{"id":"https://openalex.org/W3124806699","doi":"https://doi.org/10.1109/tpami.2021.3054304","title":"On Inductive\u2013Transductive Learning With Graph Neural Networks","display_name":"On Inductive\u2013Transductive Learning With Graph Neural Networks","publication_year":2021,"publication_date":"2021-01-25","ids":{"openalex":"https://openalex.org/W3124806699","doi":"https://doi.org/10.1109/tpami.2021.3054304","mag":"3124806699","pmid":"https://pubmed.ncbi.nlm.nih.gov/33493112"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2021.3054304","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3054304","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/A5065846066","display_name":"Giorgio Ciano","orcid":"https://orcid.org/0000-0003-2863-4315"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giorgio Ciano","raw_affiliation_strings":["University of Florence, Firenze, Italy","University of Siena, Siena, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2863-4315","affiliations":[{"raw_affiliation_string":"University of Florence, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"University of Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011763169","display_name":"Alberto Rossi","orcid":"https://orcid.org/0000-0003-1688-6961"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Rossi","raw_affiliation_strings":["University of Florence, Firenze, Italy","University of Siena, Siena, Italy"],"raw_orcid":"https://orcid.org/0000-0003-1688-6961","affiliations":[{"raw_affiliation_string":"University of Florence, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"University of Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091787895","display_name":"Monica Bianchini","orcid":"https://orcid.org/0000-0002-8206-8142"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Monica Bianchini","raw_affiliation_strings":["University of Florence, Firenze, Italy","University of Siena, Siena, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8206-8142","affiliations":[{"raw_affiliation_string":"University of Florence, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"University of Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020560480","display_name":"Franco Scarselli","orcid":"https://orcid.org/0000-0003-1307-0772"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franco Scarselli","raw_affiliation_strings":["University of Florence, Firenze, Italy","University of Siena, Siena, Italy"],"raw_orcid":"https://orcid.org/0000-0003-1307-0772","affiliations":[{"raw_affiliation_string":"University of Florence, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"University of Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0376,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.95954763,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"44","issue":"2","first_page":"758","last_page":"769"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9998999834060669,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9998999834060669,"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/T10028","display_name":"Topic Modeling","score":0.989799976348877,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7328028678894043},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6804385185241699},{"id":"https://openalex.org/keywords/inductive-bias","display_name":"Inductive bias","score":0.6551438570022583},{"id":"https://openalex.org/keywords/transduction","display_name":"Transduction (biophysics)","score":0.6361482739448547},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.595154345035553},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5849863290786743},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.570262610912323},{"id":"https://openalex.org/keywords/semi-supervised-learning","display_name":"Semi-supervised learning","score":0.44939854741096497},{"id":"https://openalex.org/keywords/multi-task-learning","display_name":"Multi-task learning","score":0.28662046790122986},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.17818483710289001}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7328028678894043},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6804385185241699},{"id":"https://openalex.org/C197352929","wikidata":"https://www.wikidata.org/wiki/Q1074074","display_name":"Inductive bias","level":4,"score":0.6551438570022583},{"id":"https://openalex.org/C15152581","wikidata":"https://www.wikidata.org/wiki/Q7833966","display_name":"Transduction (biophysics)","level":2,"score":0.6361482739448547},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.595154345035553},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5849863290786743},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.570262610912323},{"id":"https://openalex.org/C58973888","wikidata":"https://www.wikidata.org/wiki/Q1041418","display_name":"Semi-supervised learning","level":2,"score":0.44939854741096497},{"id":"https://openalex.org/C28006648","wikidata":"https://www.wikidata.org/wiki/Q6934509","display_name":"Multi-task learning","level":3,"score":0.28662046790122986},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.17818483710289001},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000069550","descriptor_name":"Machine Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000069550","descriptor_name":"Machine Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000069550","descriptor_name":"Machine Learning","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"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":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2021.3054304","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3054304","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:33493112","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33493112","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:usiena-air.unisi.it:11365/1141505","is_oa":false,"landing_page_url":"https://ieeexplore.ieee.org/abstract/document/9335498","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.699999988079071}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W35966080","https://openalex.org/W390146837","https://openalex.org/W637153065","https://openalex.org/W1479807131","https://openalex.org/W1529495223","https://openalex.org/W1585529040","https://openalex.org/W1662382123","https://openalex.org/W1875112053","https://openalex.org/W1967075510","https://openalex.org/W1999653836","https://openalex.org/W2002747011","https://openalex.org/W2016696435","https://openalex.org/W2042313354","https://openalex.org/W2051803334","https://openalex.org/W2073562093","https://openalex.org/W2087918852","https://openalex.org/W2100655604","https://openalex.org/W2102419107","https://openalex.org/W2104595371","https://openalex.org/W2106922081","https://openalex.org/W2111174249","https://openalex.org/W2116341502","https://openalex.org/W2119821739","https://openalex.org/W2121470019","https://openalex.org/W2127827747","https://openalex.org/W2130196635","https://openalex.org/W2136294701","https://openalex.org/W2142498761","https://openalex.org/W2148603752","https://openalex.org/W2150120952","https://openalex.org/W2153121902","https://openalex.org/W2157762168","https://openalex.org/W2160556205","https://openalex.org/W2163480486","https://openalex.org/W2166681504","https://openalex.org/W2167665791","https://openalex.org/W2187444093","https://openalex.org/W2261290698","https://openalex.org/W2315889990","https://openalex.org/W2547273193","https://openalex.org/W2558748708","https://openalex.org/W2800988861","https://openalex.org/W2889079456","https://openalex.org/W2889399096","https://openalex.org/W2907492528","https://openalex.org/W2950898568","https://openalex.org/W2953384591","https://openalex.org/W3002924435","https://openalex.org/W3100078588","https://openalex.org/W4210984920","https://openalex.org/W4251194840","https://openalex.org/W6600552058","https://openalex.org/W6620673361","https://openalex.org/W6637178625","https://openalex.org/W6676834449","https://openalex.org/W6680132778","https://openalex.org/W6681029592","https://openalex.org/W6682082992","https://openalex.org/W6690815549","https://openalex.org/W6695479203","https://openalex.org/W6699364125","https://openalex.org/W6713582119","https://openalex.org/W6727823310","https://openalex.org/W6736685754","https://openalex.org/W6738964360","https://openalex.org/W6754929296","https://openalex.org/W6776488958"],"related_works":["https://openalex.org/W2890433954","https://openalex.org/W2053366384","https://openalex.org/W1810370127","https://openalex.org/W2029985245","https://openalex.org/W4311865232","https://openalex.org/W3166049060","https://openalex.org/W4284678096","https://openalex.org/W38577652","https://openalex.org/W2904380457","https://openalex.org/W58770712"],"abstract_inverted_index":{"Many":[0],"real-world":[1],"domains":[2],"involve":[3],"information":[4,70],"naturally":[5],"represented":[6],"by":[7],"graphs,":[8],"where":[9],"nodes":[10],"denote":[11],"basic":[12],"patterns":[13],"while":[14],"edges":[15],"stand":[16],"for":[17,120],"relationships":[18,78],"among":[19,79],"them.":[20],"The":[21,113],"graph":[22],"neural":[23],"network":[24],"(GNN)":[25],"is":[26],"a":[27,50,86],"machine":[28],"learning":[29,52,139],"model":[30],"capable":[31],"of":[32,60,108,128],"directly":[33],"managing":[34],"graph-structured":[35],"data.":[36],"In":[37,81],"the":[38,65,75,106,121,126,129,132,137],"original":[39],"framework,":[40],"GNNs":[41,55],"are":[42],"inductively":[43],"trained,":[44],"adapting":[45],"their":[46],"parameters":[47],"based":[48],"on":[49,136],"supervised":[51],"environment.":[53],"However,":[54],"can":[56,134],"also":[57],"take":[58],"advantage":[59],"transductive":[61,111],"learning,":[62],"thanks":[63],"to":[64,102],"natural":[66],"way":[67],"they":[68],"make":[69],"flow":[71],"and":[72,94,104,110,131],"spread":[73],"across":[74],"graph,":[76],"using":[77],"patterns.":[80],"this":[82],"paper,":[83],"we":[84],"propose":[85],"mixed":[87,122],"inductive-transductive":[88],"GNN":[89],"model,":[90,123],"study":[91],"its":[92],"properties":[93,119],"introduce":[95],"an":[96],"experimental":[97,115],"strategy":[98],"that":[99],"allows":[100],"us":[101],"understand":[103],"distinguish":[105],"role":[107],"inductive":[109],"learning.":[112],"preliminary":[114],"results":[116],"show":[117],"interesting":[118],"highlighting":[124],"how":[125],"peculiarities":[127],"problems":[130],"data":[133],"impact":[135],"two":[138],"strategies.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}