{"id":"https://openalex.org/W2740785367","doi":"https://doi.org/10.24963/ijcai.2017/296","title":"Improving the Generalization Performance of Multi-class SVM via Angular Regularization","display_name":"Improving the Generalization Performance of Multi-class SVM via Angular Regularization","publication_year":2017,"publication_date":"2017-07-28","ids":{"openalex":"https://openalex.org/W2740785367","doi":"https://doi.org/10.24963/ijcai.2017/296","mag":"2740785367"},"language":"en","primary_location":{"id":"doi:10.24963/ijcai.2017/296","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2017/296","pdf_url":"https://www.ijcai.org/proceedings/2017/0296.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.ijcai.org/proceedings/2017/0296.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100380470","display_name":"Jianxin Li","orcid":"https://orcid.org/0000-0002-4085-9720"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianxin Li","raw_affiliation_strings":["Beihang University"],"affiliations":[{"raw_affiliation_string":"Beihang University","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086419494","display_name":"Haoyi Zhou","orcid":"https://orcid.org/0000-0002-2393-3634"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haoyi Zhou","raw_affiliation_strings":["School of Computer Science and Engineering, Beihang University"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Beihang University","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083884675","display_name":"Pengtao Xie","orcid":"https://orcid.org/0000-0003-0521-174X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pengtao Xie","raw_affiliation_strings":["Machine Learning Department, Carnegie Mellon University","Petuum Inc, USA","Machine Learning Department, Carnegie Mellon University; Petuum Inc, USA"],"affiliations":[{"raw_affiliation_string":"Machine Learning Department, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Petuum Inc, USA","institution_ids":[]},{"raw_affiliation_string":"Machine Learning Department, Carnegie Mellon University; Petuum Inc, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100761349","display_name":"Yingchun Zhang","orcid":"https://orcid.org/0000-0002-1927-4103"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingchun Zhang","raw_affiliation_strings":["School of Computer Science and Engineering, Beihang University"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Beihang University","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100380470"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":0.3697,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.68975312,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"2131","last_page":"2137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9966999888420105,"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":0.996399998664856,"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/overfitting","display_name":"Overfitting","score":0.9012958407402039},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7222095131874084},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.620331883430481},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6039142608642578},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5421368479728699},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5082585215568542},{"id":"https://openalex.org/keywords/early-stopping","display_name":"Early stopping","score":0.5053628087043762},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.5023958683013916},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4747486710548401},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46755731105804443},{"id":"https://openalex.org/keywords/correlation-coefficient","display_name":"Correlation coefficient","score":0.4368167519569397},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4346904754638672},{"id":"https://openalex.org/keywords/generalization-error","display_name":"Generalization error","score":0.4241126477718353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4066636264324188},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37753215432167053},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.37555283308029175},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3344901204109192},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.24454724788665771},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.18674510717391968},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16558599472045898},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11565396189689636},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.060492128133773804}],"concepts":[{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.9012958407402039},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7222095131874084},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.620331883430481},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6039142608642578},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5421368479728699},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5082585215568542},{"id":"https://openalex.org/C5465570","wikidata":"https://www.wikidata.org/wiki/Q5326898","display_name":"Early stopping","level":3,"score":0.5053628087043762},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.5023958683013916},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4747486710548401},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46755731105804443},{"id":"https://openalex.org/C2780092901","wikidata":"https://www.wikidata.org/wiki/Q3433612","display_name":"Correlation coefficient","level":2,"score":0.4368167519569397},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4346904754638672},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.4241126477718353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4066636264324188},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37753215432167053},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.37555283308029175},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3344901204109192},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.24454724788665771},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.18674510717391968},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16558599472045898},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11565396189689636},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.060492128133773804},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/ijcai.2017/296","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2017/296","pdf_url":"https://www.ijcai.org/proceedings/2017/0296.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.24963/ijcai.2017/296","is_oa":true,"landing_page_url":"https://doi.org/10.24963/ijcai.2017/296","pdf_url":"https://www.ijcai.org/proceedings/2017/0296.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2081254357","display_name":null,"funder_award_id":"61472022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2409080664","display_name":null,"funder_award_id":"SKLSDE-2016ZX-11","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3935756157","display_name":null,"funder_award_id":"142100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7073640943","display_name":null,"funder_award_id":"SKLSDE-2016ZX-11","funder_id":"https://openalex.org/F4320326978","funder_display_name":"State Key Laboratory of Software Development Environment"},{"id":"https://openalex.org/G8055127673","display_name":null,"funder_award_id":"61421003","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/F4320326978","display_name":"State Key Laboratory of Software Development Environment","ror":null},{"id":"https://openalex.org/F4320329053","display_name":"Beijing Advanced Innovation Center for Big Data and Brain Computing","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2740785367.pdf","grobid_xml":"https://content.openalex.org/works/W2740785367.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W6908809","https://openalex.org/W131187193","https://openalex.org/W187370165","https://openalex.org/W252878706","https://openalex.org/W1481061252","https://openalex.org/W1740618102","https://openalex.org/W1749992802","https://openalex.org/W1764447967","https://openalex.org/W1969048569","https://openalex.org/W2016084804","https://openalex.org/W2024223694","https://openalex.org/W2092961325","https://openalex.org/W2098420224","https://openalex.org/W2100616303","https://openalex.org/W2106979123","https://openalex.org/W2116444583","https://openalex.org/W2125993116","https://openalex.org/W2129379475","https://openalex.org/W2151211319","https://openalex.org/W2153635508","https://openalex.org/W2157791002","https://openalex.org/W2164341120","https://openalex.org/W2180530054","https://openalex.org/W2281466631","https://openalex.org/W2282078507","https://openalex.org/W2332821979","https://openalex.org/W2429914308","https://openalex.org/W2579923771","https://openalex.org/W3004533406","https://openalex.org/W3006097074","https://openalex.org/W3099514962","https://openalex.org/W3103014337","https://openalex.org/W3120421331","https://openalex.org/W4250857377","https://openalex.org/W4254721730"],"related_works":["https://openalex.org/W4254751698","https://openalex.org/W2922073769","https://openalex.org/W4320854463","https://openalex.org/W3040157805","https://openalex.org/W4288022214","https://openalex.org/W4387799548","https://openalex.org/W4385768004","https://openalex.org/W3008105014","https://openalex.org/W1724442104","https://openalex.org/W2156876426"],"abstract_inverted_index":{"In":[0,32,103],"multi-class":[1],"support":[2],"vector":[3],"machine":[4],"(MSVM)":[5],"for":[6],"classification,":[7],"one":[8],"core":[9],"issue":[10],"is":[11],"to":[12,17,51,62,101],"regularize":[13],"the":[14,48,75,79,83,89,96,123,126],"coefficient":[15,49,80,99],"vectors":[16,50,100],"reduce":[18],"overfitting.":[19,130],"Various":[20],"regularizers":[21],"have":[22,52],"been":[23],"proposed":[24],"such":[25,55],"as":[26],"L2,":[27],"L1,":[28],"and":[29,94],"trace":[30],"norm.":[31],"this":[33,111],"paper,":[34],"we":[35,107,121],"introduce":[36],"a":[37,69],"new":[38],"type":[39],"of":[40,78,85,125],"regularization":[41],"approach":[42],"--":[43],"angular":[44,71],"regularization,":[45],"that":[46,56,109],"encourages":[47],"larger":[53],"angles":[54,97],"class":[57],"regions":[58],"can":[59],"be":[60],"widen":[61],"flexibly":[63],"accommodate":[64],"unseen":[65],"samples.":[66],"We":[67],"propose":[68],"novel":[70],"regularizer":[72,112,127],"based":[73],"on":[74],"singular":[76,86],"values":[77,87],"matrix,":[81],"where":[82],"uniformity":[84],"reduces":[88,114],"correlation":[90],"among":[91],"different":[92],"classes":[93],"drives":[95],"between":[98],"increase.":[102],"generalization":[104,115],"error":[105,116],"analysis,":[106],"show":[108],"decreasing":[110],"effectively":[113],"bound.":[117],"On":[118],"various":[119],"datasets,":[120],"demonstrate":[122],"efficacy":[124],"in":[128],"reducing":[129]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}