{"id":"https://openalex.org/W2343390829","doi":"https://doi.org/10.1109/tnnls.2015.2498525","title":"Semisupervised Multiclass Classification Problems With Scarcity of Labeled Data: A Theoretical Study","display_name":"Semisupervised Multiclass Classification Problems With Scarcity of Labeled Data: A Theoretical Study","publication_year":2015,"publication_date":"2015-11-23","ids":{"openalex":"https://openalex.org/W2343390829","doi":"https://doi.org/10.1109/tnnls.2015.2498525","mag":"2343390829","pmid":"https://pubmed.ncbi.nlm.nih.gov/26625427"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2015.2498525","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2498525","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","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/A5007513831","display_name":"Jonathan Ortigosa-Hern\u00e1ndez","orcid":null},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jonathan Ortigosa-Hernandez","raw_affiliation_strings":["Intelligent Systems Group, The University of the Basque Country UPV/EHU, Donostia-San Sebasti\u00e1n, Spain"],"affiliations":[{"raw_affiliation_string":"Intelligent Systems Group, The University of the Basque Country UPV/EHU, Donostia-San Sebasti\u00e1n, Spain","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045973875","display_name":"I\u00f1aki Inza","orcid":"https://orcid.org/0000-0003-4674-1755"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Inaki Inza","raw_affiliation_strings":["Intelligent Systems Group, The University of the Basque Country UPV/EHU, Donostia-San Sebasti\u00e1n, Spain"],"affiliations":[{"raw_affiliation_string":"Intelligent Systems Group, The University of the Basque Country UPV/EHU, Donostia-San Sebasti\u00e1n, Spain","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050500830","display_name":"Jos\u00e9 A. Lozano","orcid":"https://orcid.org/0000-0002-4683-8111"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jose A. Lozano","raw_affiliation_strings":["Intelligent Systems Group, The University of the Basque Country UPV/EHU, Donostia-San Sebasti\u00e1n, Spain"],"affiliations":[{"raw_affiliation_string":"Intelligent Systems Group, The University of the Basque Country UPV/EHU, Donostia-San Sebasti\u00e1n, Spain","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007513831"],"corresponding_institution_ids":["https://openalex.org/I169108374"],"apc_list":null,"apc_paid":null,"fwci":2.5886,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91932752,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"12","first_page":"2602","last_page":"2614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.995199978351593,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.995199978351593,"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/T10057","display_name":"Face and Expression Recognition","score":0.9902999997138977,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9890999794006348,"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/multiclass-classification","display_name":"Multiclass classification","score":0.7437264323234558},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7135971188545227},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6256603598594666},{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.6123567223548889},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.569611132144928},{"id":"https://openalex.org/keywords/binary-classification","display_name":"Binary classification","score":0.5426876544952393},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.542650043964386},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5364196300506592},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5016577243804932},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4965067505836487},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48692524433135986},{"id":"https://openalex.org/keywords/generalization-error","display_name":"Generalization error","score":0.4291195571422577},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3775556981563568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3395317792892456},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.14559456706047058},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.10418608784675598}],"concepts":[{"id":"https://openalex.org/C123860398","wikidata":"https://www.wikidata.org/wiki/Q6934605","display_name":"Multiclass classification","level":3,"score":0.7437264323234558},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7135971188545227},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6256603598594666},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.6123567223548889},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.569611132144928},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.5426876544952393},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.542650043964386},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5364196300506592},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5016577243804932},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4965067505836487},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48692524433135986},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.4291195571422577},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3775556981563568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3395317792892456},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.14559456706047058},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.10418608784675598},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2015.2498525","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2498525","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:26625427","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26625427","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 neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6399999856948853}],"awards":[{"id":"https://openalex.org/G1849572247","display_name":null,"funder_award_id":"IT609-13","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G1958880261","display_name":null,"funder_award_id":"TIN2013-41272P","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7737484549","display_name":null,"funder_award_id":"247619","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8197173601","display_name":null,"funder_award_id":"MEC-FPU AP2008-00766","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320334923","display_name":"Instituto de Salud Carlos III","ror":"https://ror.org/00ca2c886"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1479807131","https://openalex.org/W1554944419","https://openalex.org/W1589919686","https://openalex.org/W2007735837","https://openalex.org/W2065069176","https://openalex.org/W2069033749","https://openalex.org/W2083515729","https://openalex.org/W2122515188","https://openalex.org/W2131775048","https://openalex.org/W2151166364","https://openalex.org/W2152111188","https://openalex.org/W2153149612","https://openalex.org/W2154546490","https://openalex.org/W2154794763","https://openalex.org/W2164255530","https://openalex.org/W2168464035","https://openalex.org/W2171033594","https://openalex.org/W2184987264","https://openalex.org/W2222512263","https://openalex.org/W2539511637","https://openalex.org/W2797746357","https://openalex.org/W2914659449","https://openalex.org/W3171280080","https://openalex.org/W4300302225","https://openalex.org/W4300956553","https://openalex.org/W6678381038","https://openalex.org/W6682204729","https://openalex.org/W6686827794","https://openalex.org/W6796760531"],"related_works":["https://openalex.org/W4376528628","https://openalex.org/W1537592868","https://openalex.org/W2470590370","https://openalex.org/W3207192536","https://openalex.org/W2910954186","https://openalex.org/W1748436461","https://openalex.org/W2002271516","https://openalex.org/W2014610539","https://openalex.org/W4281721362","https://openalex.org/W2322862995"],"abstract_inverted_index":{"In":[0,25,46],"recent":[1],"years,":[2],"the":[3,36,43,50,90,95,108,119,143,148,162,167],"performance":[4],"of":[5,15,38,55,63,80,92,94,122,142,157,164],"semisupervised":[6],"learning":[7,136],"(SSL)":[8],"has":[9,19],"been":[10],"theoretically":[11],"investigated.":[12],"However,":[13],"most":[14],"this":[16,26,114,158],"theoretical":[17],"development":[18],"focused":[20],"on":[21],"binary":[22,151,168],"classification":[23],"problems.":[24,152],"paper,":[27,115],"we":[28,48,116,131,154],"take":[29],"it":[30],"a":[31,68,74,140],"step":[32],"further":[33],"by":[34],"extending":[35],"work":[37],"Castelli":[39],"and":[40,78,84,97],"Cover":[41],"to":[42,106,126,160],"multiclass":[44,135],"paradigm.":[45],"particular,":[47],"consider":[49],"key":[51],"problem":[52],"in":[53,113,147],"SSL":[54],"classifying":[56],"an":[57,133],"unseen":[58],"instance":[59],"x":[60],"into":[61],"one":[62],"K":[64,109],"different":[65],"classes,":[66],"using":[67],"training":[69],"data":[70],"set":[71],"sampled":[72],"from":[73],"mixture":[75,96],"density":[76],"distribution":[77],"composed":[79],"l":[81],"labeled":[82,102,123],"records":[83,103],"u":[85],"unlabeled":[86,100],"examples.":[87],"Even":[88],"under":[89],"assumption":[91],"identifiability":[93],"having":[98],"infinite":[99],"examples,":[101],"are":[104],"needed":[105,125],"determine":[107],"decision":[110],"regions.":[111],"Therefore,":[112],"first":[117],"investigate":[118],"minimum":[120],"number":[121],"examples":[124],"accomplish":[127],"that":[128],"task.":[129],"Then,":[130],"propose":[132],"optimal":[134,144],"algorithm,":[137],"which":[138],"is":[139,171],"generalization":[141,159],"procedure":[145],"proposed":[146],"literature":[149],"for":[150],"Finally,":[153],"make":[155],"use":[156],"study":[161],"probability":[163],"error":[165],"when":[166],"class":[169],"constraint":[170],"relaxed.":[172]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
