{"id":"https://openalex.org/W7223663935","doi":"https://doi.org/10.1186/s40708-026-00336-8","title":"Conditional Gromov\u2013Wasserstein matching across contexts: theory, regularization, and applications to brain connectivity","display_name":"Conditional Gromov\u2013Wasserstein matching across contexts: theory, regularization, and applications to brain connectivity","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7223663935","doi":"https://doi.org/10.1186/s40708-026-00336-8"},"language":"en","primary_location":{"id":"doi:10.1186/s40708-026-00336-8","doi":"https://doi.org/10.1186/s40708-026-00336-8","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40708-026-00336-8","pdf_url":null,"source":{"id":"https://openalex.org/S2498492389","display_name":"Brain Informatics","issn_l":"2198-4018","issn":["2198-4018","2198-4026"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brain Informatics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1186/s40708-026-00336-8","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037573459","display_name":"Iman Seyedi","orcid":"https://orcid.org/0000-0003-1875-7565","observed_orcids":["https://orcid.org/0000-0003-1875-7565"]},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Iman Seyedi","raw_affiliation_strings":["Department of Computer Science Systems and Communication, University of Milano-Bicocca, 20126, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science Systems and Communication, University of Milano-Bicocca, 20126, Milan, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011390491","display_name":"Francesco Archetti","orcid":"https://orcid.org/0000-0003-1131-3830","observed_orcids":["https://orcid.org/0000-0003-1131-3830"]},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Archetti","raw_affiliation_strings":["Department of Computer Science Systems and Communication, University of Milano-Bicocca, 20126, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science Systems and Communication, University of Milano-Bicocca, 20126, Milan, Italy","institution_ids":["https://openalex.org/I66752286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037573459"],"corresponding_institution_ids":["https://openalex.org/I66752286"],"apc_list":{"value":1090,"currency":"USD","value_usd":1090},"apc_paid":{"value":1090,"currency":"USD","value_usd":1090},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.85983264,"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":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9833999872207642,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9833999872207642,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.00839999970048666,"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"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.0006000000284984708,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gromov-wasserstein-distance","display_name":"Gromov-Wasserstein distance","score":0.9710000157356262},{"id":"https://openalex.org/keywords/metric-measure-spaces","display_name":"metric measure spaces","score":0.8289999961853027},{"id":"https://openalex.org/keywords/brain-connectivity","display_name":"brain connectivity","score":0.6129999756813049},{"id":"https://openalex.org/keywords/graph-alignment","display_name":"graph alignment","score":0.4819999933242798},{"id":"https://openalex.org/keywords/schrodinger-bridge","display_name":"Schr\u00f6dinger bridge","score":0.8019999861717224},{"id":"https://openalex.org/keywords/entropy-regularization","display_name":"entropy regularization","score":0.8600000143051147}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7835999727249146},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5378999710083008},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46480000019073486},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4480000138282776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42660000920295715},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4072999954223633},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.35199999809265137},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30720001459121704},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.29330000281333923},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1186/s40708-026-00336-8","doi":"https://doi.org/10.1186/s40708-026-00336-8","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40708-026-00336-8","pdf_url":null,"source":{"id":"https://openalex.org/S2498492389","display_name":"Brain Informatics","issn_l":"2198-4018","issn":["2198-4018","2198-4026"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brain Informatics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1186/s40708-026-00336-8","doi":"https://doi.org/10.1186/s40708-026-00336-8","is_oa":true,"landing_page_url":"https://doi.org/10.1186/s40708-026-00336-8","pdf_url":null,"source":{"id":"https://openalex.org/S2498492389","display_name":"Brain Informatics","issn_l":"2198-4018","issn":["2198-4018","2198-4026"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brain Informatics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7133232288","https://openalex.org/W4280619635","https://openalex.org/W7204478199","https://openalex.org/W4384918436","https://openalex.org/W7221766424","https://openalex.org/W4407793173","https://openalex.org/W4387827856","https://openalex.org/W4379251962","https://openalex.org/W7161263714","https://openalex.org/W4322631077"],"abstract_inverted_index":{"The":[0,70],"Gromov\u2013Wasserstein":[1,50],"(GW)":[2],"distance":[3],"is":[4,30,224],"a":[5,25,52,67,81,87,92,99,133,154,180,225],"principled":[6],"framework":[7,71,227],"for":[8,57,95,116,228],"comparing":[9,58],"structured":[10],"data":[11,231],"when":[12,32],"pointwise":[13],"correspondences":[14],"are":[15],"unknown,":[16],"but":[17],"standard":[18],"formulations":[19,119,178],"assume":[20],"that":[21,79,90,102,175,222],"each":[22,96],"object":[23],"has":[24],"fixed":[26],"geometry.":[27],"This":[28],"assumption":[29],"restrictive":[31],"relational":[33,230],"structure":[34,186,235],"changes":[35],"with":[36],"context,":[37,97],"such":[38],"as":[39],"cognitive":[40],"state,":[41],"task":[42,172],"condition,":[43],"or":[44],"experimental":[45],"environment.":[46],"We":[47,110,130],"propose":[48],"Conditional":[49],"(CGW),":[51],"context-aware":[53],"extension":[54],"of":[55,106,114,125,136,157,161,184,212],"GW":[56,207],"metric":[59],"measure":[60],"spaces":[61],"whose":[62],"internal":[63],"geometry":[64],"depends":[65],"on":[66],"conditioning":[68],"variable.":[69],"comprises":[72],"three":[73],"related":[74],"formulations:":[75],"an":[76],"expected":[77],"formulation":[78,89,101],"learns":[80,91],"single":[82],"coupling":[83,94,213],"shared":[84,234],"across":[85,108],"contexts,":[86],"conditional":[88,198],"distinct":[93],"and":[98,120,143,199,208,236],"regularized":[100,138,200],"encourages":[103],"smooth":[104],"variation":[105,214],"couplings":[107],"contexts.":[109],"establish":[111],"the":[112,117,126,137,147,158,176,197,216],"existence":[113],"minimizers":[115],"discrete":[118],"show":[121,174],"stability":[122],"under":[123,151],"perturbations":[124],"context-dependent":[127],"cost":[128],"matrices.":[129],"also":[131],"provide":[132],"variational":[134],"interpretation":[135,156],"model":[139],"through":[140,215],"proximal":[141],"transport":[142],"its":[144],"connection":[145],"to":[146],"Jordan\u2013Kinderlehrer\u2013Otto":[148],"scheme":[149],"and,":[150],"entropic":[152],"regularization,":[153],"Schr\u00f6dinger-bridge":[155],"resulting":[159],"family":[160],"couplings.":[162],"Synthetic":[163],"experiments,":[164],"using":[165,191],"connectivity-style":[166],"graphs":[167],"inspired":[168],"by":[169],"rest-":[170],"versus":[171],"designs,":[173],"proposed":[177],"recover":[179],"known,":[181],"constructed":[182],"pattern":[183],"stable":[185],"plus":[187],"localized":[188],"rewiring,":[189],"without":[190],"real":[192],"brain":[193],"data.":[194],"In":[195],"particular,":[196],"variants":[201],"produce":[202],"smoother":[203],"alignments":[204],"than":[205],"classical":[206],"allow":[209],"systematic":[210],"control":[211],"regularization":[217],"parameter.":[218],"These":[219],"results":[220],"suggest":[221],"CGW":[223],"useful":[226],"modeling":[229],"in":[232],"which":[233],"context-specific":[237],"adaptation":[238],"coexist.":[239]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-27T00:00:00"}