{"id":"https://openalex.org/W1965843934","doi":"https://doi.org/10.1109/grc.2009.5255128","title":"Comparison of tolerant fuzzy c-means clustering with L<sub>2</sub>- and L<sub>1</sub>-regularization","display_name":"Comparison of tolerant fuzzy c-means clustering with L<sub>2</sub>- and L<sub>1</sub>-regularization","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W1965843934","doi":"https://doi.org/10.1109/grc.2009.5255128","mag":"1965843934"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2009.5255128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2009.5255128","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Granular Computing","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/A5060898444","display_name":"Yukihiro Hamasuna","orcid":null},"institutions":[{"id":"https://openalex.org/I205924995","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466","country_code":"JP","type":"nonprofit","lineage":["https://openalex.org/I1319490839","https://openalex.org/I205924995"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yukihiro Hamasuna","raw_affiliation_strings":["Research Fellow of the Japan Society for the Promotion of Science, JSPS, 6 Ichibancho, Chiyoda-ku, Tokyo 102-8471, Japan"],"affiliations":[{"raw_affiliation_string":"Research Fellow of the Japan Society for the Promotion of Science, JSPS, 6 Ichibancho, Chiyoda-ku, Tokyo 102-8471, Japan","institution_ids":["https://openalex.org/I205924995"]}]},{"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":["Dept. of Risk Engineering, Fac., of Sys. and Info. Eng., University of Tsukuba, 1-1-1 Tennodai, Ibaraki 305-8573, Japan"],"affiliations":[{"raw_affiliation_string":"Dept. of Risk Engineering, Fac., of Sys. and Info. Eng., University of Tsukuba, 1-1-1 Tennodai, Ibaraki 305-8573, 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":["Dept. of Risk Engineering, Fac., of Sys. and Info. Eng., University of Tsukuba, 1-1-1 Tennodai, Ibaraki 305-8573, Japan"],"affiliations":[{"raw_affiliation_string":"Dept. of Risk Engineering, Fac., of Sys. and Info. Eng., University of Tsukuba, 1-1-1 Tennodai, Ibaraki 305-8573, Japan","institution_ids":["https://openalex.org/I146399215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060898444"],"corresponding_institution_ids":["https://openalex.org/I205924995"],"apc_list":null,"apc_paid":null,"fwci":0.8724,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.78764076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"197","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9976999759674072,"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":0.9976999759674072,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9918000102043152,"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/cluster-analysis","display_name":"Cluster analysis","score":0.7613952159881592},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7002450227737427},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.49948954582214355},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4410936236381531},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4338074326515198},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36808621883392334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32394856214523315},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2500261962413788}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7613952159881592},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7002450227737427},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.49948954582214355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4410936236381531},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4338074326515198},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36808621883392334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32394856214523315},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2500261962413788}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/grc.2009.5255128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2009.5255128","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Granular Computing","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":20,"referenced_works":["https://openalex.org/W1151941676","https://openalex.org/W1491951810","https://openalex.org/W1513271081","https://openalex.org/W1584532972","https://openalex.org/W1990263288","https://openalex.org/W2011873184","https://openalex.org/W2070541424","https://openalex.org/W2076467305","https://openalex.org/W2105837790","https://openalex.org/W2113076747","https://openalex.org/W2121749283","https://openalex.org/W2133286004","https://openalex.org/W2135046866","https://openalex.org/W2138036661","https://openalex.org/W2149846618","https://openalex.org/W2278532921","https://openalex.org/W2782043882","https://openalex.org/W6627396291","https://openalex.org/W6675965484","https://openalex.org/W6694777023"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2804364458","https://openalex.org/W2053286651","https://openalex.org/W4298130764","https://openalex.org/W2181743346","https://openalex.org/W2187401768"],"abstract_inverted_index":{"In":[0,58,78],"this":[1,79],"paper,":[2,80],"we":[3,43],"will":[4],"propose":[5],"two":[6],"types":[7],"of":[8,40,53,73,89,95,116,136],"tolerant":[9,46,59,104],"fuzzy":[10,47,60,105],"c-means":[11,48,61,106],"clustering":[12,49,107,124],"with":[13,108],"regularization":[14,81,109],"terms.":[15],"One":[16],"is":[17,27,76,98,139],"L":[18,28],"<sub":[19,29],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,30],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[21],"-regularization":[22,32],"term":[23,110],"and":[24],"the":[25,51,70,90,93,130],"other":[26],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[31],"one":[33],"for":[34,65,83,103],"tolerance":[35,66,74,84,97],"vector.":[36],"Introducing":[37],"a":[38,63],"concept":[39,94],"clusterwise":[41,96],"tolerance,":[42],"have":[44],"proposed":[45,137],"from":[50],"viewpoint":[52],"handling":[54],"data":[55],"more":[56],"flexibly.":[57],"clustering,":[62],"constraint":[64],"vector":[67,75,85],"which":[68],"restricts":[69],"upper":[71],"bound":[72],"used.":[77],"terms":[82],"are":[86,111,120,126],"used":[87],"instead":[88],"constraint.":[91],"First,":[92],"introduced.":[99],"Second,":[100],"optimization":[101,118],"problems":[102,119],"formulated.":[112],"Third,":[113],"optimal":[114,132],"solutions":[115],"these":[117],"derived.":[121],"Fourth,":[122],"new":[123],"algorithms":[125,138],"constructed":[127],"based":[128],"on":[129],"explicit":[131],"solutions.":[133],"Finally,":[134],"effectiveness":[135],"verified":[140],"through":[141],"numerical":[142],"examples.":[143]},"counts_by_year":[{"year":2019,"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"}