{"id":"https://openalex.org/W2343970360","doi":"https://doi.org/10.1109/tpami.2015.2501802","title":"Factorized Graph Matching","display_name":"Factorized Graph Matching","publication_year":2015,"publication_date":"2015-11-20","ids":{"openalex":"https://openalex.org/W2343970360","doi":"https://doi.org/10.1109/tpami.2015.2501802","mag":"2343970360","pmid":"https://pubmed.ncbi.nlm.nih.gov/26595909"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2015.2501802","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2015.2501802","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/A5054137460","display_name":"Feng Zhou","orcid":"https://orcid.org/0000-0001-9184-2040"},"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":false,"raw_author_name":"Feng Zhou","raw_affiliation_strings":["Robotics Institute, Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Robotics Institute, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108127869","display_name":"Fernando De la Torre","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":false,"raw_author_name":"Fernando De la Torre","raw_affiliation_strings":["Robotics Institute, Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Robotics Institute, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8036,"has_fulltext":false,"cited_by_count":194,"citation_normalized_percentile":{"value":0.97432237,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"38","issue":"9","first_page":"1774","last_page":"1789"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":1.0,"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/T11106","display_name":"Data Management and Algorithms","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9922000169754028,"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/pairwise-comparison","display_name":"Pairwise comparison","score":0.8168206810951233},{"id":"https://openalex.org/keywords/quadratic-assignment-problem","display_name":"Quadratic assignment problem","score":0.5504037141799927},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5233166217803955},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5119625329971313},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.48776060342788696},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47065892815589905},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4510568380355835},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4325239956378937},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43089157342910767},{"id":"https://openalex.org/keywords/assignment-problem","display_name":"Assignment problem","score":0.41365063190460205},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4082028269767761},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3964918851852417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3725515604019165},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27707624435424805}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.8168206810951233},{"id":"https://openalex.org/C98036226","wikidata":"https://www.wikidata.org/wiki/Q7268356","display_name":"Quadratic assignment problem","level":3,"score":0.5504037141799927},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5233166217803955},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5119625329971313},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.48776060342788696},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47065892815589905},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4510568380355835},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4325239956378937},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43089157342910767},{"id":"https://openalex.org/C85044808","wikidata":"https://www.wikidata.org/wiki/Q620614","display_name":"Assignment problem","level":2,"score":0.41365063190460205},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4082028269767761},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3964918851852417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3725515604019165},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27707624435424805},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2015.2501802","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2015.2501802","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:26595909","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26595909","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}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.41999998688697815}],"awards":[{"id":"https://openalex.org/G215384666","display_name":null,"funder_award_id":"CPS-0931999","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5227708377","display_name":null,"funder_award_id":"EEEC-0540865","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7596508711","display_name":null,"funder_award_id":"RI-1116583","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":72,"referenced_works":["https://openalex.org/W48175873","https://openalex.org/W1495953172","https://openalex.org/W1507964143","https://openalex.org/W1518078339","https://openalex.org/W1521461170","https://openalex.org/W1587878450","https://openalex.org/W1590776313","https://openalex.org/W1607862333","https://openalex.org/W1744214816","https://openalex.org/W1972278541","https://openalex.org/W1985123706","https://openalex.org/W1987161519","https://openalex.org/W1997356360","https://openalex.org/W2013603106","https://openalex.org/W2014425592","https://openalex.org/W2049981393","https://openalex.org/W2057175746","https://openalex.org/W2067288219","https://openalex.org/W2068627296","https://openalex.org/W2084512390","https://openalex.org/W2085261163","https://openalex.org/W2099897767","https://openalex.org/W2103375950","https://openalex.org/W2104808398","https://openalex.org/W2104978738","https://openalex.org/W2107855892","https://openalex.org/W2107884096","https://openalex.org/W2108182844","https://openalex.org/W2109294083","https://openalex.org/W2113894747","https://openalex.org/W2115139257","https://openalex.org/W2116801532","https://openalex.org/W2117983893","https://openalex.org/W2119851068","https://openalex.org/W2121225280","https://openalex.org/W2122961704","https://openalex.org/W2124465992","https://openalex.org/W2125186487","https://openalex.org/W2126359798","https://openalex.org/W2134236847","https://openalex.org/W2136885855","https://openalex.org/W2137275576","https://openalex.org/W2138910149","https://openalex.org/W2147405597","https://openalex.org/W2147975091","https://openalex.org/W2150760714","https://openalex.org/W2152953631","https://openalex.org/W2154400678","https://openalex.org/W2154583877","https://openalex.org/W2157084238","https://openalex.org/W2158256890","https://openalex.org/W2159537329","https://openalex.org/W2161444532","https://openalex.org/W2166524953","https://openalex.org/W2166765763","https://openalex.org/W2166820607","https://openalex.org/W2168002178","https://openalex.org/W2171490473","https://openalex.org/W2173758409","https://openalex.org/W2293888570","https://openalex.org/W2343970360","https://openalex.org/W2401213470","https://openalex.org/W2493312408","https://openalex.org/W2937970997","https://openalex.org/W3111937800","https://openalex.org/W3121235808","https://openalex.org/W4239749705","https://openalex.org/W6651104122","https://openalex.org/W6675352095","https://openalex.org/W6676075050","https://openalex.org/W6682759379","https://openalex.org/W6712925784"],"related_works":["https://openalex.org/W3091931714","https://openalex.org/W2793371964","https://openalex.org/W1560792291","https://openalex.org/W1973739845","https://openalex.org/W119752240","https://openalex.org/W2937059810","https://openalex.org/W1586515950","https://openalex.org/W2002489438","https://openalex.org/W2067336310","https://openalex.org/W2153234111"],"abstract_inverted_index":{"Graph":[0],"matching":[1,86,155,208],"(GM)":[2],"is":[3,54,123,188,232],"a":[4,13,33,144,177,203],"fundamental":[5],"problem":[6,36,44,183],"in":[7,20,73],"computer":[8,21,74],"science,":[9],"and":[10,56,106,132,154,169,184,193,219],"it":[11,161,187],"plays":[12],"central":[14],"role":[15],"to":[16,58,126,150,164,171,190],"solve":[17],"correspondence":[18,43],"problems":[19,24],"vision.":[22],"GM":[23,46,61,173,182,197],"that":[25,70,98,116,148],"incorporate":[26,65,165],"pairwise":[27,92,108,134],"constraints":[28,67],"can":[29],"be":[30],"formulated":[31],"as":[32,211],"quadratic":[34],"assignment":[35],"(QAP).":[37],"Although":[38],"widely":[39],"used,":[40],"solving":[41],"the":[42,52,90,100,107,114,128,141,159,172,181,185],"through":[45],"has":[47],"two":[48],"main":[49],"limitations:":[50],"(1)":[51,121],"QAP":[53],"NP-hard":[55],"difficult":[57],"approximate;":[59],"(2)":[60,137],"algorithms":[62,209,227],"do":[63],"not":[64],"geometric":[66,166],"between":[68,110,195],"nodes":[69],"are":[71,113],"natural":[72],"vision":[75],"problems.":[76],"To":[77],"address":[78],"aforementioned":[79],"problems,":[80],"this":[81,119],"paper":[82],"proposes":[83],"factorized":[84],"graph":[85,105],"(FGM).":[87],"FGM":[88,224],"factorizes":[89],"large":[91],"affinity":[93,109,135],"matrix":[94,178],"into":[95],"smaller":[96],"matrices":[97],"encode":[99],"local":[101],"structure":[102],"of":[103,143],"each":[104],"edges.":[111],"Four":[112],"benefits":[115],"follow":[117],"from":[118],"factorization:":[120],"There":[122],"no":[124],"need":[125],"compute":[127],"costly":[129],"(in":[130],"space":[131],"time)":[133],"matrix;":[136],"The":[138,199,230],"factorization":[139,200],"allows":[140],"use":[142],"path-following":[145],"optimization":[146,152],"algorithm,":[147],"leads":[149],"improved":[151],"strategies":[153],"performance;":[156],"(3)":[157],"Given":[158],"factorization,":[160,186],"becomes":[162],"straight-forward":[163],"transformations":[167],"(rigid":[168],"non-rigid)":[170],"problem.":[174],"(4)":[175],"Using":[176],"formulation":[179],"for":[180,228],"easy":[189],"reveal":[191],"commonalities":[192],"differences":[194],"different":[196],"methods.":[198],"also":[201],"provides":[202],"clean":[204],"connection":[205],"with":[206],"other":[207],"such":[210],"iterative":[212],"closest":[213],"point;":[214],"Experimental":[215],"results":[216],"on":[217],"synthetic":[218],"real":[220],"databases":[221],"illustrate":[222],"how":[223],"outperforms":[225],"state-of-the-art":[226],"GM.":[229],"code":[231],"available":[233],"at":[234],"http://humansensing.cs.cmu.edu/fgm.":[235]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":20},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":25},{"year":2020,"cited_by_count":28},{"year":2019,"cited_by_count":32},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
