{"id":"https://openalex.org/W2146848909","doi":"https://doi.org/10.1109/fuzzy.2007.4295344","title":"Pareto Optimality of Cluster Objective and Validity Functions","display_name":"Pareto Optimality of Cluster Objective and Validity Functions","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2146848909","doi":"https://doi.org/10.1109/fuzzy.2007.4295344","mag":"2146848909"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2007.4295344","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2007.4295344","pdf_url":null,"source":{"id":"https://openalex.org/S4210187232","display_name":"Proceedings of ... IEEE International Conference on Fuzzy Systems","issn_l":"1098-7584","issn":["1098-7584"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Fuzzy Systems Conference","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/A5002518694","display_name":"Thomas A. Runkler","orcid":"https://orcid.org/0000-0002-5465-198X"},"institutions":[{"id":"https://openalex.org/I1325886976","display_name":"Siemens (Germany)","ror":"https://ror.org/059mq0909","country_code":"DE","type":"company","lineage":["https://openalex.org/I1325886976"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Thomas A. Runkler","raw_affiliation_strings":["Information and Communications, Siemens Corporate Technology, Munich, Germany","Siemens Corp. Technol., Munich"],"affiliations":[{"raw_affiliation_string":"Information and Communications, Siemens Corporate Technology, Munich, Germany","institution_ids":["https://openalex.org/I1325886976"]},{"raw_affiliation_string":"Siemens Corp. Technol., Munich","institution_ids":["https://openalex.org/I1325886976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002518694"],"corresponding_institution_ids":["https://openalex.org/I1325886976"],"apc_list":null,"apc_paid":null,"fwci":0.7611,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.71472185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9858999848365784,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9764000177383423,"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/cluster-analysis","display_name":"Cluster analysis","score":0.845486044883728},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.6446173191070557},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.5529744625091553},{"id":"https://openalex.org/keywords/fuzzy-clustering","display_name":"Fuzzy clustering","score":0.5429338216781616},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5256539583206177},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.49866342544555664},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45608067512512207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39022937417030334},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37562060356140137},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.314893901348114}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.845486044883728},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.6446173191070557},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.5529744625091553},{"id":"https://openalex.org/C17212007","wikidata":"https://www.wikidata.org/wiki/Q5511111","display_name":"Fuzzy clustering","level":3,"score":0.5429338216781616},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5256539583206177},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.49866342544555664},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45608067512512207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39022937417030334},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37562060356140137},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.314893901348114},{"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/fuzzy.2007.4295344","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2007.4295344","pdf_url":null,"source":{"id":"https://openalex.org/S4210187232","display_name":"Proceedings of ... IEEE International Conference on Fuzzy Systems","issn_l":"1098-7584","issn":["1098-7584"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE International Fuzzy Systems Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1515360232","https://openalex.org/W1561886765","https://openalex.org/W1607203124","https://openalex.org/W1983772724","https://openalex.org/W1992903803","https://openalex.org/W1996747841","https://openalex.org/W2019875374","https://openalex.org/W2029906715","https://openalex.org/W2051224630","https://openalex.org/W2099495349","https://openalex.org/W2113076747","https://openalex.org/W2120688485","https://openalex.org/W2130070473"],"related_works":["https://openalex.org/W2945382830","https://openalex.org/W4224807364","https://openalex.org/W2596632494","https://openalex.org/W2535986621","https://openalex.org/W1980197432","https://openalex.org/W2382432689","https://openalex.org/W2000612978","https://openalex.org/W4388110928","https://openalex.org/W1483228865","https://openalex.org/W4292434959"],"abstract_inverted_index":{"Clustering":[0],"is":[1,28],"often":[2,29],"done":[3],"by":[4,31],"minimizing":[5],"an":[6,56],"objective":[7,38,81],"function":[8],"of":[9,25,79],"a":[10,65],"clustering":[11,58,99],"model.":[12],"Several":[13],"runs":[14],"with":[15,88],"different":[16],"initializations":[17],"or":[18],"parameters":[19],"yield":[20],"multiple":[21],"solutions.":[22],"The":[23],"best":[24],"these":[26],"solutions":[27],"selected":[30],"cluster":[32,37],"validity":[33,40,83],"measures.":[34],"We":[35],"analyze":[36],"and":[39,42,49,82,92],"functions":[41],"show":[43],"that":[44,73],"they":[45],"can":[46],"be":[47,52],"contradictory":[48],"therefore":[50],"should":[51],"considered":[53],"jointly":[54],"in":[55],"integrated":[57],"approach.":[59],"For":[60],"this":[61],"reason":[62],"we":[63],"define":[64],"<i":[66],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[67],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Pareto":[68],"fuzzy":[69],"c-means":[70],"clustering</i>":[71],"model":[72],"produces":[74],"the":[75,89,93],"Pareto":[76,98],"optimal":[77],"set":[78],"both":[80],"functions.":[84],"In":[85],"our":[86],"experiments":[87],"single":[90],"outlier":[91],"lung":[94],"cancer":[95],"data":[96],"sets":[97],"considerably":[100],"outperforms":[101],"conventional":[102],"clustering.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}