{"id":"https://openalex.org/W7108209500","doi":"https://doi.org/10.1016/j.patcog.2025.112828","title":"Deep positional encoders for graph classification","display_name":"Deep positional encoders for graph classification","publication_year":2025,"publication_date":"2025-12-02","ids":{"openalex":"https://openalex.org/W7108209500","doi":"https://doi.org/10.1016/j.patcog.2025.112828"},"language":"en","primary_location":{"id":"doi:10.1016/j.patcog.2025.112828","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.patcog.2025.112828","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.patcog.2025.112828","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ahmed Begga","orcid":"https://orcid.org/0009-0000-8733-2072"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Ahmed Begga","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Alicante, Alicante, Spain"],"raw_orcid":"https://orcid.org/0009-0000-8733-2072","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Miguel \u00c1ngel Lozano","orcid":"https://orcid.org/0000-0003-3238-4021"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Miguel \u00c1ngel Lozano","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Alicante, Alicante, Spain"],"raw_orcid":"https://orcid.org/0000-0003-3238-4021","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"last","author":{"id":null,"display_name":"Francisco Escolano","orcid":"https://orcid.org/0000-0002-4757-5587"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco Escolano","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Alicante, Alicante, Spain"],"raw_orcid":"https://orcid.org/0000-0002-4757-5587","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130194489"],"apc_list":{"value":2850,"currency":"USD","value_usd":2850},"apc_paid":{"value":2850,"currency":"USD","value_usd":2850},"fwci":1.2644,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.88570128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"173","issue":null,"first_page":"112828","last_page":"112828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9883999824523926,"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":0.9883999824523926,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.0044999998062849045,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.000699999975040555,"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/spectral-graph-theory","display_name":"Spectral graph theory","score":0.5241000056266785},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5034000277519226},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.47290000319480896},{"id":"https://openalex.org/keywords/encoder","display_name":"Encoder","score":0.45719999074935913},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.4546999931335449},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.44690001010894775},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.41449999809265137},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3571000099182129},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.351500004529953}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.691100001335144},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.5241000056266785},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.515500009059906},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5034000277519226},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.47290000319480896},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.45719999074935913},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.44690001010894775},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4341000020503998},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39660000801086426},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.31189998984336853},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.2890999913215637},{"id":"https://openalex.org/C145580432","wikidata":"https://www.wikidata.org/wiki/Q6497118","display_name":"Lattice graph","level":5,"score":0.2874000072479248},{"id":"https://openalex.org/C112953755","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph drawing","level":3,"score":0.2865999937057495},{"id":"https://openalex.org/C106937863","wikidata":"https://www.wikidata.org/wiki/Q7236518","display_name":"Power graph analysis","level":3,"score":0.28290000557899475},{"id":"https://openalex.org/C134727501","wikidata":"https://www.wikidata.org/wiki/Q5597073","display_name":"Graph bandwidth","level":5,"score":0.2791000008583069},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.2750000059604645},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.2621999979019165},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C100595998","wikidata":"https://www.wikidata.org/wiki/Q11731931","display_name":"Graph kernel","level":5,"score":0.25619998574256897},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.patcog.2025.112828","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.patcog.2025.112828","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.patcog.2025.112828","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.patcog.2025.112828","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8449618581","display_name":null,"funder_award_id":"PID2022-142516OB-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1966596927","https://openalex.org/W1977806565","https://openalex.org/W2061214064","https://openalex.org/W2097308346","https://openalex.org/W2130470622","https://openalex.org/W2150217673","https://openalex.org/W2607507412","https://openalex.org/W2962810718","https://openalex.org/W3152893301","https://openalex.org/W4386102370","https://openalex.org/W4397031725","https://openalex.org/W4403848204"],"related_works":[],"abstract_inverted_index":{"Structural":[0],"Pattern":[1],"Recognition":[2],"(SPR)":[3],"includes":[4],"the":[5,25,58,65,89,92,110],"study":[6],"of":[7,11,61,91,112],"graphs":[8,46],"as":[9,35,99],"encoders":[10,101],"non-sequential":[12],"and":[13,95],"permutation-invariant":[14],"patterns.":[15],"In":[16,73],"this":[17,74,78],"regard,":[18],"Graph":[19,83],"Neural":[20],"Networks":[21],"(GNNs)":[22],"are":[23],"paving":[24],"way":[26],"towards":[27],"\u201cinductive":[28],"SPR\u201d":[29],"where":[30],"classical":[31],"structural":[32,59],"problems":[33],"such":[34],"graph":[36,71,93,114],"classification":[37],"can":[38],"be":[39],"approached":[40],"through":[41],"learnable":[42],"priors.":[43],"However,":[44],"since":[45],"do":[47],"not":[48],"have":[49],"a":[50],"canonical":[51],"order,":[52],"existing":[53],"GNNs":[54],"struggle":[55],"to":[56],"learn":[57],"role":[60],"each":[62],"node":[63],"in":[64,70],"graph,":[66],"which":[67],"becomes":[68],"key":[69],"classification.":[72,115],"paper,":[75],"we":[76,107],"address":[77],"problem":[79],"by":[80,87],"making":[81],"Spectral":[82],"Theory":[84],"\u201cinductive\u201d,":[85],"i.e.":[86],"learning":[88],"eigenvectors":[90],"Laplacian,":[94],"then":[96],"using":[97],"them":[98],"positional":[100],"(PEs).":[102],"Our":[103],"experiments":[104],"show":[105],"that":[106],"improve":[108],"significantly":[109],"SOTA":[111],"GNN-based":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-12-03T00:00:00"}