{"id":"https://openalex.org/W2099680562","doi":"https://doi.org/10.1162/089976603322385108","title":"Radius Margin Bounds for Support Vector Machines with the RBF Kernel","display_name":"Radius Margin Bounds for Support Vector Machines with the RBF Kernel","publication_year":2003,"publication_date":"2003-09-25","ids":{"openalex":"https://openalex.org/W2099680562","doi":"https://doi.org/10.1162/089976603322385108","mag":"2099680562","pmid":"https://pubmed.ncbi.nlm.nih.gov/14577857"},"language":"en","primary_location":{"id":"doi:10.1162/089976603322385108","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976603322385108","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","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/A5100679596","display_name":"Kai-Min Chung","orcid":"https://orcid.org/0000-0002-3356-369X"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Kai-Min Chung","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090681615","display_name":"Wei\u2010Chun Kao","orcid":"https://orcid.org/0000-0001-8687-6334"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wei-Chun Kao","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004903146","display_name":"Chia\u2010Liang Sun","orcid":"https://orcid.org/0000-0001-8886-5014"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chia-Liang Sun","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028623883","display_name":"Li-Lun Wang","orcid":"https://orcid.org/0009-0007-6341-4285"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Li-Lun Wang","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068223640","display_name":"Chih\u2010Jen Lin","orcid":"https://orcid.org/0000-0003-4684-8747"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chih-Jen Lin","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan,","institution_ids":["https://openalex.org/I16733864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I16733864"],"apc_list":null,"apc_paid":null,"fwci":12.9949,"has_fulltext":false,"cited_by_count":219,"citation_normalized_percentile":{"value":0.98891967,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"15","issue":"11","first_page":"2643","last_page":"2681"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9975000023841858,"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"}},{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9969000220298767,"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/support-vector-machine","display_name":"Support vector machine","score":0.8839367628097534},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.786567747592926},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6003842353820801},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5774597525596619},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5580212473869324},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5102131366729736},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.49487489461898804},{"id":"https://openalex.org/keywords/margin-classifier","display_name":"Margin classifier","score":0.44842439889907837},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44121283292770386},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.4156422019004822},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.38464146852493286},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3437280058860779},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3378172516822815},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21006882190704346},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07912024855613708}],"concepts":[{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.8839367628097534},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.786567747592926},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6003842353820801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5774597525596619},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5580212473869324},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5102131366729736},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.49487489461898804},{"id":"https://openalex.org/C173102733","wikidata":"https://www.wikidata.org/wiki/Q6760396","display_name":"Margin classifier","level":3,"score":0.44842439889907837},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44121283292770386},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.4156422019004822},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.38464146852493286},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3437280058860779},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3378172516822815},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21006882190704346},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07912024855613708}],"mesh":[{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","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":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1162/089976603322385108","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976603322385108","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718","https://openalex.org/P4310316440"],"host_organization_lineage_names":["The MIT Press","Massachusetts Institute of Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:14577857","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/14577857","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":"Neural computation","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321040","display_name":"National Science Council","ror":"https://ror.org/02kv4zf79"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1485026097","https://openalex.org/W1496612019","https://openalex.org/W1539150806","https://openalex.org/W1548139318","https://openalex.org/W1554944419","https://openalex.org/W1568892534","https://openalex.org/W1576520375","https://openalex.org/W1604938182","https://openalex.org/W1979382551","https://openalex.org/W2000125728","https://openalex.org/W2039402388","https://openalex.org/W2064217481","https://openalex.org/W2067717243","https://openalex.org/W2082988498","https://openalex.org/W2113584252","https://openalex.org/W2118286367","https://openalex.org/W2143628522","https://openalex.org/W2148603752","https://openalex.org/W2153635508","https://openalex.org/W2156909104","https://openalex.org/W2157083019","https://openalex.org/W2158001550","https://openalex.org/W2165401139","https://openalex.org/W2408196097","https://openalex.org/W2546108655","https://openalex.org/W4244829582"],"related_works":["https://openalex.org/W2345184372","https://openalex.org/W3013515612","https://openalex.org/W2136184105","https://openalex.org/W2041399278","https://openalex.org/W2160451891","https://openalex.org/W2937631562","https://openalex.org/W2336974148","https://openalex.org/W2056016498","https://openalex.org/W3195168932","https://openalex.org/W2187500075"],"abstract_inverted_index":{"An":[0],"important":[1,99],"approach":[2],"for":[3,58,78,113,131],"efficient":[4],"support":[5,157,163,175],"vector":[6],"machine":[7],"(SVM)":[8],"model":[9],"selection":[10],"is":[11,40,122],"to":[12,125,136],"use":[13],"differentiable":[14],"bounds":[15,27,112],"of":[16,28,61,156,161,172],"the":[17,62,119,126,170],"leave-one-out":[18],"(loo)":[19],"error.":[20],"Past":[21],"efforts":[22],"focused":[23],"on":[24,104],"finding":[25,83],"tight":[26],"loo":[29,94],"(e.g.,":[30],"radius":[31,52,110],"margin":[32,53,111],"bounds,":[33],"span":[34],"bounds).":[35],"However,":[36],"their":[37,153],"practical":[38],"viability":[39],"still":[41],"not":[42],"very":[43],"satisfactory.":[44],"Duan,":[45],"Keerthi,":[46],"and":[47,159],"Poo":[48],"(2003)":[49],"showed":[50],"that":[51,82],"bound":[54,75,85,121],"gives":[55],"good":[56],"prediction":[57],"L2-SVM,":[59,79],"one":[60],"cases":[63],"we":[64,80,107,147,183],"look":[65],"at.":[66],"In":[67,165],"this":[68,74,105,166],"letter,":[69],"through":[70],"analyses":[71],"about":[72],"why":[73],"performs":[76],"well":[77],"show":[81],"a":[84,90],"whose":[86],"minima":[87],"are":[88,179],"in":[89,187],"region":[91],"with":[92],"small":[93],"values":[95],"may":[96],"be":[97,145],"more":[98],"than":[100],"its":[101],"tightness.":[102],"Based":[103],"principle,":[106],"propose":[108],"modified":[109],"L1-SVM":[114,132,168],"(the":[115],"other":[116,149],"case)":[117],"where":[118],"original":[120],"applicable":[123],"only":[124],"hard-margin":[127],"case.":[128],"Our":[129],"modification":[130],"achieves":[133],"comparable":[134],"performance":[135],"L2-SVM.":[137],"To":[138],"study":[139],"whether":[140],"L1-":[141],"or":[142],"L2-SVM":[143],"should":[144],"used,":[146],"analyze":[148],"properties,":[150],"such":[151],"as":[152],"differentiability,":[154],"number":[155,160],"vectors,":[158],"free":[162],"vectors.":[164,176],"aspect,":[167],"possesses":[169],"advantage":[171],"having":[173],"fewer":[174],"Their":[177],"implementations":[178],"also":[180],"different,":[181],"so":[182],"discuss":[184],"related":[185],"issues":[186],"detail.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}