{"id":"https://openalex.org/W2076080556","doi":"https://doi.org/10.1109/cvpr.2012.6247667","title":"Factorized graph matching","display_name":"Factorized graph matching","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2076080556","doi":"https://doi.org/10.1109/cvpr.2012.6247667","mag":"2076080556"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2012.6247667","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2012.6247667","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Factorized_Graph_Matching/6554858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047702220","display_name":"Feng Zhou","orcid":"https://orcid.org/0000-0001-6123-073X"},"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, USA","Robotics Institute, Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Robotics Institute, Carnegie Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Robotics Institute, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003508045","display_name":"Fernando De la Torre","orcid":"https://orcid.org/0000-0002-5143-3709"},"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":"F. De la Torre","raw_affiliation_strings":["Robotics Institute, Carnegie Mellon University, USA","Robotics Institute, Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Robotics Institute, Carnegie Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]},{"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":20.2679,"has_fulltext":false,"cited_by_count":275,"citation_normalized_percentile":{"value":0.99516027,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"127","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9954000115394592,"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":0.994700014591217,"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/factorization","display_name":"Factorization","score":0.5585541725158691},{"id":"https://openalex.org/keywords/3-dimensional-matching","display_name":"3-dimensional matching","score":0.5552119612693787},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5174530148506165},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5139617323875427},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5122329592704773},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4677187502384186},{"id":"https://openalex.org/keywords/quadratic-assignment-problem","display_name":"Quadratic assignment problem","score":0.4558500051498413},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.43072158098220825},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3961678743362427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3185526430606842},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2657019793987274},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.18882769346237183}],"concepts":[{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5585541725158691},{"id":"https://openalex.org/C72545166","wikidata":"https://www.wikidata.org/wiki/Q10866593","display_name":"3-dimensional matching","level":4,"score":0.5552119612693787},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5174530148506165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5139617323875427},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5122329592704773},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4677187502384186},{"id":"https://openalex.org/C98036226","wikidata":"https://www.wikidata.org/wiki/Q7268356","display_name":"Quadratic assignment problem","level":3,"score":0.4558500051498413},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43072158098220825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3961678743362427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3185526430606842},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2657019793987274},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.18882769346237183},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1109/cvpr.2012.6247667","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2012.6247667","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmh:oai:repository.cmu.edu:robotics-2183","is_oa":false,"landing_page_url":"http://repository.cmu.edu/robotics/1173","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Robotics Institute","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6554858","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal contribution"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.227.6076","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.6076","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ri.cmu.edu/pub_files/2012/6/fgm.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.309.2038","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.2038","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.f-zhou.com/gm/2012_CVPR_FGM.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.406.3981","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.3981","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.f-zhou.com/gm/2013_PAMI_FGM_Draft.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/6554858","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Factorized_Graph_Matching/6554858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.1184/r1/6554858.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6554858.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/6554858","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Factorized_Graph_Matching/6554858","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"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":48,"referenced_works":["https://openalex.org/W1495953172","https://openalex.org/W1507964143","https://openalex.org/W1521461170","https://openalex.org/W1539145856","https://openalex.org/W1587878450","https://openalex.org/W1607862333","https://openalex.org/W1744214816","https://openalex.org/W1987161519","https://openalex.org/W1990283121","https://openalex.org/W1997356360","https://openalex.org/W1999584386","https://openalex.org/W2011039300","https://openalex.org/W2013603106","https://openalex.org/W2067288219","https://openalex.org/W2097784989","https://openalex.org/W2107855892","https://openalex.org/W2108182844","https://openalex.org/W2109294083","https://openalex.org/W2117983893","https://openalex.org/W2121225280","https://openalex.org/W2124465992","https://openalex.org/W2127952943","https://openalex.org/W2136885855","https://openalex.org/W2137275576","https://openalex.org/W2138910149","https://openalex.org/W2150760714","https://openalex.org/W2152953631","https://openalex.org/W2154583877","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/W2186094539","https://openalex.org/W2401213470","https://openalex.org/W4239749705","https://openalex.org/W4285719527","https://openalex.org/W6629623700","https://openalex.org/W6630498891","https://openalex.org/W6631281345","https://openalex.org/W6632268802","https://openalex.org/W6635241246","https://openalex.org/W6637760914","https://openalex.org/W6676075050","https://openalex.org/W6682759379","https://openalex.org/W6712925784"],"related_works":["https://openalex.org/W2567825307","https://openalex.org/W2054458431","https://openalex.org/W2371352078","https://openalex.org/W4295762832","https://openalex.org/W1592682627","https://openalex.org/W1973739845","https://openalex.org/W119752240","https://openalex.org/W2945016732","https://openalex.org/W4382724515","https://openalex.org/W2785998768"],"abstract_inverted_index":{"Graph":[0,13],"matching":[1,14,48,58,115],"plays":[2],"a":[3,24,50,73,111,129],"central":[4],"role":[5],"in":[6,10,88,140,145],"solving":[7],"correspondence":[8],"problems":[9,15],"computer":[11],"vision.":[12],"that":[16,65,136],"incorporate":[17],"pair-wise":[18,104],"constraints":[19],"can":[20,69],"be":[21,70],"cast":[22],"as":[23,72],"quadratic":[25],"assignment":[26],"problem":[27,135],"(QAP).":[28],"Unfortunately,":[29],"QAP":[30],"is":[31,93,157],"NP-hard":[32],"and":[33,55,102,116,147],"many":[34],"algorithms":[35,139],"have":[36],"been":[37],"proposed":[38],"to":[39,96],"solve":[40],"different":[41],"relaxations.":[42],"This":[43],"paper":[44],"presents":[45],"factorized":[46,71],"graph":[47,57,89,114,141],"(FGM),":[49],"novel":[51],"framework":[52],"for":[53,113],"interpreting":[54],"optimizing":[56],"problems.":[59],"In":[60],"this":[61,86],"work":[62],"we":[63,127],"show":[64],"the":[66,98,118,125,133,151],"affinity":[67,105],"matrix":[68],"Kronecker":[74],"product":[75],"of":[76,84,132,153],"smaller":[77],"matrices.":[78],"There":[79,92],"are":[80],"three":[81],"main":[82],"benefits":[83,152],"using":[85],"factorization":[87,109,126],"matching:":[90],"(1)":[91],"no":[94],"need":[95],"compute":[97],"costly":[99],"(in":[100],"space":[101],"time)":[103],"matrix;":[106],"(2)":[107],"The":[108,155],"provides":[110],"taxonomy":[112],"reveals":[117],"connection":[119],"among":[120],"several":[121],"methods;":[122],"(3)":[123],"Using":[124],"derive":[128],"new":[130],"approximation":[131],"original":[134],"improves":[137],"state-of-the-art":[138],"matching.":[142],"Experimental":[143],"results":[144],"synthetic":[146],"real":[148],"databases":[149],"illustrate":[150],"FGM.":[154],"code":[156],"available":[158],"at":[159],"http://humansensing.cs.cmu.edu/fgm.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":27},{"year":2020,"cited_by_count":34},{"year":2019,"cited_by_count":22},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":35},{"year":2016,"cited_by_count":44},{"year":2015,"cited_by_count":34},{"year":2014,"cited_by_count":24},{"year":2013,"cited_by_count":15}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
