{"id":"https://openalex.org/W2356696605","doi":"https://doi.org/10.1109/tpami.2015.2477830","title":"Learning SVM in Kre\u012dn Spaces","display_name":"Learning SVM in Kre\u012dn Spaces","publication_year":2015,"publication_date":"2015-09-10","ids":{"openalex":"https://openalex.org/W2356696605","doi":"https://doi.org/10.1109/tpami.2015.2477830","mag":"2356696605","pmid":"https://pubmed.ncbi.nlm.nih.gov/26372207"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2015.2477830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2015.2477830","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-01593553","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065869008","display_name":"Ga\u00eblle Loosli","orcid":"https://orcid.org/0000-0002-3429-2422"},"institutions":[{"id":"https://openalex.org/I198244214","display_name":"Universit\u00e9 Clermont Auvergne","ror":"https://ror.org/01a8ajp46","country_code":"FR","type":"education","lineage":["https://openalex.org/I198244214"]},{"id":"https://openalex.org/I4210099416","display_name":"Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes","ror":"https://ror.org/00t3fpp34","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I198244214","https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993","https://openalex.org/I4210099416","https://openalex.org/I4210123221","https://openalex.org/I4210159245","https://openalex.org/I4387154249"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Gaelle Loosli","raw_affiliation_strings":["Clermont Universit\u00e9, Universit\u00e9 Blaise Pascal, CNRS, UMR 6158, LIMOS, Aubi\u00e8re, France","LIMOS - Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes (Campus Universitaire des C\u00e9zeaux, 1 rue de la Chebarde, TSA 60125 / CS 60026, 63178 Aubi\u00e8re Cedex - France)","UCA  [2017-2020] - Universit\u00e9 Clermont Auvergne [2017-2020] (49, bd Fran\u00e7ois-Mitterrand / CS 60032 / 63001 Clermont-Ferrand Cedex 1 - France)"],"affiliations":[{"raw_affiliation_string":"Clermont Universit\u00e9, Universit\u00e9 Blaise Pascal, CNRS, UMR 6158, LIMOS, Aubi\u00e8re, France","institution_ids":["https://openalex.org/I198244214","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIMOS - Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes (Campus Universitaire des C\u00e9zeaux, 1 rue de la Chebarde, TSA 60125 / CS 60026, 63178 Aubi\u00e8re Cedex - France)","institution_ids":["https://openalex.org/I4210099416"]},{"raw_affiliation_string":"UCA  [2017-2020] - Universit\u00e9 Clermont Auvergne [2017-2020] (49, bd Fran\u00e7ois-Mitterrand / CS 60032 / 63001 Clermont-Ferrand Cedex 1 - France)","institution_ids":["https://openalex.org/I198244214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017956425","display_name":"St\u00e9phane Canu","orcid":"https://orcid.org/0000-0002-7602-4557"},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I88814501","display_name":"Institut National des Sciences Appliqu\u00e9es Rouen Normandie","ror":"https://ror.org/020ws7586","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I88814501"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Stephane Canu","raw_affiliation_strings":["Laboratoire LITIS-EA 4108 INSA de Rouen Saint-\u00c9tienne-du-Rouvray, France","DocApp - LITIS - Equipe Apprentissage (France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire LITIS-EA 4108 INSA de Rouen Saint-\u00c9tienne-du-Rouvray, France","institution_ids":["https://openalex.org/I88814501","https://openalex.org/I4210108118"]},{"raw_affiliation_string":"DocApp - LITIS - Equipe Apprentissage (France)","institution_ids":["https://openalex.org/I4210108118"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016073964","display_name":"Cheng Soon Ong","orcid":"https://orcid.org/0000-0002-2302-9733"},"institutions":[{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I4210112925","display_name":"Max Planck Institute for Biological Cybernetics","ror":"https://ror.org/026nmvv73","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210112925"]}],"countries":["AU","DE"],"is_corresponding":false,"raw_author_name":"Cheng Soon Ong","raw_affiliation_strings":["NICTA, Canberra, Australia","Max Planck Institute for Biological Cybernetics (Spemannstr. 44, 72076 T\u00fcbingen, Germany - Germany)"],"affiliations":[{"raw_affiliation_string":"NICTA, Canberra, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"Max Planck Institute for Biological Cybernetics (Spemannstr. 44, 72076 T\u00fcbingen, Germany - Germany)","institution_ids":["https://openalex.org/I4210112925"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065869008"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210099416"],"apc_list":null,"apc_paid":null,"fwci":9.0602,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.97843914,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"38","issue":"6","first_page":"1204","last_page":"1216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12031","display_name":"Speech and dialogue systems","score":0.9918000102043152,"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"}},"topics":[{"id":"https://openalex.org/T12031","display_name":"Speech and dialogue systems","score":0.9918000102043152,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9904000163078308,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9760000109672546,"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/embedding","display_name":"Embedding","score":0.6349486112594604},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.6317307353019714},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6218116283416748},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5445438027381897},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5333110690116882},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4648899435997009},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45207783579826355},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4387936592102051},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42931699752807617},{"id":"https://openalex.org/keywords/feature-vector","display_name":"Feature vector","score":0.4280335307121277},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.42168742418289185},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3755492568016052},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3470911383628845},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.27683866024017334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.10500261187553406}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6349486112594604},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.6317307353019714},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6218116283416748},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5445438027381897},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5333110690116882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4648899435997009},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45207783579826355},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4387936592102051},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42931699752807617},{"id":"https://openalex.org/C83665646","wikidata":"https://www.wikidata.org/wiki/Q42139305","display_name":"Feature vector","level":2,"score":0.4280335307121277},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42168742418289185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3755492568016052},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3470911383628845},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27683866024017334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.10500261187553406},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2015.2477830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2015.2477830","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:26372207","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26372207","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:HAL:hal-01593553v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01593553","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016, 38 (6), pp.1204-1216. &#x27E8;10.1109/TPAMI.2015.2477830&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01593553v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01593553","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016, 38 (6), pp.1204-1216. &#x27E8;10.1109/TPAMI.2015.2477830&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310369","display_name":"National ICT Australia","ror":"https://ror.org/03q397159"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W97222033","https://openalex.org/W111418999","https://openalex.org/W194875375","https://openalex.org/W271499721","https://openalex.org/W1487115931","https://openalex.org/W1491841157","https://openalex.org/W1579305052","https://openalex.org/W1588424744","https://openalex.org/W1589603734","https://openalex.org/W1633751774","https://openalex.org/W1990494141","https://openalex.org/W2015855658","https://openalex.org/W2031656503","https://openalex.org/W2034726418","https://openalex.org/W2044876669","https://openalex.org/W2045386260","https://openalex.org/W2064884852","https://openalex.org/W2065759858","https://openalex.org/W2100781145","https://openalex.org/W2102579186","https://openalex.org/W2104323334","https://openalex.org/W2109025268","https://openalex.org/W2115933183","https://openalex.org/W2118216287","https://openalex.org/W2123818990","https://openalex.org/W2125598731","https://openalex.org/W2129971280","https://openalex.org/W2140621370","https://openalex.org/W2141057577","https://openalex.org/W2147281608","https://openalex.org/W2149995433","https://openalex.org/W2153272791","https://openalex.org/W2155537504","https://openalex.org/W2158878034","https://openalex.org/W2160840682","https://openalex.org/W2293636571","https://openalex.org/W2624103904","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W6603933243","https://openalex.org/W6610051752","https://openalex.org/W6629162469","https://openalex.org/W6634941687","https://openalex.org/W6635282431","https://openalex.org/W6636690510","https://openalex.org/W6675689619","https://openalex.org/W6677301753","https://openalex.org/W6677557080","https://openalex.org/W6681289898","https://openalex.org/W6683410077","https://openalex.org/W6697302825","https://openalex.org/W6739352637"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2186864281","https://openalex.org/W4255427455","https://openalex.org/W1966025497","https://openalex.org/W68941528","https://openalex.org/W4206451355","https://openalex.org/W1553604823","https://openalex.org/W8322802","https://openalex.org/W2195994862","https://openalex.org/W314331466"],"abstract_inverted_index":{"This":[0,52,100],"paper":[1],"presents":[2],"a":[3,38,58,75,112],"theoretical":[4],"foundation":[5],"for":[6],"an":[7],"SVM":[8,77,124],"solver":[9],"in":[10,47,114,156],"Kre\u012dn":[11,50,117],"spaces.":[12],"Up":[13],"to":[14,71,84,90,94,110,151],"now,":[15],"all":[16,147],"methods":[17],"are":[18],"based":[19,78],"either":[20],"on":[21,26,30,79],"the":[22,42,48,55,63,66,95,108,115],"matrix":[23],"correction,":[24],"or":[25,29,132],"non-convex":[27],"minimization,":[28],"feature-space":[31],"embedding.":[32],"Here":[33],"we":[34],"justify":[35],"and":[36,74,104],"evaluate":[37],"solution":[39,53,113],"that":[40,142],"uses":[41],"original":[43,49,116],"(indefinite)":[44],"similarity":[45],"measure,":[46],"space.":[51,118],"is":[54,82,107],"result":[56],"of":[57,135],"stabilization":[59,67,103],"procedure.":[60],"We":[61,86,138],"establish":[62],"correspondence":[64],"between":[65,102],"problem":[68],"(which":[69,81],"has":[70],"be":[72],"solved)":[73],"classical":[76],"minimization":[80,105],"easy":[83],"solve).":[85],"provide":[87],"simple":[88],"equations":[89],"go":[91],"from":[92],"one":[93,121],"other":[96],"(in":[97],"both":[98],"directions).":[99],"link":[101],"problems":[106],"key":[109],"obtain":[111],"Using":[119],"KSVM,":[120],"can":[122],"solve":[123],"with":[125,153],"usually":[126],"troublesome":[127],"kernels":[128],"(large":[129],"negative":[130,136],"eigenvalues":[131],"large":[133],"numbers":[134],"eigenvalues).":[137],"show":[139],"experiments":[140],"showing":[141],"our":[143],"algorithm":[144],"KSVM":[145],"outperforms":[146],"previously":[148],"proposed":[149],"approaches":[150],"deal":[152],"indefinite":[154],"matrices":[155],"SVM-like":[157],"kernel":[158],"methods.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":30},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
