{"id":"https://openalex.org/W2100668960","doi":"https://doi.org/10.1109/fuzzy.2011.6007431","title":"On hard and fuzzy c-means clustering with conditionally positive definite kernel","display_name":"On hard and fuzzy c-means clustering with conditionally positive definite kernel","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W2100668960","doi":"https://doi.org/10.1109/fuzzy.2011.6007431","mag":"2100668960"},"language":"en","primary_location":{"id":"doi:10.1109/fuzzy.2011.6007431","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2011.6007431","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)","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/A5033247953","display_name":"Yuchi Kanzawa","orcid":"https://orcid.org/0000-0002-4421-3513"},"institutions":[{"id":"https://openalex.org/I171481255","display_name":"Shibaura Institute of Technology","ror":"https://ror.org/020wjcq07","country_code":"JP","type":"education","lineage":["https://openalex.org/I171481255"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yuchi Kanzawa","raw_affiliation_strings":["Shibaura Institute of Technology, Tokyo, Japan","Shibaura Institute of Technology, Tokyo, Japan 135---8548#TAB#"],"affiliations":[{"raw_affiliation_string":"Shibaura Institute of Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I171481255"]},{"raw_affiliation_string":"Shibaura Institute of Technology, Tokyo, Japan 135---8548#TAB#","institution_ids":["https://openalex.org/I171481255"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101943648","display_name":"Yasunori Endo","orcid":"https://orcid.org/0000-0003-2968-4613"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasunori Endo","raw_affiliation_strings":["University of Tsukuba, Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102283856","display_name":"Sadaaki Miyamoto","orcid":null},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Sadaaki Miyamoto","raw_affiliation_strings":["University of Tsukuba, Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"University of Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I146399215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5033247953"],"corresponding_institution_ids":["https://openalex.org/I171481255"],"apc_list":null,"apc_paid":null,"fwci":0.4276,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73000472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"220","issue":null,"first_page":"816","last_page":"820"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.988099992275238,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.988099992275238,"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":0.9860000014305115,"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":0.9803000092506409,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7200901508331299},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6934520602226257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6607767343521118},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.5364020466804504},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.5327568054199219},{"id":"https://openalex.org/keywords/string-kernel","display_name":"String kernel","score":0.5318287014961243},{"id":"https://openalex.org/keywords/kernel-principal-component-analysis","display_name":"Kernel principal component analysis","score":0.5049133896827698},{"id":"https://openalex.org/keywords/radial-basis-function-kernel","display_name":"Radial basis function kernel","score":0.5047930479049683},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.48935574293136597},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.4829689562320709},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4436291456222534},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4237160384654999},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3418753445148468},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30070167779922485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2702992260456085},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08445477485656738},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.07943138480186462},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0633244514465332}],"concepts":[{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7200901508331299},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6934520602226257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6607767343521118},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.5364020466804504},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.5327568054199219},{"id":"https://openalex.org/C55851704","wikidata":"https://www.wikidata.org/wiki/Q7623983","display_name":"String kernel","level":5,"score":0.5318287014961243},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.5049133896827698},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.5047930479049683},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.48935574293136597},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.4829689562320709},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4436291456222534},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4237160384654999},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3418753445148468},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30070167779922485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2702992260456085},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08445477485656738},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.07943138480186462},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0633244514465332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/fuzzy.2011.6007431","is_oa":false,"landing_page_url":"https://doi.org/10.1109/fuzzy.2011.6007431","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W47086337","https://openalex.org/W113272678","https://openalex.org/W158853751","https://openalex.org/W181974580","https://openalex.org/W1569189826","https://openalex.org/W1974069854","https://openalex.org/W1984831507","https://openalex.org/W2013841912","https://openalex.org/W2017941395","https://openalex.org/W2024060531","https://openalex.org/W2033923276","https://openalex.org/W2049778360","https://openalex.org/W2061708588","https://openalex.org/W2066349792","https://openalex.org/W2067603665","https://openalex.org/W2081749411","https://openalex.org/W2090085801","https://openalex.org/W2090320469","https://openalex.org/W2113076747","https://openalex.org/W2119529803","https://openalex.org/W2131034441","https://openalex.org/W2133324003","https://openalex.org/W2148603752","https://openalex.org/W2151037347","https://openalex.org/W2152195021","https://openalex.org/W2169934749","https://openalex.org/W6646599892"],"related_works":["https://openalex.org/W3013206934","https://openalex.org/W3100948281","https://openalex.org/W2535206775","https://openalex.org/W2393746448","https://openalex.org/W4311138679","https://openalex.org/W4291669689","https://openalex.org/W1984421104","https://openalex.org/W2005311689","https://openalex.org/W2071590642","https://openalex.org/W2366185040"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"investigate":[4],"three":[5],"types":[6],"of":[7,61],"c-means":[8,107,112],"clustering":[9],"algorithms":[10,54],"with":[11,114],"a":[12,37,43,85,88,102,110,115,136],"conditionally":[13,38,77,103,122,137],"positive":[14,39,73,78,104,116,123,138],"definite":[15,40,74,79,105,117,124,139],"kernel.":[16],"One":[17],"is":[18,95,99,141],"based":[19,27,35,67],"on":[20,28,36,68],"hard":[21],"c-means,":[22],"and":[23,30,76,87,109],"the":[24,50,62,69,72,81,92,121],"others":[25],"are":[26,55,126],"standard":[29],"entropy-regularized":[31],"fuzzy":[32],"c-means.":[33,65],"First,":[34],"kernel":[41,64,75,106,111,118,125,140],"describing":[42],"squared":[44],"Euclidean":[45],"distance":[46],"between":[47,71,84],"data":[48],"in":[49,91],"feature":[51,93],"space,":[52],"these":[53],"derived":[56,119],"from":[57,120],"revised":[58,82],"optimization":[59],"problems":[60],"conventional":[63],"Next,":[66],"relationship":[70],"kernel,":[80],"dissimilarity":[83],"datum":[86],"cluster":[89],"center":[90],"space":[94],"shown.":[96],"Finally,":[97],"it":[98],"shown":[100],"that":[101],"algorithm":[108,113],"essentially":[127],"identical":[128],"to":[129],"each":[130],"other.":[131],"An":[132],"explicit":[133],"mapping":[134],"for":[135],"also":[142],"described":[143],"geometrically.":[144]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
