{"id":"https://openalex.org/W3134504373","doi":"https://doi.org/10.3390/e23030292","title":"Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network","display_name":"Ricci Curvature-Based Semi-Supervised Learning on an Attributed Network","publication_year":2021,"publication_date":"2021-02-27","ids":{"openalex":"https://openalex.org/W3134504373","doi":"https://doi.org/10.3390/e23030292","mag":"3134504373","pmid":"https://pubmed.ncbi.nlm.nih.gov/33673440"},"language":"en","primary_location":{"id":"doi:10.3390/e23030292","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23030292","pdf_url":"https://www.mdpi.com/1099-4300/23/3/292/pdf?version=1616140801","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/3/292/pdf?version=1616140801","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101428331","display_name":"Wei Wu","orcid":"https://orcid.org/0000-0001-5938-9004"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Wu","raw_affiliation_strings":["School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058780083","display_name":"Guangmin Hu","orcid":"https://orcid.org/0000-0002-4694-9145"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangmin Hu","raw_affiliation_strings":["School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100331880","display_name":"Fucai Yu","orcid":"https://orcid.org/0009-0001-5659-1642"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fucai Yu","raw_affiliation_strings":["School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"],"affiliations":[{"raw_affiliation_string":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100331880"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.4956,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.85208596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"3","first_page":"292","last_page":"292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9997000098228455,"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":0.9997000098228455,"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/T12702","display_name":"Brain Tumor Detection and Classification","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2808","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T14510","display_name":"Medical Imaging and Analysis","score":0.9699000120162964,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.7230792045593262},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5882748365402222},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5512312054634094},{"id":"https://openalex.org/keywords/geometric-networks","display_name":"Geometric networks","score":0.5049031376838684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5010135173797607},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4924815595149994},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4518829584121704},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.42721864581108093},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41422784328460693},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41086363792419434},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4070870876312256},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.358794629573822},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.33197808265686035},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32469049096107483},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.2751128077507019},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14431196451187134},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1294611692428589}],"concepts":[{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.7230792045593262},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5882748365402222},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5512312054634094},{"id":"https://openalex.org/C49777392","wikidata":"https://www.wikidata.org/wiki/Q5535495","display_name":"Geometric networks","level":3,"score":0.5049031376838684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5010135173797607},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4924815595149994},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4518829584121704},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.42721864581108093},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41422784328460693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41086363792419434},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4070870876312256},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.358794629573822},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.33197808265686035},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32469049096107483},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2751128077507019},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14431196451187134},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1294611692428589}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23030292","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23030292","pdf_url":"https://www.mdpi.com/1099-4300/23/3/292/pdf?version=1616140801","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33673440","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33673440","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:571af960e9c64f2182ea32eb24434d4e","is_oa":true,"landing_page_url":"https://doaj.org/article/571af960e9c64f2182ea32eb24434d4e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 3, p 292 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/3/292/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23030292","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 23; Issue 3; Pages: 292","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7997130","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7997130","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23030292","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23030292","pdf_url":"https://www.mdpi.com/1099-4300/23/3/292/pdf?version=1616140801","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6499999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3134504373.pdf","grobid_xml":"https://content.openalex.org/works/W3134504373.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1888005072","https://openalex.org/W2000124739","https://openalex.org/W2019786737","https://openalex.org/W2021155376","https://openalex.org/W2027643594","https://openalex.org/W2068278462","https://openalex.org/W2081643526","https://openalex.org/W2087667141","https://openalex.org/W2090891622","https://openalex.org/W2154851992","https://openalex.org/W2242161203","https://openalex.org/W2315403234","https://openalex.org/W2387462954","https://openalex.org/W2393319904","https://openalex.org/W2508137831","https://openalex.org/W2579372251","https://openalex.org/W2585247128","https://openalex.org/W2766453196","https://openalex.org/W2773145138","https://openalex.org/W2903501821","https://openalex.org/W2950723285","https://openalex.org/W2962756421","https://openalex.org/W2963312446","https://openalex.org/W2964129753","https://openalex.org/W3038588914","https://openalex.org/W3104097132","https://openalex.org/W6690230747","https://openalex.org/W6732461846"],"related_works":["https://openalex.org/W55883722","https://openalex.org/W2394379345","https://openalex.org/W4317888157","https://openalex.org/W2079726820","https://openalex.org/W3104800576","https://openalex.org/W2014128112","https://openalex.org/W4312212642","https://openalex.org/W3157019080","https://openalex.org/W4300236414","https://openalex.org/W4389983812"],"abstract_inverted_index":{"In":[0,85,131],"recent":[1],"years,":[2],"on":[3,260],"the":[4,23,54,75,86,93,101,104,107,143,165,181,184,187,195,203,207,211,223,226,230,233,241,246],"basis":[5],"of":[6,25,77,82,88,106,155,161,186,206,210,243],"drawing":[7],"lessons":[8],"from":[9,57],"traditional":[10,58],"neural":[11,26,38,47,148],"network":[12,27,48,166],"models,":[13],"people":[14],"have":[15],"been":[16],"paying":[17],"more":[18,20],"and":[19,66,171,229],"attention":[21],"to":[22,63,96,100,118,127,176,180,194],"design":[24],"architectures":[28],"for":[29,139],"processing":[30],"graph":[31,37,43,64,146],"structure":[32,205],"data,":[33,65],"which":[34,73,199],"are":[35,46,113],"called":[36,142],"networks":[39],"(GNN).":[40],"GCN,":[41],"namely,":[42,124],"convolution":[44,55],"networks,":[45],"models":[49],"in":[50,103,232,245],"GNN.":[51],"GCN":[52,91],"extends":[53],"operation":[56],"data":[59,112],"(such":[60],"as":[61,167],"images)":[62],"it":[67],"is":[68,157,192],"essentially":[69],"a":[70,120,136,168,253],"feature":[71],"extractor,":[72],"aggregates":[74],"features":[76],"neighborhood":[78,105,185],"nodes":[79,102,182,231],"into":[80],"those":[81],"target":[83,108,188,227],"nodes.":[84,109,189],"process":[87],"aggregating":[89],"features,":[90],"uses":[92],"Laplacian":[94],"matrix":[95],"assign":[97,177],"different":[98,178],"importance":[99,179,215],"Since":[110],"graph-structured":[111],"inherently":[114],"non-Euclidean,":[115],"we":[116,134],"seek":[117],"use":[119,173],"non-Euclidean":[121],"mathematical":[122],"tool,":[123],"Riemannian":[125],"geometry,":[126],"analyze":[128],"graphs":[129],"(networks).":[130],"this":[132],"paper,":[133],"present":[135],"novel":[137],"model":[138,237],"semi-supervised":[140],"learning":[141],"Ricci":[144,174,190,218],"curvature-based":[145],"convolutional":[147],"network,":[149],"i.e.,":[150],"RCGCN.":[151],"The":[152,213,235],"aggregation":[153],"pattern":[154],"RCGCN":[156,251],"inspired":[158],"by":[159,217],"that":[160,250],"GCN.":[162],"We":[163],"regard":[164],"discrete":[169],"manifold,":[170],"then":[172],"curvature":[175,191,219],"within":[183],"related":[193],"optimal":[196],"transport":[197],"distance,":[198],"can":[200,220],"well":[201],"reflect":[202,222],"geometric":[204],"underlying":[208],"space":[209],"network.":[212,247],"node":[214,228],"given":[216],"better":[221],"relationships":[224],"between":[225],"neighborhood.":[234],"proposed":[236],"scales":[238],"linearly":[239],"with":[240],"number":[242],"edges":[244],"Experiments":[248],"demonstrated":[249],"achieves":[252],"significant":[254],"performance":[255],"gain":[256],"over":[257],"baseline":[258],"methods":[259],"benchmark":[261],"datasets.":[262]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}