{"id":"https://openalex.org/W3206426022","doi":"https://doi.org/10.1109/iisa52424.2021.9555497","title":"A comparative study of validity indices on estimating the optimal number of clusters","display_name":"A comparative study of validity indices on estimating the optimal number of clusters","publication_year":2021,"publication_date":"2021-07-12","ids":{"openalex":"https://openalex.org/W3206426022","doi":"https://doi.org/10.1109/iisa52424.2021.9555497","mag":"3206426022"},"language":"en","primary_location":{"id":"doi:10.1109/iisa52424.2021.9555497","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iisa52424.2021.9555497","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 12th International Conference on Information, Intelligence, Systems & Applications (IISA)","raw_type":"proceedings-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/A5088798284","display_name":"Aikaterini Karanikola","orcid":"https://orcid.org/0009-0006-4226-6597"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Aikaterini Karanikola","raw_affiliation_strings":["University of Patras, Patras, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Patras, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045145081","display_name":"Charalampos M. Liapis","orcid":"https://orcid.org/0000-0002-4717-031X"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Charalampos M. Liapis","raw_affiliation_strings":["University of Patras, Patras, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Patras, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066370772","display_name":"Sotiris Kotsiantis","orcid":"https://orcid.org/0000-0002-2247-3082"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Sotiris Kotsiantis","raw_affiliation_strings":["University of Patras, Patras, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Patras, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2799,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64973176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9929999709129333,"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"}},{"id":"https://openalex.org/T12114","display_name":"Sensory Analysis and Statistical Methods","score":0.9309999942779541,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7439448833465576},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6422922611236572},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5732699632644653},{"id":"https://openalex.org/keywords/determining-the-number-of-clusters-in-a-data-set","display_name":"Determining the number of clusters in a data set","score":0.4989774227142334},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.47766146063804626},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.47623780369758606},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.47275906801223755},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.43321698904037476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38605639338493347},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30371206998825073},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"Correlation clustering","score":0.27068445086479187},{"id":"https://openalex.org/keywords/cure-data-clustering-algorithm","display_name":"CURE data clustering algorithm","score":0.12298554182052612}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7439448833465576},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6422922611236572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5732699632644653},{"id":"https://openalex.org/C149872217","wikidata":"https://www.wikidata.org/wiki/Q5265701","display_name":"Determining the number of clusters in a data set","level":5,"score":0.4989774227142334},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.47766146063804626},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.47623780369758606},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.47275906801223755},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.43321698904037476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38605639338493347},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30371206998825073},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.27068445086479187},{"id":"https://openalex.org/C33704608","wikidata":"https://www.wikidata.org/wiki/Q5014717","display_name":"CURE data clustering algorithm","level":4,"score":0.12298554182052612},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iisa52424.2021.9555497","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iisa52424.2021.9555497","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 12th International Conference on Information, Intelligence, Systems & Applications (IISA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W108464071","https://openalex.org/W152900593","https://openalex.org/W189063709","https://openalex.org/W1270205671","https://openalex.org/W1493454437","https://openalex.org/W1498782169","https://openalex.org/W1600820873","https://openalex.org/W1697154133","https://openalex.org/W1944603233","https://openalex.org/W1974758710","https://openalex.org/W1975152892","https://openalex.org/W1977556410","https://openalex.org/W1987971958","https://openalex.org/W2002767255","https://openalex.org/W2008788779","https://openalex.org/W2016381774","https://openalex.org/W2026882380","https://openalex.org/W2029064186","https://openalex.org/W2043793719","https://openalex.org/W2051224630","https://openalex.org/W2053718475","https://openalex.org/W2061554433","https://openalex.org/W2085572798","https://openalex.org/W2088879945","https://openalex.org/W2090658088","https://openalex.org/W2091480648","https://openalex.org/W2101234009","https://openalex.org/W2107946060","https://openalex.org/W2113586398","https://openalex.org/W2127218421","https://openalex.org/W2129066856","https://openalex.org/W2132047750","https://openalex.org/W2165187708","https://openalex.org/W2229908198","https://openalex.org/W2314965981","https://openalex.org/W2324662912","https://openalex.org/W2586919930","https://openalex.org/W2611775752","https://openalex.org/W2752363677","https://openalex.org/W2752973482","https://openalex.org/W2911429292","https://openalex.org/W2913066018","https://openalex.org/W2949488362","https://openalex.org/W2952380632","https://openalex.org/W2999729612","https://openalex.org/W3007204986","https://openalex.org/W3016210511","https://openalex.org/W3083424454","https://openalex.org/W3120740533","https://openalex.org/W4235169531","https://openalex.org/W4237058027","https://openalex.org/W4242401062","https://openalex.org/W4248391971","https://openalex.org/W4253794406","https://openalex.org/W4285719527","https://openalex.org/W4294141750","https://openalex.org/W6675354045","https://openalex.org/W6678914141","https://openalex.org/W6689475862","https://openalex.org/W6698813454"],"related_works":["https://openalex.org/W2085801246","https://openalex.org/W2050713761","https://openalex.org/W2040929534","https://openalex.org/W2385718412","https://openalex.org/W2065539689","https://openalex.org/W2513832396","https://openalex.org/W4367295867","https://openalex.org/W2945255906","https://openalex.org/W1584028106","https://openalex.org/W1987780927"],"abstract_inverted_index":{"In":[0,35,43,127],"clustering,":[1],"finding":[2],"the":[3,12,17,24,37,46,55,62,66,74,93,99,105,123,141,144,179],"optimal":[4,25,47,111],"number":[5,26,48,132],"of":[6,11,27,49,65,73,96,107,119,133,143,154,181,190],"clusters":[7,50,78,85],"is":[8,30,40,51,176],"usually":[9],"one":[10,165,169],"most":[13,90],"crucial":[14],"steps":[15],"in":[16,101,112,160,166,170,199],"whole":[18],"partitioning":[19],"process.":[20],"The":[21,195],"decision":[22],"about":[23],"clusters,":[28],"however,":[29],"not":[31],"easy":[32],"to":[33,58,103],"make.":[34],"addition,":[36],"term":[38],"\u201doptimal\u201d":[39],"rather":[41],"vague.":[42],"general,":[44],"determining":[45],"directly":[52],"dependent":[53],"on":[54,140],"method":[56],"used":[57],"measure":[59],"similarities":[60],"and":[61,168],"parameter":[63],"selection":[64],"partition":[67],"method.":[68],"Moreover,":[69],"certain":[70],"inherent":[71],"characteristics":[72],"datasets,":[75],"such":[76,109,134],"as":[77],"that":[79,86],"overlap":[80],"with":[81],"each":[82,113],"other":[83],"or":[84],"contain":[87],"subclusters,":[88],"may,":[89],"often,":[91],"increase":[92],"task\u2019s":[94],"level":[95],"difficulty.":[97],"Given":[98],"above,":[100],"order":[102],"tackle":[104],"problem":[106],"estimating":[108],"an":[110],"distinct":[114],"clustering":[115,184],"case,":[116],"different":[117,183,192],"kind":[118],"indicators":[120],"have":[121],"over":[122],"years":[124],"been":[125],"proposed.":[126],"this":[128],"study,":[129],"a":[130,152,188],"large":[131],"indicators,":[135],"called":[136],"validity":[137,156],"indices,":[138],"based":[139],"approach":[142],"so-called":[145],"relative":[146],"criteria,":[147],"are":[148,158,197],"examined":[149,159],"comparatively.":[150],"Specifically,":[151],"total":[153,189],"26":[155],"indices":[157],"two":[161],"separate":[162],"study":[163],"cases:":[164],"real-world":[167],"artificially":[171],"generated":[172],"data.":[173],"Every":[174],"index":[175],"utilized":[177],"under":[178],"schemes":[180],"9":[182],"methods":[185],"which":[186],"incorporate":[187],"5":[191],"distance":[193],"metrics.":[194],"results":[196],"presented":[198],"various":[200],"explanatory":[201],"forms.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}