{"id":"https://openalex.org/W2744110160","doi":"https://doi.org/10.1137/17m1140431","title":"Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning","display_name":"Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2744110160","doi":"https://doi.org/10.1137/17m1140431","mag":"2744110160"},"language":"en","primary_location":{"id":"doi:10.1137/17m1140431","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140431","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1708.01955","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Morgan A. Schmitz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Morgan A. Schmitz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Matthieu Heitz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthieu Heitz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Nicolas Bonneel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicolas Bonneel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Fred Ngol\u00e8","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fred Ngol\u00e8","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"David Coeurjolly","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Coeurjolly","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Marco Cuturi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco Cuturi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Gabriel Peyr\u00e9","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabriel Peyr\u00e9","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Jean-Luc Starck","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-Luc Starck","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3978,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.98208092,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":"1","first_page":"643","last_page":"678"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.09350000321865082,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.09350000321865082,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.05209999904036522,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.050999999046325684,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/histogram","display_name":"Histogram","score":0.5748999714851379},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5166000127792358},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4812999963760376},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.47920000553131104},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3765999972820282},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.364300012588501},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.3549000024795532},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3127000033855438}],"concepts":[{"id":"https://openalex.org/C53533937","wikidata":"https://www.wikidata.org/wiki/Q185020","display_name":"Histogram","level":3,"score":0.5748999714851379},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5166000127792358},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4812999963760376},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.47920000553131104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4754999876022339},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4684000015258789},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39149999618530273},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38429999351501465},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.364300012588501},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.3549000024795532},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30390000343322754},{"id":"https://openalex.org/C2988886741","wikidata":"https://www.wikidata.org/wiki/Q25304494","display_name":"Dictionary learning","level":3,"score":0.3001999855041504},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2606000006198883}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1140431","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140431","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1708.01955","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.01955","pdf_url":"https://arxiv.org/pdf/1708.01955","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:HAL:hal-01717943v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01717943","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"EISSN: 1936-4954","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-01717943v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01717943","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Imaging Sciences, 2018, 11 (1), pp.643-678. &#x27E8;10.1137/17M1140431&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1708.01955","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1708.01955","pdf_url":"https://arxiv.org/pdf/1708.01955","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5956598502","display_name":"Regression with Optimal Transport for Computer Graphics and Vision","funder_award_id":"ANR-16-CE23-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321519","display_name":"Centre National d\u2019Etudes Spatiales","ror":"https://ror.org/04h1h0y33"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1660572054","https://openalex.org/W1880403203","https://openalex.org/W1902027874","https://openalex.org/W1968333723","https://openalex.org/W1969549583","https://openalex.org/W1988720110","https://openalex.org/W1994521023","https://openalex.org/W2004465977","https://openalex.org/W2009070933","https://openalex.org/W2009172320","https://openalex.org/W2012924849","https://openalex.org/W2013918710","https://openalex.org/W2019106840","https://openalex.org/W2029420412","https://openalex.org/W2036996178","https://openalex.org/W2043083193","https://openalex.org/W2045361520","https://openalex.org/W2046874905","https://openalex.org/W2052424080","https://openalex.org/W2052717131","https://openalex.org/W2078293886","https://openalex.org/W2094100343","https://openalex.org/W2100495367","https://openalex.org/W2125949583","https://openalex.org/W2127674094","https://openalex.org/W2133478409","https://openalex.org/W2138451337","https://openalex.org/W2143668817","https://openalex.org/W2160547390","https://openalex.org/W2222512263","https://openalex.org/W2294798173","https://openalex.org/W2312355711","https://openalex.org/W2464628725","https://openalex.org/W2615253071","https://openalex.org/W2963170010","https://openalex.org/W2963995333"],"related_works":["https://openalex.org/W4226198050","https://openalex.org/W3196155444","https://openalex.org/W4281615271","https://openalex.org/W2929676662","https://openalex.org/W4287665842","https://openalex.org/W3087576162","https://openalex.org/W3095538999","https://openalex.org/W3210156800","https://openalex.org/W3123344745","https://openalex.org/W3165437720"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,117],"new":[4],"nonlinear":[5,160],"dictionary":[6,39,153],"learning":[7],"method":[8,16,52,79,157],"for":[9,58,159],"histograms":[10,30,46],"in":[11,21,47,174],"the":[12,22,48,61,85,92,128,148,165],"probability":[13,49],"simplex.":[14,50],"The":[15],"leverages":[17],"optimal":[18,72,94],"transport":[19,73],"theory,":[20],"sense":[23],"that":[24,65,102,132],"our":[25,156],"aim":[26],"is":[27,80,103],"to":[28,84,91,98,108],"reconstruct":[29,68],"using":[31,116],"so-called":[32],"displacement":[33],"interpolations":[34],"(a.k.a.":[35],"Wasserstein":[36,144],"barycenters)":[37],"between":[38,152,162],"atoms;":[40],"such":[41,55,76],"atoms":[42,56,111,163],"are":[43,114,122],"themselves":[44],"synthetic":[45],"Our":[51,78],"simultaneously":[53],"estimates":[54],"and,":[57],"each":[59],"datapoint,":[60],"vector":[62],"of":[63,75,87,127,139,147,167],"weights":[64,113],"can":[66],"optimally":[67],"it":[69],"as":[70],"an":[71,88,99],"barycenter":[74],"atoms.":[77],"computationally":[81],"tractable":[82],"thanks":[83],"addition":[86],"entropic":[89,136],"regularization":[90],"usual":[93,149],"transportation":[95],"problem,":[96],"leading":[97],"approximation":[100],"scheme":[101],"efficient,":[104],"parallel,":[105],"and":[106,112,154,164],"simple":[107],"differentiate.":[109],"Both":[110],"learned":[115],"gradient-based":[118],"descent":[119],"method.":[120],"Gradients":[121],"obtained":[123],"by":[124],"automatic":[125],"differentiation":[126],"generalized":[129],"Sinkhorn":[130],"iterations":[131],"yield":[133],"barycenters":[134,145],"with":[135],"smoothing.":[137],"Because":[138],"its":[140,172],"formulation":[141],"relying":[142],"on":[143],"instead":[146],"matrix":[150],"product":[151],"codes,":[155],"allows":[158],"relationships":[161],"reconstruction":[166],"input":[168],"data.":[169],"We":[170],"illustrate":[171],"application":[173],"several":[175],"different":[176],"image":[177],"processing":[178],"settings.":[179]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2017-08-17T00:00:00"}
