{"id":"https://openalex.org/W2058224894","doi":"https://doi.org/10.1109/fuzz-ieee.2012.6250820","title":"Cluster validity for kernel fuzzy clustering","display_name":"Cluster validity for kernel fuzzy clustering","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2058224894","doi":"https://doi.org/10.1109/fuzz-ieee.2012.6250820","mag":"2058224894"},"language":"en","primary_location":{"id":"doi:10.1109/fuzz-ieee.2012.6250820","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2012.6250820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-article"},"type":"conference-paper","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/A5060923133","display_name":"Timothy C. Havens","orcid":"https://orcid.org/0000-0002-5746-3749"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy C. Havens","raw_affiliation_strings":["Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA","Department of Computer Science and Engineering, Michigan State University, East Lansing 48824, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Computer Science and Engineering, Michigan State University, East Lansing 48824, USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043324448","display_name":"James C. Bezdek","orcid":"https://orcid.org/0000-0003-3901-7021"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"James C. Bezdek","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC, Australia","Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Victoria, 3010, Australia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Victoria, 3010, Australia#TAB#","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080554686","display_name":"Marimuthu Palaniswami","orcid":"https://orcid.org/0000-0002-3635-4252"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Marimuthu Palaniswami","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC, Australia","Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Victoria, 3010, Australia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Victoria, 3010, Australia#TAB#","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":0.9990000128746033,"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":0.9990000128746033,"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/T10057","display_name":"Face and Expression Recognition","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9758999943733215,"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/kernel","display_name":"Kernel (algebra)","score":0.7154550552368164},{"id":"https://openalex.org/keywords/fuzzy-clustering","display_name":"Fuzzy clustering","score":0.6806489825248718},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6181942224502563},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6042331457138062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4975598156452179},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.49329155683517456},{"id":"https://openalex.org/keywords/flame-clustering","display_name":"FLAME clustering","score":0.4727051258087158},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.464089572429657},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.43992123007774353},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42940157651901245},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4278026223182678},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3842686414718628},{"id":"https://openalex.org/keywords/cure-data-clustering-algorithm","display_name":"CURE data clustering algorithm","score":0.16613948345184326},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.08715260028839111}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.7154550552368164},{"id":"https://openalex.org/C17212007","wikidata":"https://www.wikidata.org/wiki/Q5511111","display_name":"Fuzzy clustering","level":3,"score":0.6806489825248718},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6181942224502563},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6042331457138062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4975598156452179},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49329155683517456},{"id":"https://openalex.org/C44859942","wikidata":"https://www.wikidata.org/wiki/Q5426511","display_name":"FLAME clustering","level":5,"score":0.4727051258087158},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.464089572429657},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.43992123007774353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42940157651901245},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4278026223182678},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3842686414718628},{"id":"https://openalex.org/C33704608","wikidata":"https://www.wikidata.org/wiki/Q5014717","display_name":"CURE data clustering algorithm","level":4,"score":0.16613948345184326},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.08715260028839111},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzz-ieee.2012.6250820","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzz-ieee.2012.6250820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Fuzzy Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W76477875","https://openalex.org/W1520757484","https://openalex.org/W1585535067","https://openalex.org/W1956762544","https://openalex.org/W1971784203","https://openalex.org/W1978527081","https://openalex.org/W2043793719","https://openalex.org/W2053677366","https://openalex.org/W2055808834","https://openalex.org/W2057109784","https://openalex.org/W2066933428","https://openalex.org/W2070771945","https://openalex.org/W2094018360","https://openalex.org/W2112440119","https://openalex.org/W2113076747","https://openalex.org/W2120688485","https://openalex.org/W2127385182","https://openalex.org/W2127385662","https://openalex.org/W2130070473","https://openalex.org/W2144751992","https://openalex.org/W2169698116","https://openalex.org/W2170938037","https://openalex.org/W2319660501","https://openalex.org/W2795859997","https://openalex.org/W2913066018","https://openalex.org/W2999729612","https://openalex.org/W3120740533","https://openalex.org/W4253794406","https://openalex.org/W4301689241","https://openalex.org/W6603125384","https://openalex.org/W6634925791"],"related_works":["https://openalex.org/W3129335559","https://openalex.org/W2157383128","https://openalex.org/W2399084168","https://openalex.org/W4292964559","https://openalex.org/W2363077075","https://openalex.org/W3087769312","https://openalex.org/W2747006034","https://openalex.org/W2609785842","https://openalex.org/W1513651805","https://openalex.org/W4388658494"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"cluster":[3,13,60],"validity":[4,14,33,61],"for":[5,87],"kernel":[6,25,48,67,88],"fuzzy":[7,26,49,68,89],"clustering.":[8,50],"First,":[9],"we":[10,30,52],"describe":[11],"existing":[12,59],"indices":[15,34,62,81,86],"that":[16,35,56],"can":[17,44],"be":[18,45,64],"directly":[19],"applied":[20,46],"to":[21,47,63,66],"partitions":[22,92],"obtained":[23],"by":[24],"clustering":[27],"algorithms.":[28],"Second,":[29],"show":[31],"how":[32,74],"take":[36],"dissimilarity":[37],"(or":[38],"relational)":[39],"data":[40],"D":[41],"as":[42],"input":[43],"Third,":[51],"present":[53],"four":[54],"propositions":[55,76],"allow":[57],"other":[58],"adapted":[65],"partitions.":[69],"As":[70],"an":[71],"example":[72],"of":[73,93],"these":[75],"are":[77,82],"used,":[78],"five":[79],"well-known":[80],"formulated.We":[83],"demonstrate":[84],"several":[85],"c-means":[90],"(kFCM)":[91],"both":[94],"synthetic":[95],"and":[96],"real":[97],"data.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
