{"id":"https://openalex.org/W7128636113","doi":"https://doi.org/10.48550/arxiv.2602.09936","title":"The Catastrophic Failure of The k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It","display_name":"The Catastrophic Failure of The k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It","publication_year":2026,"publication_date":"2026-02-10","ids":{"openalex":"https://openalex.org/W7128636113","doi":"https://doi.org/10.48550/arxiv.2602.09936"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.09936","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lederman, Roy R.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lederman, Roy R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022154740","display_name":"David Silva-S\u00e1nchez","orcid":"https://orcid.org/0000-0002-1301-9945"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Silva-S\u00e1nchez, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125660434","display_name":"Ziling Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Ziling","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071357040","display_name":"Gilles Mordant","orcid":"https://orcid.org/0000-0003-1821-5168"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mordant, Gilles","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125682927","display_name":"Amnon Balanov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Balanov, Amnon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125633507","display_name":"Tamir Bendory","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bendory, Tamir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"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":0.8082000017166138,"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":0.8082000017166138,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.014600000344216824,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.013700000010430813,"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/catastrophic-failure","display_name":"Catastrophic failure","score":0.5986999869346619},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.597599983215332},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5753999948501587},{"id":"https://openalex.org/keywords/algorithm-design","display_name":"Algorithm design","score":0.3815999925136566},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.2732999920845032}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.8378999829292297},{"id":"https://openalex.org/C112987892","wikidata":"https://www.wikidata.org/wiki/Q5051574","display_name":"Catastrophic failure","level":2,"score":0.5986999869346619},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5753999948501587},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4959000051021576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3862999975681305},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2492000013589859}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.09936","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.09936","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.09936","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":"pmh:doi:10.48550/arxiv.2602.09936","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Lloyd's":[0,38],"k-means":[1,63,91],"algorithm":[2,20,39,64],"is":[3,33],"one":[4],"of":[5,30],"the":[6,19,31,48,73,85],"most":[7],"widely":[8],"used":[9],"clustering":[10],"methods.":[11,56],"We":[12],"prove":[13,60],"that":[14,61],"in":[15,92],"high-dimensional,":[16],"high-noise":[17],"settings,":[18],"exhibits":[21],"catastrophic":[22],"failure:":[23],"with":[24,90],"high":[25,93],"probability,":[26],"essentially":[27],"every":[28],"partition":[29,44],"data":[32],"a":[34,81],"fixed":[35],"point.":[36],"Consequently,":[37],"simply":[40],"returns":[41],"its":[42],"initial":[43],"-":[45],"even":[46],"when":[47],"underlying":[49],"clusters":[50],"are":[51],"trivially":[52],"recoverable":[53],"by":[54],"other":[55],"In":[57],"contrast,":[58],"we":[59],"Hartigan's":[62],"does":[65],"not":[66],"exhibit":[67],"this":[68],"pathology.":[69],"Our":[70],"results":[71],"show":[72],"stark":[74],"difference":[75],"between":[76],"these":[77],"algorithms":[78],"and":[79],"offer":[80],"theoretical":[82],"explanation":[83],"for":[84],"empirical":[86],"difficulties":[87],"often":[88],"observed":[89],"dimensions.":[94]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-12T00:00:00"}