{"id":"https://openalex.org/W7117447140","doi":"https://doi.org/10.1109/access.2025.3649210","title":"M <i>k</i> -Means: Improving Partition-Based Clustering With Optimized Centroid Initialization","display_name":"M <i>k</i> -Means: Improving Partition-Based Clustering With Optimized Centroid Initialization","publication_year":2025,"publication_date":"2025-12-29","ids":{"openalex":"https://openalex.org/W7117447140","doi":"https://doi.org/10.1109/access.2025.3649210"},"language":null,"primary_location":{"id":"doi:10.1109/access.2025.3649210","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3649210","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2025.3649210","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091529265","display_name":"Rosy Sarmah","orcid":"https://orcid.org/0000-0003-2564-426X"},"institutions":[{"id":"https://openalex.org/I126601174","display_name":"Tezpur University","ror":"https://ror.org/005x56091","country_code":"IN","type":"education","lineage":["https://openalex.org/I126601174"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rosy Sarmah","raw_affiliation_strings":["Department of CSE, Tezpur University, Tezpur, Assam, India"],"raw_orcid":"https://orcid.org/0000-0003-2564-426X","affiliations":[{"raw_affiliation_string":"Department of CSE, Tezpur University, Tezpur, Assam, India","institution_ids":["https://openalex.org/I126601174"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044005225","display_name":"Rabinder Kumar Prasad","orcid":"https://orcid.org/0000-0002-0182-156X"},"institutions":[{"id":"https://openalex.org/I64128412","display_name":"Dibrugarh University","ror":"https://ror.org/045kfbt16","country_code":"IN","type":"education","lineage":["https://openalex.org/I64128412"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rabinder Kumar Prasad","raw_affiliation_strings":["Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India"],"raw_orcid":"https://orcid.org/0000-0002-0182-156X","affiliations":[{"raw_affiliation_string":"Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India","institution_ids":["https://openalex.org/I64128412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019862234","display_name":"Moirangthem Tiken Singh","orcid":"https://orcid.org/0000-0002-5819-4149"},"institutions":[{"id":"https://openalex.org/I64128412","display_name":"Dibrugarh University","ror":"https://ror.org/045kfbt16","country_code":"IN","type":"education","lineage":["https://openalex.org/I64128412"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Moirangthem Tiken Singh","raw_affiliation_strings":["Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India"],"raw_orcid":"https://orcid.org/0000-0002-5819-4149","affiliations":[{"raw_affiliation_string":"Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India","institution_ids":["https://openalex.org/I64128412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091529265","display_name":"Rosy Sarmah","orcid":"https://orcid.org/0000-0003-2564-426X"},"institutions":[{"id":"https://openalex.org/I2800857658","display_name":"North East Institute of Science and Technology","ror":"https://ror.org/02p8nt844","country_code":"IN","type":"facility","lineage":["https://openalex.org/I2799351866","https://openalex.org/I2800857658","https://openalex.org/I4210134808","https://openalex.org/I66760702"]},{"id":"https://openalex.org/I35839044","display_name":"Assam Agricultural University","ror":"https://ror.org/05836pk12","country_code":"IN","type":"education","lineage":["https://openalex.org/I35839044"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sauravjyoti Sarmah","raw_affiliation_strings":["Department of CSE, Jorhat Engineering College, Jorhat, Assam, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of CSE, Jorhat Engineering College, Jorhat, Assam, India","institution_ids":["https://openalex.org/I35839044","https://openalex.org/I2800857658"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Abhijit Boruah","orcid":"https://orcid.org/0000-0001-6141-0191"},"institutions":[{"id":"https://openalex.org/I64128412","display_name":"Dibrugarh University","ror":"https://ror.org/045kfbt16","country_code":"IN","type":"education","lineage":["https://openalex.org/I64128412"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Abhijit Boruah","raw_affiliation_strings":["Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India"],"raw_orcid":"https://orcid.org/0000-0001-6141-0191","affiliations":[{"raw_affiliation_string":"Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India","institution_ids":["https://openalex.org/I64128412"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Sudipta Majumder","orcid":"https://orcid.org/0000-0002-1748-8685"},"institutions":[{"id":"https://openalex.org/I64128412","display_name":"Dibrugarh University","ror":"https://ror.org/045kfbt16","country_code":"IN","type":"education","lineage":["https://openalex.org/I64128412"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sudipta Majumder","raw_affiliation_strings":["Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India"],"raw_orcid":"https://orcid.org/0000-0002-1748-8685","affiliations":[{"raw_affiliation_string":"Department of CSE, DUIET, Dibrugarh University, Dibrugarh, Assam, India","institution_ids":["https://openalex.org/I64128412"]}]},{"author_position":"last","author":{"id":null,"display_name":"Minhazur Rahman","orcid":"https://orcid.org/0009-0004-4308-0343"},"institutions":[{"id":"https://openalex.org/I126601174","display_name":"Tezpur University","ror":"https://ror.org/005x56091","country_code":"IN","type":"education","lineage":["https://openalex.org/I126601174"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Minhazur Rahman","raw_affiliation_strings":["Department of CSE, Tezpur University, Tezpur, Assam, India"],"raw_orcid":"https://orcid.org/0009-0004-4308-0343","affiliations":[{"raw_affiliation_string":"Department of CSE, Tezpur University, Tezpur, Assam, India","institution_ids":["https://openalex.org/I126601174"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.77982486,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":null,"first_page":"1758","last_page":"1779"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9376999735832214,"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":0.9376999735832214,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.007300000172108412,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.004800000227987766,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.7664999961853027},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7429999709129333},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.7192000150680542},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6804999709129333},{"id":"https://openalex.org/keywords/rand-index","display_name":"Rand index","score":0.5450000166893005},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.45829999446868896},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4401000142097473},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.43959999084472656}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.7664999961853027},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7429999709129333},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.7192000150680542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7127000093460083},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6804999709129333},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.5568000078201294},{"id":"https://openalex.org/C111442797","wikidata":"https://www.wikidata.org/wiki/Q7291446","display_name":"Rand index","level":3,"score":0.5450000166893005},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4401000142097473},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.43959999084472656},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39149999618530273},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38530001044273376},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.3732999861240387},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C115328559","wikidata":"https://www.wikidata.org/wiki/Q4041956","display_name":"k-medians clustering","level":5,"score":0.3425000011920929},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C207968372","wikidata":"https://www.wikidata.org/wiki/Q310401","display_name":"k-means clustering","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2587999999523163}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/access.2025.3649210","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3649210","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/access.2025.3649210","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3649210","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W151377110","https://openalex.org/W1493454437","https://openalex.org/W1512252227","https://openalex.org/W1540089290","https://openalex.org/W1995450389","https://openalex.org/W2075117036","https://openalex.org/W2113054345","https://openalex.org/W2126626732","https://openalex.org/W2140405352","https://openalex.org/W2160642098","https://openalex.org/W2313250172","https://openalex.org/W2789548662","https://openalex.org/W2806620899","https://openalex.org/W2884586244","https://openalex.org/W2888022229","https://openalex.org/W2990595156","https://openalex.org/W3037528720","https://openalex.org/W3119102269","https://openalex.org/W3160252920","https://openalex.org/W3198231723","https://openalex.org/W3204359140","https://openalex.org/W3215495050","https://openalex.org/W4214817073","https://openalex.org/W4235169531","https://openalex.org/W4293558809","https://openalex.org/W4310494058","https://openalex.org/W4317796401","https://openalex.org/W4367301052","https://openalex.org/W4387521814","https://openalex.org/W4394621648","https://openalex.org/W4400360712","https://openalex.org/W4408359828"],"related_works":[],"abstract_inverted_index":{"The":[0,131,200,260],"<italic":[1,84,167,171,181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,85,89,136,168,172,182,184,187,189,192,194,198,205,243,266],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>-means":[3,90,137,206,244,267],"algorithm":[4,268],"is":[5,139,269],"a":[6,32,36,82,98],"well-known":[7],"technique":[8],"in":[9,73,97,210],"partition-based":[10],"clustering,":[11],"drawing":[12],"plenty":[13],"of":[14,49,77,111,120,124,133,212,230],"attention":[15],"by":[16,26,60,101],"researchers":[17,62],"over":[18],"the":[19,47,74,109,117,121,134,153,165,264],"years.":[20],"It":[21],"identifies":[22],"distinct,":[23],"non-overlapping":[24],"patterns":[25],"assigning":[27],"each":[28,125],"data":[29],"point":[30],"to":[31,63,92,107,127,257],"specific":[33],"cluster":[34,126,129],"using":[35,141],"minimum":[37],"squared":[38,112,122,231],"distance":[39],"approach.":[40],"However,":[41],"its\u2019":[42],"effectiveness":[43],"heavily":[44],"depends":[45],"on":[46],"selection":[48],"initial":[50],"centroid":[51],"values,":[52],"which":[53],"are":[54],"chosen":[55],"randomly.":[56],"Despite":[57],"numerous":[58],"attempts":[59],"different":[61],"address":[64],"this":[65],"limitation,":[66],"there":[67],"remains":[68],"significant":[69],"room":[70],"for":[71,263],"improvement":[72],"effective":[75],"initialization":[76],"centroids.":[78],"Here,":[79],"we":[80],"introduce":[81],"modified":[83],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>-means,":[86,169,185,190],"that":[87,203,241],"is,M<italic":[88],"method":[91,115,138],"precisely":[93],"detect":[94],"all":[95],"clusters":[96],"given":[99],"dataset":[100],"utilizing":[102],"as":[103,108,179,226,228],"objective":[104],"function":[105],"referred":[106],"sum":[110,119,229],"errors.":[113],"This":[114],"utilizes":[116],"partial":[118],"errors":[123],"improve":[128],"identification.":[130],"efficacy":[132],"M<italic":[135,204,242,265],"evaluated":[140],"15":[142,147],"synthetic":[143],"benchmark":[144,149],"datasets":[145,150],"and":[146,174,196,224],"real-world":[148],"obtained":[151],"from":[152],"UCI":[154],"repository.":[155],"Performance":[156],"comparisons":[157],"were":[158],"conducted":[159],"against":[160],"several":[161],"clustering":[162,250],"algorithms,":[163],"including":[164],"traditional":[166],"FCM,":[170],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>-means++,":[173,195],"more":[175,248],"recent":[176],"approaches":[177],"such":[178],"IKMN,":[180],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t</i>-<italic":[183,188,193],"fast-<italic":[186,191],"Global-<italic":[197],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>-means++.":[199],"results":[201],"demonstrate":[202],"outperforms":[207],"these":[208],"methods":[209],"terms":[211],"external":[213],"validity":[214,236],"indices-":[215],"Adjusted":[216],"Rand":[217],"Index":[218],"(ARI),":[219],"Normalized":[220],"Mutual":[221],"Information":[222],"(NMI),":[223],"Purity,":[225],"well":[227],"error":[232],"(SSE),":[233],"an":[234],"internal":[235],"index.":[237],"These":[238],"findings":[239],"highlight":[240],"not":[245],"only":[246],"achieves":[247],"accurate":[249],"but":[251],"also":[252],"reduces":[253],"within-cluster":[254],"variance":[255],"compared":[256],"its":[258],"counterparts.":[259],"source":[261],"code":[262],"publicly":[270],"available.":[271]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-12-29T00:00:00"}