{"id":"https://openalex.org/W4312990009","doi":"https://doi.org/10.1109/tit.2022.3222266","title":"Simplex-Based Proximal Multicategory Support Vector Machine","display_name":"Simplex-Based Proximal Multicategory Support Vector Machine","publication_year":2022,"publication_date":"2022-11-15","ids":{"openalex":"https://openalex.org/W4312990009","doi":"https://doi.org/10.1109/tit.2022.3222266"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3222266","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3222266","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://repository.tudelft.nl/file/File_577df899-7f16-424e-93e8-2d112d61f018","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108079791","display_name":"Sheng Fu","orcid":"https://orcid.org/0000-0002-2441-3120"},"institutions":[{"id":"https://openalex.org/I4210140884","display_name":"National Cancer Institute","ror":"https://ror.org/040gcmg81","country_code":"US","type":"government","lineage":["https://openalex.org/I1299022934","https://openalex.org/I1299303238","https://openalex.org/I4210140884"]},{"id":"https://openalex.org/I4391012607","display_name":"Division of Cancer Epidemiology and Genetics","ror":"https://ror.org/00vkwep27","country_code":null,"type":"facility","lineage":["https://openalex.org/I1299022934","https://openalex.org/I1299303238","https://openalex.org/I4210140884","https://openalex.org/I4391012607"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sheng Fu","raw_affiliation_strings":["Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, USA","institution_ids":["https://openalex.org/I4210140884","https://openalex.org/I4391012607"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071605315","display_name":"Piao Chen","orcid":"https://orcid.org/0000-0001-9714-450X"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Piao Chen","raw_affiliation_strings":["Delft Institute of Applied Mathematics, Delft University of Technology, CD Delft, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-9714-450X","affiliations":[{"raw_affiliation_string":"Delft Institute of Applied Mathematics, Delft University of Technology, CD Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053268509","display_name":"Zhi\u2010Sheng Ye","orcid":"https://orcid.org/0000-0001-5731-3911"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhisheng Ye","raw_affiliation_strings":["Department of Industrial Systems Engineering & Management, National University of Singapore, Queenstown, Singapore"],"raw_orcid":"https://orcid.org/0000-0001-5731-3911","affiliations":[{"raw_affiliation_string":"Department of Industrial Systems Engineering & Management, National University of Singapore, Queenstown, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3238,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.52871613,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"69","issue":"4","first_page":"2427","last_page":"2451"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9984999895095825,"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":0.9984999895095825,"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/T12676","display_name":"Machine Learning and ELM","score":0.9965999722480774,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hinge-loss","display_name":"Hinge loss","score":0.8377571702003479},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5774683952331543},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5671389102935791},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5564148426055908},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5360425114631653},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.528201162815094},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.48322877287864685},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.43372029066085815},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4189281165599823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39846837520599365},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3528347909450531},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33338600397109985},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10741943120956421}],"concepts":[{"id":"https://openalex.org/C39891107","wikidata":"https://www.wikidata.org/wiki/Q5767098","display_name":"Hinge loss","level":3,"score":0.8377571702003479},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5774683952331543},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5671389102935791},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5564148426055908},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5360425114631653},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.528201162815094},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.48322877287864685},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.43372029066085815},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4189281165599823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39846837520599365},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3528347909450531},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33338600397109985},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10741943120956421}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2022.3222266","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3222266","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:tudelft.nl:uuid:5d1401ab-b41d-4433-9f9d-16ab6bf9515b","is_oa":true,"landing_page_url":"http://resolver.tudelft.nl/uuid:5d1401ab-b41d-4433-9f9d-16ab6bf9515b","pdf_url":"https://repository.tudelft.nl/file/File_577df899-7f16-424e-93e8-2d112d61f018","source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:tudelft.nl:uuid:5d1401ab-b41d-4433-9f9d-16ab6bf9515b","is_oa":true,"landing_page_url":"http://resolver.tudelft.nl/uuid:5d1401ab-b41d-4433-9f9d-16ab6bf9515b","pdf_url":"https://repository.tudelft.nl/file/File_577df899-7f16-424e-93e8-2d112d61f018","source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3475405167","display_name":"\u57fa\u4e8e\u8fd1\u4f3c\u5e7f\u4e49\u67a2\u8f74\u91cf\u7684\u5feb\u901f\u9ad8\u7cbe\u5ea6\u6027\u80fd\u9000\u5316\u5206\u6790\u65b9\u6cd5\u7814\u7a76","funder_award_id":"72071138","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312990009.pdf","grobid_xml":"https://content.openalex.org/works/W4312990009.grobid-xml"},"referenced_works_count":119,"referenced_works":["https://openalex.org/W187370165","https://openalex.org/W1480538416","https://openalex.org/W1560724230","https://openalex.org/W1568892534","https://openalex.org/W1596717185","https://openalex.org/W1618905105","https://openalex.org/W1676820704","https://openalex.org/W1763412770","https://openalex.org/W1768257245","https://openalex.org/W1859373906","https://openalex.org/W1977406948","https://openalex.org/W1982032418","https://openalex.org/W1993200481","https://openalex.org/W2000818163","https://openalex.org/W2002355073","https://openalex.org/W2015745977","https://openalex.org/W2015904350","https://openalex.org/W2018186689","https://openalex.org/W2030843733","https://openalex.org/W2035720976","https://openalex.org/W2037679392","https://openalex.org/W2039958503","https://openalex.org/W2043919728","https://openalex.org/W2051177122","https://openalex.org/W2053377145","https://openalex.org/W2056983531","https://openalex.org/W2061243452","https://openalex.org/W2069231281","https://openalex.org/W2070266333","https://openalex.org/W2073241381","https://openalex.org/W2086623929","https://openalex.org/W2087347434","https://openalex.org/W2091825929","https://openalex.org/W2096520669","https://openalex.org/W2101819520","https://openalex.org/W2103568877","https://openalex.org/W2103614420","https://openalex.org/W2106842132","https://openalex.org/W2107976320","https://openalex.org/W2109445534","https://openalex.org/W2116296021","https://openalex.org/W2116444583","https://openalex.org/W2116915136","https://openalex.org/W2118585731","https://openalex.org/W2118978333","https://openalex.org/W2119076097","https://openalex.org/W2119107710","https://openalex.org/W2121730009","https://openalex.org/W2125993116","https://openalex.org/W2128409240","https://openalex.org/W2128529555","https://openalex.org/W2134767360","https://openalex.org/W2136627475","https://openalex.org/W2148603752","https://openalex.org/W2153635508","https://openalex.org/W2154558852","https://openalex.org/W2162331139","https://openalex.org/W2165966284","https://openalex.org/W2166198808","https://openalex.org/W2167197286","https://openalex.org/W2170308301","https://openalex.org/W2170487914","https://openalex.org/W2218557140","https://openalex.org/W2403763698","https://openalex.org/W2466877391","https://openalex.org/W2544380701","https://openalex.org/W2562319768","https://openalex.org/W2579923771","https://openalex.org/W2768140828","https://openalex.org/W2787894218","https://openalex.org/W2789976824","https://openalex.org/W2932520883","https://openalex.org/W2936503027","https://openalex.org/W2945041569","https://openalex.org/W2945523111","https://openalex.org/W2952594493","https://openalex.org/W2954868363","https://openalex.org/W2956584943","https://openalex.org/W2962708723","https://openalex.org/W2962712569","https://openalex.org/W2963918665","https://openalex.org/W2964231067","https://openalex.org/W2964910440","https://openalex.org/W2999771887","https://openalex.org/W3004533406","https://openalex.org/W3048411551","https://openalex.org/W3092679966","https://openalex.org/W3120740533","https://openalex.org/W3159649695","https://openalex.org/W3194313756","https://openalex.org/W3200669006","https://openalex.org/W4206742934","https://openalex.org/W4210933278","https://openalex.org/W4213290817","https://openalex.org/W4230009517","https://openalex.org/W4239510810","https://openalex.org/W4243794444","https://openalex.org/W4249280610","https://openalex.org/W4294541781","https://openalex.org/W4298166422","https://openalex.org/W4298876635","https://openalex.org/W4302564868","https://openalex.org/W6600089577","https://openalex.org/W6630424276","https://openalex.org/W6634338318","https://openalex.org/W6636501900","https://openalex.org/W6674516588","https://openalex.org/W6676257489","https://openalex.org/W6677656871","https://openalex.org/W6679116844","https://openalex.org/W6679179291","https://openalex.org/W6682953061","https://openalex.org/W6684413595","https://openalex.org/W6684877096","https://openalex.org/W6712894128","https://openalex.org/W6732517885","https://openalex.org/W6751796155","https://openalex.org/W6764647576","https://openalex.org/W6790596753"],"related_works":["https://openalex.org/W2133667137","https://openalex.org/W2380756614","https://openalex.org/W2384679317","https://openalex.org/W2477407501","https://openalex.org/W1570109187","https://openalex.org/W2366013513","https://openalex.org/W3125083766","https://openalex.org/W4244786412","https://openalex.org/W2028887049","https://openalex.org/W3143155029"],"abstract_inverted_index":{"The":[0],"multicategory":[1,11],"support":[2],"vector":[3],"machine":[4],"(MSVM)":[5],"has":[6],"been":[7],"widely":[8],"used":[9],"for":[10,125],"classification.":[12],"Despite":[13],"its":[14,158,162],"widespread":[15],"popularity,":[16],"regular":[17,57,145],"MSVM":[18,64],"cannot":[19],"provide":[20],"direct":[21],"probabilistic":[22],"results":[23],"and":[24,39,83,161,164,172,184],"suffers":[25],"from":[26],"excessive":[27],"computational":[28],"cost,":[29],"as":[30,60,157],"it":[31,40,84,122],"is":[32,123,141,150,180],"formulated":[33],"on":[34],"the":[35,61,80,86,91,95,110,129,136,148,177],"hinge":[36,81],"loss":[37,75,82],"function":[38],"solves":[41],"a":[42,53,69,116,181],"sum-to-zero":[43,88],"constrained":[44],"quadratic":[45],"programming":[46],"problem.":[47],"In":[48,108],"this":[49],"study,":[50],"we":[51],"propose":[52],"general":[54],"refinement":[55],"of":[56,72,79,135],"MSVM,":[58],"termed":[59],"simplex-based":[62],"proximal":[63],"(SPMSVM).":[65],"Our":[66],"SPMSVM":[67,96,111,130,149,179],"uses":[68],"novel":[70],"family":[71],"squared":[73],"error":[74],"functions":[76],"in":[77],"place":[78],"removes":[85],"explicit":[87],"constraint":[89],"by":[90],"simplex":[92],"structure.":[93],"Consequently,":[94],"only":[97],"requires":[98],"solving":[99],"an":[100,133],"unconstrained":[101],"linear":[102],"system,":[103],"leading":[104],"to":[105,152],"closed-form":[106],"solutions.":[107],"addition,":[109],"can":[112],"be":[113],"cast":[114],"into":[115],"weighted":[117],"regression":[118],"problem":[119],"so":[120],"that":[121,176],"scalable":[124,183],"large-scale":[126],"applications.":[127],"Moreover,":[128],"naturally":[131],"yields":[132],"estimate":[134],"conditional":[137],"category":[138],"probability,":[139],"which":[140],"more":[142],"informative":[143],"than":[144],"MSVM.":[146],"Theoretically,":[147],"shown":[151],"include":[153],"many":[154],"existing":[155],"MSVMs":[156],"special":[159],"cases,":[160],"asymptotic":[163],"finite-sample":[165],"statistical":[166],"properties":[167],"are":[168],"well":[169],"established.":[170],"Simulations":[171],"real":[173],"examples":[174],"show":[175],"proposed":[178],"stable,":[182],"competitive":[185],"classifier.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-08-12T21:12:35.861297","created_date":"2025-10-10T00:00:00"}