":[37,65,93,174],"data":[38,66,78,94],"point's":[39,67,95],"loss":[40,68,96,150,162],"is":[41,69,97,125],"determined":[42,70],"its":[44,53,72,81,101,116],"distance":[45,74,143],"to":[46,75,87,134],"a":[47,98,126,131],"representative":[48],"point":[49,79],"(centroid)":[50],"chosen":[51],"cluster.":[54,82],"Caragiannis":[55],"[NeurIPS":[58],"2024]":[59],"non-centroid":[61,104,149],"maximum":[73],"any":[76],"other":[77],"We":[83,154],"generalize":[84],"both":[85],"paradigms":[86],"introduce":[88],"semi-centroid":[89],"combination":[99],"and":[103,106,148,164,169],"losses,":[105],"--":[112],"core":[114],"and,":[115],"relaxation,":[117],"fully":[118],"justified":[119],"(FJR).":[121],"Our":[122],"main":[123],"result":[124],"novel":[127],"algorithm":[128],"achieves":[130],"constant":[132],"approximation":[133],"core,":[136],"polynomial":[138],"time,":[139],"even":[140],"when":[141],"metrics":[144],"used":[145],"for":[146,159],"measurements":[151],"are":[152],"different.":[153],"also":[155],"derive":[156],"improved":[157],"results":[158],"more":[160],"restricted":[161],"functions":[163],"weaker":[166],"FJR":[167],"criterion,":[168],"establish":[170],"lower":[171],"bounds":[172],"case.":[175]},"counts_by_year":[],"updated_date":"2026-01-08T20:10:11.968330","created_date":"2026-01-08T00:00:00"}
