{"id":"https://openalex.org/W6903599628","doi":"https://doi.org/10.1184/r1/22186843.v1","title":"Geometric Deep Learning: Impact of Graph Structure on Graph Neural Networks","display_name":"Geometric Deep Learning: Impact of Graph Structure on Graph Neural Networks","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W6903599628","doi":"https://doi.org/10.1184/r1/22186843.v1"},"language":"en","primary_location":{"id":"pmh:oai:figshare.com:article/22186843","is_oa":true,"landing_page_url":"https://figshare.com/articles/thesis/Geometric_Deep_Learning_Impact_of_Graph_Structure_on_Graph_Neural_Networks/22186843","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/thesis/Geometric_Deep_Learning_Impact_of_Graph_Structure_on_Graph_Neural_Networks/22186843","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Cheung, Mark","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cheung, Mark","raw_affiliation_strings":["Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2792385,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.988099992275238,"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":0.988099992275238,"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":0.0019000000320374966,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/graph","display_name":"Graph","score":0.5060999989509583},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.49239999055862427},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.45899999141693115},{"id":"https://openalex.org/keywords/null-graph","display_name":"Null graph","score":0.43860000371932983},{"id":"https://openalex.org/keywords/graph-property","display_name":"Graph property","score":0.43230000138282776},{"id":"https://openalex.org/keywords/geometric-networks","display_name":"Geometric networks","score":0.41019999980926514},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3716000020503998},{"id":"https://openalex.org/keywords/synthetic-data","display_name":"Synthetic data","score":0.36390000581741333},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.359499990940094}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.619700014591217},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5060999989509583},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49459999799728394},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.49239999055862427},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.45899999141693115},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.43860000371932983},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.43230000138282776},{"id":"https://openalex.org/C49777392","wikidata":"https://www.wikidata.org/wiki/Q5535495","display_name":"Geometric networks","level":3,"score":0.41019999980926514},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39660000801086426},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39010000228881836},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3716000020503998},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.359499990940094},{"id":"https://openalex.org/C157406716","wikidata":"https://www.wikidata.org/wiki/Q4115842","display_name":"Topological graph theory","level":5,"score":0.33489999175071716},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.33410000801086426},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.3296000063419342},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C134727501","wikidata":"https://www.wikidata.org/wiki/Q5597073","display_name":"Graph bandwidth","level":5,"score":0.3102000057697296},{"id":"https://openalex.org/C19332903","wikidata":"https://www.wikidata.org/wiki/Q7623247","display_name":"Strength of a graph","level":5,"score":0.28200000524520874},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C18819970","wikidata":"https://www.wikidata.org/wiki/Q3035340","display_name":"Butterfly graph","level":5,"score":0.27250000834465027},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2639000117778778},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.2540000081062317},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:figshare.com:article/22186843","is_oa":true,"landing_page_url":"https://figshare.com/articles/thesis/Geometric_Deep_Learning_Impact_of_Graph_Structure_on_Graph_Neural_Networks/22186843","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},{"id":"doi:10.1184/r1/22186843.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/22186843.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/22186843","is_oa":true,"landing_page_url":"https://figshare.com/articles/thesis/Geometric_Deep_Learning_Impact_of_Graph_Structure_on_Graph_Neural_Networks/22186843","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Deep":[0,69],"learning":[1,56,116],"techniques":[2],"have":[3,216,465],"led":[4],"to":[5,32,57,179,228,276,304,306,394,416,440,444,448,484,504],"major":[6],"improvements":[7],"in":[8,22,249],"fields":[9],"like":[10],"natural":[11],"language":[12],"processing,":[13],"computer":[14],"vision,":[15],"and":[16,48,110,119,129,143,190,212,224,233,254,299,338,347,391,446,453,460,473],"other":[17,49,426],"Euclidean":[18],"data":[19,25,60,98,112],"domains,":[20],"yet":[21],"many":[23,175],"domains":[24],"are":[26,177,380],"irregular,":[27],"requiring":[28],"graphs":[29,368],"or":[30,410,418],"manifolds":[31],"be":[33],"explicitly":[34],"modeled.":[35],"Such":[36],"applications":[37],"include":[38],"social":[39],"networks,":[40],"sensor":[41],"feeds,":[42],"logistics,":[43],"supply":[44],"chains,":[45],"chemistry,":[46],"neuroscience,":[47],"biological":[50],"systems.":[51],"The":[52],"extension":[53],"of":[54,64,78,96,104,127,133,160,167,231,236,258,317,329,374,397,408,412,502],"deep":[55],"these":[58,398,435],"nonEuclidean":[59],"is":[61,188,302,323,482,493],"an":[62,246,310],"area":[63],"research":[65],"now":[66],"called":[67],"Geometric":[68],"Learning":[70],"(GDL).":[71],"This":[72],"thesis":[73],"focuses":[74],"on":[75,86,101,201,406,434,532],"a":[76,198,277,356,505,511],"subfield":[77],"GDL,":[79],"graph":[80,87,99,105,115,120,139,150,184,186,203,351,353,362,372,422],"neural":[81,90,106,423],"networks":[82,107,141,152],"(GNNs)":[83],"that":[84,272],"learn":[85],"signals":[88,204],"using":[89,108,197,369],"networks.":[91,424],"We":[92,122,260,269,333,400,498,509],"explore":[93],"the":[94,97,102,125,168,202,229,234,237,251,256,263,284,330,361,371,375,395,489,500,529],"impact":[95],"structure":[100,354],"performance":[103,396,420,451,487],"real":[109,194,384],"synthetic":[111,209,457],"for":[113,221,266,280,289,344,402,470,495,514],"two":[114,131,520],"tasks:":[117],"node":[118,172,267],"classification.":[121,268],"start":[123],"with":[124,164,226,294,314,325],"formalization":[126],"GNNs,":[128],"consider":[130],"flavors":[132],"approaches:":[134],"spectral":[135],"approach":[136,145,513],"typified":[137,146],"by":[138,147,518],"convolutional":[140,151],"(GCNs)":[142],"spatial":[144],"topology":[148],"adaptive":[149],"(TAGCNs).":[153],"In":[154],"general,":[155],"TAGCN":[156,225,447,503],"requires":[157],"fewer":[158],"number":[159,230,316,407,411],"layers":[161,176,232],"than":[162,360,479],"GCN,":[163],"moderate":[165],"degrees":[166],"polynomial":[169,238,297,331],"filters.":[170,239,332],"For":[171,192,208,240,350,383,425,456,475],"classification,":[173,185,352],"not":[174],"needed":[178,483],"achieve":[180,485],"optimal":[181,252],"performance.":[182],"Unlike":[183],"signal":[187,392,428],"necessary":[189],"important.":[191],"some":[193,403],"datasets,":[195,210,385,404,427,458],"classifying":[196],"simple":[199,388,442],"estimator":[200],"can":[205,365,414,430],"outperform":[206],"GNNs.":[207],"Erdos-R\u00e9nyi":[211],"preferential":[213,461],"attachment":[214,462],"models":[215,463],"similar":[217,419,466],"test":[218,467],"accuracy":[219,253,468],"curves":[220,469],"both":[222,345,471],"GCN":[223,445,472],"respect":[227],"degree":[235,295],"smallworld":[241,476],"model,":[242,477],"TAGCN\u2019s":[243],"filters":[244],"play":[245],"important":[247,358],"role":[248,359],"achieving":[250],"accelerating":[255],"effect":[257],"over-smoothing.":[259],"also":[261],"study":[262],"training":[264,273,287,340],"convergence":[265,322,341],"show":[270,339,401],"theoretically":[271],"loss":[274,288],"converges":[275],"global":[278,307],"minimum":[279,308],"linearized":[281,346],"TAGCN.":[282,349,474],"Despite":[283],"non-convex":[285],"objectives,":[286],"1-degree<em>":[290],"H</em>-layer":[291],"TAGCN,":[292,321],"i.e.,":[293],"1":[296,480],"filter":[298],"<em>H</em>":[300],"layers,":[301],"guaranteed":[303],"converge":[305],"at":[309],"exponential":[311],"rate,":[312],"faster":[313],"higher":[315,326],"layers.":[318],"With":[319],"K-degree":[320],"accelerated":[324],"degree<em>":[327],"K</em>":[328],"experimentally":[334],"validate":[335],"our":[336],"theory":[337],"holds":[342],"true":[343],"nonlinearized":[348],"plays":[355],"more":[357,478],"signal.":[363],"GNNs":[364],"often":[366],"classify":[367],"just":[370],"structures":[373],"different":[376,496],"classes":[377],"if":[378,488],"they":[379],"distinct":[381,494],"enough.":[382],"we":[386,437],"relate":[387],"network":[389],"metrics":[390],"statistics":[393,429],"models.":[399],"classifiers":[405],"edges":[409],"nodes":[413],"lead":[415],"better":[417],"as":[421],"perform":[431],"well.":[432],"Based":[433],"observations,":[436],"were":[438],"able":[439],"apply":[441,499],"modifications":[443],"improve":[449],"their":[450],"(sumpool":[452],"degree-aware":[454],"TAGCN).":[455],"Erd\u02ddos-R\u00e9nyi":[459],"again":[464],"layer":[481],"good":[486],"edge":[490],"rewiring":[491],"probability":[492],"classes.":[497],"architecture":[501],"COVID-19":[506],"case":[507],"study.":[508],"introduce":[510],"novel":[512],"molecular":[515],"property":[516],"prediction":[517],"combining":[519],"existing":[521],"GNN":[522],"methods.":[523],"Our":[524],"model":[525],"(D-MPNN+TAGCN)":[526],"consistently":[527],"outperforms":[528],"state-of-the-art":[530],"baseline":[531],"five":[533],"coronavirus":[534],"datasets.":[535]},"counts_by_year":[],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
