{"id":"https://openalex.org/W7155550963","doi":"https://doi.org/10.48550/arxiv.2604.21798","title":"An effective variant of the Hartigan $k$-means algorithm","display_name":"An effective variant of the Hartigan $k$-means algorithm","publication_year":2026,"publication_date":"2026-04-23","ids":{"openalex":"https://openalex.org/W7155550963","doi":"https://doi.org/10.48550/arxiv.2604.21798"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.21798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21798","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.21798","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134471259","display_name":"Fran\u00e7ois Cl\u00e9ment","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment, Fran\u00e7ois","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054778975","display_name":"Stefan Steinerberger","orcid":"https://orcid.org/0000-0002-7745-4217"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steinerberger, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.7106000185012817,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.7106000185012817,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.05950000137090683,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.024900000542402267,"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":0.5410000085830688},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5329999923706055},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45660001039505005},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.4011000096797943},{"id":"https://openalex.org/keywords/algorithm-design","display_name":"Algorithm design","score":0.4009999930858612},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.34200000762939453}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6668000221252441},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5410000085830688},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5329999923706055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5230000019073486},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4090999960899353},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.4011000096797943},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.4009999930858612},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2924000024795532},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2572000026702881}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.21798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21798","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:10.48550/arxiv.2604.21798","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.21798","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"k-means":[1],"problem":[2,8],"is":[3],"perhaps":[4],"the":[5,58],"classical":[6],"clustering":[7],"and":[9],"often":[10],"synonymous":[11],"with":[12],"Lloyd's":[13],"algorithm":[14,22],"(1957).":[15],"It":[16],"has":[17],"become":[18,62],"clear":[19],"that":[20,43],"Hartigan's":[21,49],"(1975)":[23],"gives":[24],"better":[25],"results":[26],"in":[27],"almost":[28],"all":[29],"cases,":[30],"Telgarsky-Vattani":[31],"note":[32],"a":[33,44],"typical":[34],"improvement":[35,59],"of":[36,48],"$5\\%$":[37,56],"--":[38,55],"$10\\%$.":[39],"We":[40],"point":[41],"out":[42],"very":[45],"minor":[46],"variation":[47],"method":[50],"leads":[51],"to":[52,61],"another":[53],"$2\\%$":[54],"improvement;":[57],"tends":[60],"larger":[63],"when":[64],"either":[65],"dimension":[66],"or":[67],"$k$":[68],"increase.":[69]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-25T00:00:00"}
