{"id":"https://openalex.org/W3174488350","doi":"https://doi.org/10.1109/tpami.2021.3092177","title":"Support Vector Machine Classifier via Soft-Margin Loss","display_name":"Support Vector Machine Classifier via Soft-Margin Loss","publication_year":2021,"publication_date":"2021-06-24","ids":{"openalex":"https://openalex.org/W3174488350","doi":"https://doi.org/10.1109/tpami.2021.3092177","mag":"3174488350","pmid":"https://pubmed.ncbi.nlm.nih.gov/34166185"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2021.3092177","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3092177","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5100602262","display_name":"Huajun Wang","orcid":"https://orcid.org/0000-0002-2371-1150"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huajun Wang","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-2371-1150","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051850582","display_name":"Yuan\u2010Hai Shao","orcid":"https://orcid.org/0000-0002-1628-6133"},"institutions":[{"id":"https://openalex.org/I20942203","display_name":"Hainan University","ror":"https://ror.org/03q648j11","country_code":"CN","type":"education","lineage":["https://openalex.org/I20942203"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanhai Shao","raw_affiliation_strings":["School of Management, Hainan University, Haikou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, Hainan University, Haikou, China","institution_ids":["https://openalex.org/I20942203"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023017250","display_name":"Shenglong Zhou","orcid":"https://orcid.org/0000-0003-2843-1614"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Shenglong Zhou","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, London, U.K"],"raw_orcid":"https://orcid.org/0000-0003-2843-1614","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, London, U.K","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100383732","display_name":"Ce Zhang","orcid":"https://orcid.org/0000-0002-8964-9206"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ce Zhang","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-8964-9206","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071551240","display_name":"Naihua Xiu","orcid":"https://orcid.org/0000-0002-3129-2005"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naihua Xiu","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3129-2005","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.3158,"has_fulltext":false,"cited_by_count":145,"citation_normalized_percentile":{"value":0.98624438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"44","issue":"10","first_page":"7253","last_page":"7265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9991999864578247,"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":0.9991999864578247,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9980999827384949,"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":0.9972000122070312,"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/margin-classifier","display_name":"Margin classifier","score":0.7082754373550415},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.7016571760177612},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6790257096290588},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6446599364280701},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5646060705184937},{"id":"https://openalex.org/keywords/classifier","display_name":"Classifier (UML)","score":0.5062000155448914},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.4712282419204712},{"id":"https://openalex.org/keywords/structured-support-vector-machine","display_name":"Structured support vector machine","score":0.45765814185142517},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.42393285036087036}],"concepts":[{"id":"https://openalex.org/C173102733","wikidata":"https://www.wikidata.org/wiki/Q6760396","display_name":"Margin classifier","level":3,"score":0.7082754373550415},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.7016571760177612},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6790257096290588},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6446599364280701},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5646060705184937},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.5062000155448914},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.4712282419204712},{"id":"https://openalex.org/C125168437","wikidata":"https://www.wikidata.org/wiki/Q7625184","display_name":"Structured support vector machine","level":3,"score":0.45765814185142517},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.42393285036087036}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D060388","descriptor_name":"Support Vector Machine","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D060388","descriptor_name":"Support Vector Machine","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D060388","descriptor_name":"Support Vector Machine","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2021.3092177","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3092177","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:34166185","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34166185","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/89897","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/89897","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"7265","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2376461917","display_name":null,"funder_award_id":"120RC449","funder_id":"https://openalex.org/F4320322866","funder_display_name":"Natural Science Foundation of Hainan Province"},{"id":"https://openalex.org/G2425456055","display_name":"\u5927\u89c4\u6a21\u6570\u636e\u6316\u6398\u4e2d\u5d4c\u5165\u5f0f\u6570\u636e\u5f52\u7ea6\u7684\u7a00\u758f\u6a21\u578b\u4e0e\u7b97\u6cd5\u7814\u7a76","funder_award_id":"61866010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3980372984","display_name":"\u566a\u58f0\u6570\u636e\u7684\u975e\u51f8\u635f\u5931\u51fd\u6570\u652f\u6301\u5411\u91cf\u673a\u6700\u4f18\u5316\u6a21\u578b\u4e0e\u7b97\u6cd5\u7814\u7a76","funder_award_id":"11871183","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5111687257","display_name":null,"funder_award_id":"11971052","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7225251486","display_name":null,"funder_award_id":"11926348-9","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322866","display_name":"Natural Science Foundation of Hainan Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W1524688041","https://openalex.org/W1546411676","https://openalex.org/W1560724230","https://openalex.org/W1596717185","https://openalex.org/W1597529531","https://openalex.org/W1605479404","https://openalex.org/W1840338487","https://openalex.org/W1845718094","https://openalex.org/W1969158966","https://openalex.org/W1973650202","https://openalex.org/W1980454827","https://openalex.org/W1982032418","https://openalex.org/W1994566659","https://openalex.org/W1994720006","https://openalex.org/W2024046085","https://openalex.org/W2028781966","https://openalex.org/W2032708784","https://openalex.org/W2056145308","https://openalex.org/W2063506498","https://openalex.org/W2063761188","https://openalex.org/W2064593130","https://openalex.org/W2075779886","https://openalex.org/W2107976320","https://openalex.org/W2119821739","https://openalex.org/W2125993116","https://openalex.org/W2131328016","https://openalex.org/W2136627475","https://openalex.org/W2143030432","https://openalex.org/W2161813894","https://openalex.org/W2162152253","https://openalex.org/W2163232332","https://openalex.org/W2163608767","https://openalex.org/W2181470043","https://openalex.org/W2241799117","https://openalex.org/W2262559846","https://openalex.org/W2295652899","https://openalex.org/W2312471699","https://openalex.org/W2594577230","https://openalex.org/W2788039246","https://openalex.org/W2796982392","https://openalex.org/W2890282059","https://openalex.org/W2919088647","https://openalex.org/W2945634539","https://openalex.org/W2962853966","https://openalex.org/W2963322354","https://openalex.org/W2963579802","https://openalex.org/W2963607709","https://openalex.org/W2963647795","https://openalex.org/W3005972568","https://openalex.org/W3011526999","https://openalex.org/W3020910274","https://openalex.org/W3021013692","https://openalex.org/W3023496898","https://openalex.org/W3105393233","https://openalex.org/W3124966411","https://openalex.org/W4312258136","https://openalex.org/W6632670727","https://openalex.org/W6636033586","https://openalex.org/W6676257489","https://openalex.org/W6676737069","https://openalex.org/W6679765724","https://openalex.org/W6680137255","https://openalex.org/W6684105480","https://openalex.org/W6685928903","https://openalex.org/W6686240244","https://openalex.org/W6762903502","https://openalex.org/W6773703338","https://openalex.org/W6776534123"],"related_works":["https://openalex.org/W2384390720","https://openalex.org/W4253128984","https://openalex.org/W2539940072","https://openalex.org/W2122277321","https://openalex.org/W2206547991","https://openalex.org/W2101819884","https://openalex.org/W2769345709","https://openalex.org/W2367262922","https://openalex.org/W4377224252","https://openalex.org/W3152479269"],"abstract_inverted_index":{"Support":[0],"vector":[1],"machines":[2],"(SVM)":[3],"have":[4],"drawn":[5],"wide":[6],"attention":[7],"for":[8,92],"the":[9,62,73,76,89,93,98,101,104,160,195,199],"last":[10],"two":[11],"decades":[12],"due":[13],"to":[14,28,87,116,130,159],"its":[15,82,151,202],"extensive":[16],"applications,":[17],"so":[18],"a":[19,118,132,137,140,155,187],"vast":[20],"body":[21],"of":[22,61,72,75,100,121,145,182,190],"work":[23],"has":[24],"developed":[25],"optimization":[26],"algorithms":[27],"solve":[29],"SVM":[30,54,178],"with":[31,150],"various":[32],"soft-margin":[33,47,52,65,79],"losses.":[34],"To":[35],"distinguish":[36],"all,":[37],"in":[38,180],"this":[39],"paper,":[40],"we":[41,85],"aim":[42],"at":[43],"solving":[44],"an":[45],"ideal":[46],"loss":[48,53],"SVM:":[49],"<inline-formula><tex-math":[50,57,77,94,122,161],"notation=\"LaTeX\">$L_{0/1}$</tex-math></inline-formula>":[51,58,78,95,123,162],"(dubbed":[55],"as":[56,70],"-SVM).":[59],"Many":[60],"existing":[63],"(non)convex":[64],"losses":[66],"can":[67],"be":[68],"viewed":[69],"one":[71],"surrogates":[74],"loss.":[80],"Despite":[81],"discrete":[83],"nature,":[84],"manage":[86],"establish":[88],"optimality":[90],"theory":[91],"-SVM":[96],"including":[97],"existence":[99],"optimal":[102,157],"solutions,":[103],"relationship":[105],"between":[106],"them":[107],"and":[108,186],"P-stationary":[109],"points.":[110],"These":[111],"not":[112],"only":[113],"enable":[114],"us":[115,129],"deliver":[117],"rigorous":[119],"definition":[120],"support":[124,191],"vectors":[125],"but":[126],"also":[127],"allow":[128],"define":[131],"working":[133,138],"set.":[134],"Integrating":[135],"such":[136],"set,":[139],"fast":[141],"alternating":[142],"direction":[143],"method":[144,171],"multipliers":[146],"is":[147],"then":[148],"proposed":[149,170],"limit":[152],"point":[153],"being":[154],"locally":[156],"solution":[158],"-SVM.":[163],"Finally,":[164],"numerical":[165],"experiments":[166],"demonstrate":[167],"that":[168],"our":[169],"outperforms":[172],"some":[173],"leading":[174],"classification":[175],"solvers":[176],"from":[177],"communities,":[179],"terms":[181],"faster":[183],"computational":[184],"speed":[185],"fewer":[188],"number":[189],"vectors.":[192],"The":[193],"bigger":[194],"data":[196],"size":[197],"is,":[198],"more":[200],"evident":[201],"advantage":[203],"appears.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":18},{"year":2025,"cited_by_count":34},{"year":2024,"cited_by_count":47},{"year":2023,"cited_by_count":31},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-18T10:00:31.954636","created_date":"2021-07-05T00:00:00"}
