{"id":"https://openalex.org/W2135325000","doi":"https://doi.org/10.1109/grc.2006.1635787","title":"A cutting plane algorithm for multiclass kernel discriminations","display_name":"A cutting plane algorithm for multiclass kernel discriminations","publication_year":2006,"publication_date":"2006-06-08","ids":{"openalex":"https://openalex.org/W2135325000","doi":"https://doi.org/10.1109/grc.2006.1635787","mag":"2135325000"},"language":"en","primary_location":{"id":"doi:10.1109/grc.2006.1635787","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2006.1635787","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 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/A5047837772","display_name":"Tien-Fang Kuo","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tien-Fang Kuo","raw_affiliation_strings":["Department of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070154425","display_name":"Yasutoshi Yajima","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Y. Yajima","raw_affiliation_strings":["Department of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17339164,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"223","last_page":"228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9886999726295471,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9886999726295471,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.9524000287055969,"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":0.6343353986740112},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6107443571090698},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47383078932762146},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4583529829978943},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.4177056550979614},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3727290630340576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2556384205818176},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10687223076820374},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0836406946182251}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6343353986740112},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6107443571090698},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47383078932762146},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4583529829978943},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.4177056550979614},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3727290630340576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2556384205818176},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10687223076820374},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0836406946182251},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/grc.2006.1635787","is_oa":false,"landing_page_url":"https://doi.org/10.1109/grc.2006.1635787","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE International Conference on Granular Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:t2r2.star.titech.ac.jp:00220740","is_oa":false,"landing_page_url":"http://t2r2.star.titech.ac.jp/cgi-bin/publicationinfo.cgi?q_publication_content_number=CTT100409354","pdf_url":null,"source":{"id":"https://openalex.org/S4377196385","display_name":"Tokyo Tech Research Repository (Tokyo Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114531698","host_organization_name":"Tokyo Institute of Technology","host_organization_lineage":["https://openalex.org/I114531698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6499999761581421,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W150916163","https://openalex.org/W175058090","https://openalex.org/W1494922272","https://openalex.org/W1512098439","https://openalex.org/W1574862351","https://openalex.org/W1578772208","https://openalex.org/W1932963602","https://openalex.org/W2091072813","https://openalex.org/W2143559846","https://openalex.org/W2148603752","https://openalex.org/W2157239837","https://openalex.org/W2157791002","https://openalex.org/W2282078507","https://openalex.org/W3004533406","https://openalex.org/W6606159633","https://openalex.org/W6630527977","https://openalex.org/W6634328381","https://openalex.org/W6634795092","https://openalex.org/W6640415645","https://openalex.org/W6682953061","https://openalex.org/W6683380652"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2362705850","https://openalex.org/W2317200988","https://openalex.org/W2379672298","https://openalex.org/W2080278356","https://openalex.org/W1513565830","https://openalex.org/W3012113686","https://openalex.org/W1996239617","https://openalex.org/W3197304203"],"abstract_inverted_index":{"The":[0,122],"problem":[1,18,89,115],"of":[2,12,28,95,120,124],"multiclass":[3,17,35],"discrimination":[4],"consists":[5],"in":[6,42,67,116],"classifying":[7],"patterns":[8],"into":[9,21],"a":[10,16,86,91,103,109,117],"set":[11],"finite":[13,118],"classes.":[14],"Usually,":[15],"is":[19,98],"decomposed":[20],"multiple":[22],"binary":[23,30,144],"ones":[24],"and":[25,81],"the":[26,29,56,76,114,131,139],"results":[27,123],"problems":[31],"are":[32],"integrated":[33],"for":[34],"discrimination.":[36],"These":[37],"discriminators,":[38],"however,":[39],"could":[40],"result":[41],"multi-classified":[43],"and/or":[44],"unclassified":[45],"points.":[46],"Therefore,":[47],"we":[48,74,107],"need":[49],"some":[50],"tie":[51],"breaking":[52],"mechanisms":[53],"to":[54,100],"handle":[55],"conflict.":[57],"There":[58],"exist":[59],"several":[60],"approaches":[61],"which":[62,97,112],"generate":[63],"all":[64],"discrimi-":[65],"nators":[66],"one":[68],"optimization":[69],"problem.":[70],"In":[71],"this":[72],"paper,":[73],"consider":[75],"formulation":[77],"introduced":[78],"by":[79,142],"Crammer":[80],"Singer":[82],"(3).":[83],"They":[84],"introduce":[85],"quadratic":[87],"programming":[88],"with":[90],"very":[92],"large":[93],"number":[94,119],"variables":[96],"hard":[99],"optimize.":[101],"Using":[102],"cutting":[104],"plane":[105],"procedure,":[106],"propose":[108],"new":[110],"algorithm":[111],"solves":[113],"iterations.":[121],"experiments":[125],"on":[126],"five":[127],"datasets":[128],"show":[129],"that":[130],"proposed":[132],"method":[133],"achieves":[134],"higher":[135],"classification":[136],"performance":[137],"than":[138],"traditional":[140],"methods":[141],"using":[143],"algorithms.":[145]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}