{"id":"https://openalex.org/W3036726025","doi":"https://doi.org/10.1109/tkde.2020.3002926","title":"An efficient Split-Merge re-start for the K-means algorithm","display_name":"An efficient Split-Merge re-start for the K-means algorithm","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3036726025","doi":"https://doi.org/10.1109/tkde.2020.3002926","mag":"3036726025"},"language":"en","primary_location":{"id":"doi:10.1109/tkde.2020.3002926","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2020.3002926","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","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/A5048498433","display_name":"Marco Cap\u00f3","orcid":"https://orcid.org/0000-0001-7166-6940"},"institutions":[{"id":"https://openalex.org/I2802176441","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32","country_code":"ES","type":"education","lineage":["https://openalex.org/I2802176441"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Marco Capo","raw_affiliation_strings":["Basque Center of Applied Mathematics, Bilbao, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basque Center of Applied Mathematics, Bilbao, Spain","institution_ids":["https://openalex.org/I2802176441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053399459","display_name":"Aritz P\u00e9rez","orcid":"https://orcid.org/0000-0002-8128-1099"},"institutions":[{"id":"https://openalex.org/I2802176441","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32","country_code":"ES","type":"education","lineage":["https://openalex.org/I2802176441"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Aritz Perez","raw_affiliation_strings":["Basque Center of Applied Mathematics, Bilbao, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basque Center of Applied Mathematics, Bilbao, Spain","institution_ids":["https://openalex.org/I2802176441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103912696","display_name":"Jose A. Antonio Lozano","orcid":null},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]},{"id":"https://openalex.org/I2802176441","display_name":"Basque Center for Applied Mathematics","ror":"https://ror.org/03b21sh32","country_code":"ES","type":"education","lineage":["https://openalex.org/I2802176441"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jose A. Antonio Lozano","raw_affiliation_strings":["Basque Center of Applied Mathematics, Bilbao, Spain","Department of Computer Science and Artificial Intelligence, Intelligent Systems Group, University of the Basque Country UPV/EHU, San Sebasti\u00e1n, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basque Center of Applied Mathematics, Bilbao, Spain","institution_ids":["https://openalex.org/I2802176441"]},{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, Intelligent Systems Group, University of the Basque Country UPV/EHU, San Sebasti\u00e1n, Spain","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":2.9857,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.92711703,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12761","display_name":"Data Stream Mining Techniques","score":0.998199999332428,"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/T12761","display_name":"Data Stream Mining Techniques","score":0.998199999332428,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9975000023841858,"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/T11106","display_name":"Data Management and Algorithms","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/initialization","display_name":"Initialization","score":0.6356868147850037},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6141942143440247},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5769281983375549},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.5586138963699341},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47525474429130554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4024611711502075},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37062108516693115},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11480101943016052}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.6356868147850037},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6141942143440247},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5769281983375549},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.5586138963699341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47525474429130554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4024611711502075},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37062108516693115},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11480101943016052},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tkde.2020.3002926","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2020.3002926","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Knowledge and Data Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W87092222","https://openalex.org/W1489608363","https://openalex.org/W1498782169","https://openalex.org/W1501500081","https://openalex.org/W1819316285","https://openalex.org/W1973264045","https://openalex.org/W1977556410","https://openalex.org/W1980317569","https://openalex.org/W1989270503","https://openalex.org/W2002586964","https://openalex.org/W2011430131","https://openalex.org/W2045964207","https://openalex.org/W2051293718","https://openalex.org/W2059515884","https://openalex.org/W2086959852","https://openalex.org/W2103718624","https://openalex.org/W2103868202","https://openalex.org/W2108399535","https://openalex.org/W2110105238","https://openalex.org/W2113540758","https://openalex.org/W2121853761","https://openalex.org/W2128087969","https://openalex.org/W2142827986","https://openalex.org/W2142838865","https://openalex.org/W2150593711","https://openalex.org/W2156097299","https://openalex.org/W2161160262","https://openalex.org/W2171125141","https://openalex.org/W2319660501","https://openalex.org/W2462044331","https://openalex.org/W2807006342","https://openalex.org/W2940320374","https://openalex.org/W2950437976","https://openalex.org/W3011417748","https://openalex.org/W6606319353","https://openalex.org/W6629092883","https://openalex.org/W6630018080","https://openalex.org/W6635035540","https://openalex.org/W6636734143","https://openalex.org/W6640131216","https://openalex.org/W6668990524","https://openalex.org/W6677408164","https://openalex.org/W6685529966","https://openalex.org/W6729392090"],"related_works":["https://openalex.org/W3204184292","https://openalex.org/W3176564347","https://openalex.org/W1985458517","https://openalex.org/W2355833770","https://openalex.org/W3031039437","https://openalex.org/W3095877357","https://openalex.org/W183202219","https://openalex.org/W2072565696","https://openalex.org/W10861731","https://openalex.org/W2050451745"],"abstract_inverted_index":{"The$K$-means":[0],"algorithm":[1,66,116],"is":[2,12,60,86,154,164],"one":[3,70,125],"of":[4,21,23,71,94,98,134,144,184],"the":[5,24,46,76,79,95,132,135,187],"most":[6],"popular":[7],"clustering":[8],"methods.":[9],"However,":[10],"it":[11,59],"a":[13,84,91,105,119,181],"well-known":[14],"fact":[15],"that":[16,109,128,151,163],"its":[17,33,50],"performance,":[18],"in":[19],"terms":[20],"quality":[22],"obtained":[25],"solution":[26,77],"and":[27,74,176],"computational":[28],"load,":[29],"highly":[30],"depends":[31],"upon":[32],"initialization":[34,40],"phase.":[35],"For":[36],"this":[37,57,101,129,152],"reason,":[38],"different":[39,169],"techniques":[41,73],"have":[42],"been":[43],"developed":[44],"throughout":[45],"years":[47],"to":[48,53,63,89,113,156,166],"enable":[49],"fast":[51],"convergence":[52],"competitive":[54],"solutions.":[55],"In":[56,100],"sense,":[58],"common":[61],"practice":[62],"re-start":[64,114],"the$K$-means":[65,115,145],"several":[67],"times":[68],"via":[69],"these":[72],"keep":[75],"with":[78,159],"lowest":[80],"error.":[81],"Unfortunately,":[82],"such":[83,172],"choice":[85],"still":[87],"likely":[88],"be":[90,111],"poor":[92],"approximation":[93],"optimal":[96],"set":[97],"centroids.":[99],"article,":[102],"we":[103],"introduce":[104],"cheap":[106],"Split-Merge":[107],"step":[108],"can":[110,126],"used":[112],"after":[117],"reaching":[118],"fixed":[120,137],"point.":[121],"Under":[122],"some":[123],"settings,":[124],"show":[127,150],"approach":[130],"reduces":[131],"error":[133,162],"given":[136],"point":[138],"without":[139],"requiring":[140],"any":[141],"further":[142],"iteration":[143],"algorithm.":[146],"Moreover,":[147],"experimental":[148],"results":[149],"strategy":[153],"able":[155],"generate":[157],"approximations":[158],"an":[160],"associated":[161],"hard":[165],"reach":[167],"for":[168],"multi-start":[170,174],"methods,":[171],"as":[173],"Forgy$K$-means,$K$-means++":[175],"Hartigan$K$-means,":[177],"while":[178],"also":[179],"computing":[180],"lower":[182],"amount":[183],"distances":[185],"than":[186],"previous":[188],"algorithms.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}