{"id":"https://openalex.org/W4313829323","doi":"https://doi.org/10.1080/10618600.2023.2165500","title":"Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification","display_name":"Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification","publication_year":2023,"publication_date":"2023-01-09","ids":{"openalex":"https://openalex.org/W4313829323","doi":"https://doi.org/10.1080/10618600.2023.2165500"},"language":"en","primary_location":{"id":"doi:10.1080/10618600.2023.2165500","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10618600.2023.2165500","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5100722835","display_name":"Mengyu Li","orcid":"https://orcid.org/0000-0002-5286-7525"},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengyu Li","raw_affiliation_strings":["Institute of Statistics and Big Data, Renmin University of China, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-5286-7525","affiliations":[{"raw_affiliation_string":"Institute of Statistics and Big Data, Renmin University of China, Beijing, China","institution_ids":["https://openalex.org/I78988378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019853998","display_name":"Jun Yu","orcid":"https://orcid.org/0000-0001-6068-8415"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Yu","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-6068-8415","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035141289","display_name":"Hongteng Xu","orcid":"https://orcid.org/0000-0003-4192-5360"},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongteng Xu","raw_affiliation_strings":["Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-4192-5360","affiliations":[{"raw_affiliation_string":"Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China","institution_ids":["https://openalex.org/I78988378"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102923021","display_name":"Cheng Meng","orcid":"https://orcid.org/0000-0002-7111-0966"},"institutions":[{"id":"https://openalex.org/I78988378","display_name":"Renmin University of China","ror":"https://ror.org/041pakw92","country_code":"CN","type":"education","lineage":["https://openalex.org/I78988378"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cheng Meng","raw_affiliation_strings":["Center for Applied Statistics, Institute of Statistics and Big Data, Renmin University of China, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-7111-0966","affiliations":[{"raw_affiliation_string":"Center for Applied Statistics, Institute of Statistics and Big Data, Renmin University of China, Beijing, China","institution_ids":["https://openalex.org/I78988378"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102923021"],"corresponding_institution_ids":["https://openalex.org/I78988378"],"apc_list":null,"apc_paid":null,"fwci":2.6917,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89175375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"32","issue":"4","first_page":"1512","last_page":"1523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/distance-matrix","display_name":"Distance matrix","score":0.6619619131088257},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5966615080833435},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5937256813049316},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5455408096313477},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.49700430035591125},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4869159460067749},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.4835050404071808},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4815412163734436},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.47705355286598206},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4746818244457245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4536149501800537},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.44437849521636963},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4410722255706787},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3713352084159851},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14275887608528137},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.10192662477493286},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10164862871170044},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07893386483192444}],"concepts":[{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.6619619131088257},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5966615080833435},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5937256813049316},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5455408096313477},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.49700430035591125},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4869159460067749},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4835050404071808},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4815412163734436},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.47705355286598206},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4746818244457245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4536149501800537},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.44437849521636963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4410722255706787},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3713352084159851},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14275887608528137},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.10192662477493286},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10164862871170044},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07893386483192444},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10618600.2023.2165500","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10618600.2023.2165500","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1132625208","display_name":null,"funder_award_id":"12101606","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3981035160","display_name":null,"funder_award_id":"12001042","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4747985527","display_name":null,"funder_award_id":"12271522","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W1920097550","https://openalex.org/W1977452941","https://openalex.org/W2003447360","https://openalex.org/W2008857988","https://openalex.org/W2019106840","https://openalex.org/W2027842533","https://openalex.org/W2033057584","https://openalex.org/W2033403400","https://openalex.org/W2069739265","https://openalex.org/W2098770975","https://openalex.org/W2101234009","https://openalex.org/W2116780995","https://openalex.org/W2129893339","https://openalex.org/W2132022337","https://openalex.org/W2158131535","https://openalex.org/W2184329057","https://openalex.org/W2417433140","https://openalex.org/W2474265885","https://openalex.org/W2528005577","https://openalex.org/W2531563875","https://openalex.org/W2604738573","https://openalex.org/W2724892359","https://openalex.org/W2728183739","https://openalex.org/W2786851242","https://openalex.org/W2789285779","https://openalex.org/W2807744099","https://openalex.org/W2808408933","https://openalex.org/W2899486018","https://openalex.org/W2909805545","https://openalex.org/W2911397097","https://openalex.org/W2918342466","https://openalex.org/W2936342412","https://openalex.org/W2944977712","https://openalex.org/W2945314112","https://openalex.org/W2945793051","https://openalex.org/W2948330935","https://openalex.org/W2962867868","https://openalex.org/W2963472233","https://openalex.org/W2971007906","https://openalex.org/W2991210238","https://openalex.org/W2998437625","https://openalex.org/W3005233248","https://openalex.org/W3005380363","https://openalex.org/W3005526472","https://openalex.org/W3028903392","https://openalex.org/W3033888062","https://openalex.org/W3034574626","https://openalex.org/W3036400684","https://openalex.org/W3082556740","https://openalex.org/W3084165997","https://openalex.org/W3103030880","https://openalex.org/W3106529377","https://openalex.org/W3113286149","https://openalex.org/W3169502490","https://openalex.org/W3184455115","https://openalex.org/W3202204105","https://openalex.org/W3203898565","https://openalex.org/W4206471589","https://openalex.org/W4213437519","https://openalex.org/W4225982766","https://openalex.org/W4230927393","https://openalex.org/W4233762729","https://openalex.org/W4248500611","https://openalex.org/W4280494023","https://openalex.org/W4281704193","https://openalex.org/W4288350653","https://openalex.org/W4289258965","https://openalex.org/W4295723444","https://openalex.org/W4304084190","https://openalex.org/W4306317292","https://openalex.org/W4312361099","https://openalex.org/W4388846637","https://openalex.org/W4394782384","https://openalex.org/W6675354045","https://openalex.org/W6677280552","https://openalex.org/W6755187585","https://openalex.org/W6767113772"],"related_works":["https://openalex.org/W2063021680","https://openalex.org/W2357922472","https://openalex.org/W2384278689","https://openalex.org/W2563365141","https://openalex.org/W2386777115","https://openalex.org/W2888513445","https://openalex.org/W2376265369","https://openalex.org/W3152399948","https://openalex.org/W2156718603","https://openalex.org/W2151152091"],"abstract_inverted_index":{"As":[0],"a":[1,44,61,68,76],"valid":[2],"metric":[3],"of":[4,17,59,119,143,164],"metric-measure":[5],"spaces,":[6],"Gromov-Wasserstein":[7],"(GW)":[8],"distance":[9,54,95,125],"has":[10],"shown":[11],"the":[12,34,93,103,115,120,141,147,151,156,162],"potential":[13],"for":[14,109,123,178],"matching":[15],"problems":[16],"structured":[18],"data":[19],"like":[20],"point":[21],"clouds":[22],"and":[23,80,100,117,155,173],"graphs.":[24],"However,":[25],"its":[26],"application":[27],"in":[28,170],"practice":[29],"is":[30,90],"limited":[31],"due":[32],"to":[33,51,74,92,107,139,167],"high":[35],"computational":[36],"complexity.":[37],"To":[38],"overcome":[39],"this":[40,134,179],"challenge,":[41],"we":[42],"propose":[43],"novel":[45],"importance":[46],"sparsification":[47],"method,":[48],"called":[49],"Spar-GW,":[50],"approximate":[52,140],"GW":[53,94,124,144,149,153,158],"efficiently.":[55],"In":[56,132],"particular,":[57],"instead":[58],"considering":[60],"dense":[62],"coupling":[63,78],"matrix,":[64],"our":[65,165],"method":[66,89,135],"leverages":[67],"simple":[69],"but":[70],"effective":[71],"sampling":[72],"strategy":[73],"construct":[75],"sparse":[77],"matrix":[79],"update":[81],"it":[82,101],"with":[83,96],"few":[84],"computations.":[85],"The":[86],"proposed":[87,121],"Spar-GW":[88,166],"applicable":[91],"arbitrary":[97,111],"ground":[98],"cost,":[99],"reduces":[102],"complexity":[104],"from":[105],"O(n4)":[106],"O(n2+\u03b4)":[108],"an":[110],"small":[112],"\u03b4>0.":[113],"Theoretically,":[114],"convergence":[116],"consistency":[118],"estimation":[122],"are":[126,181],"established":[127],"under":[128],"mild":[129],"regularity":[130],"conditions.":[131],"addition,":[133],"can":[136],"be":[137],"extended":[138],"variants":[142],"distance,":[145,150,154],"including":[146],"entropic":[148],"fused":[152],"unbalanced":[157],"distance.":[159],"Experiments":[160],"show":[161],"superiority":[163],"state-of-the-art":[168],"methods":[169],"both":[171],"synthetic":[172],"real-world":[174],"tasks.":[175],"Supplementary":[176],"materials":[177],"article":[180],"available":[182],"online.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
