{"id":"https://openalex.org/W4379647309","doi":"https://doi.org/10.1137/22m1490053","title":"Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning","display_name":"Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning","publication_year":2023,"publication_date":"2023-06-07","ids":{"openalex":"https://openalex.org/W4379647309","doi":"https://doi.org/10.1137/22m1490053"},"language":"en","primary_location":{"id":"doi:10.1137/22m1490053","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1490053","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/22m1490053","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064380948","display_name":"Keaton Hamm","orcid":"https://orcid.org/0000-0003-0719-6045"},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Keaton Hamm","raw_affiliation_strings":["Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019 USA"],"raw_orcid":"https://orcid.org/0000-0003-0719-6045","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019 USA","institution_ids":["https://openalex.org/I189196454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010348079","display_name":"Nick Henscheid","orcid":"https://orcid.org/0000-0002-9361-6976"},"institutions":[{"id":"https://openalex.org/I4210124665","display_name":"Banner - University Medical Center Tucson","ror":"https://ror.org/02xbk5j62","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210124665"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nick Henscheid","raw_affiliation_strings":["Department of Medical Imaging, University of Arizona, Tucson, AZ 85724 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Medical Imaging, University of Arizona, Tucson, AZ 85724 USA","institution_ids":["https://openalex.org/I4210124665"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041656725","display_name":"Shujie Kang","orcid":null},"institutions":[{"id":"https://openalex.org/I189196454","display_name":"The University of Texas at Arlington","ror":"https://ror.org/019kgqr73","country_code":"US","type":"education","lineage":["https://openalex.org/I189196454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shujie Kang","raw_affiliation_strings":["Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019 USA","institution_ids":["https://openalex.org/I189196454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064380948"],"corresponding_institution_ids":["https://openalex.org/I189196454"],"apc_list":null,"apc_paid":null,"fwci":3.2786,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.93317112,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"5","issue":"2","first_page":"475","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9958999752998352,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9958999752998352,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9908000230789185,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.81025230884552},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.7118998169898987},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.704421877861023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5797935724258423},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5698987245559692},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5394095182418823},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5365042686462402},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5107012391090393},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.49446988105773926},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4854651093482971},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42273223400115967},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4204733967781067},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3908234238624573},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.12036165595054626}],"concepts":[{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.81025230884552},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.7118998169898987},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.704421877861023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5797935724258423},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5698987245559692},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5394095182418823},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5365042686462402},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5107012391090393},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.49446988105773926},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4854651093482971},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42273223400115967},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4204733967781067},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3908234238624573},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.12036165595054626},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1490053","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1490053","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/22m1490053","is_oa":true,"landing_page_url":"https://doi.org/10.1137/22m1490053","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4665397012","display_name":null,"funder_award_id":"R01EB000803","funder_id":"https://openalex.org/F4320337363","funder_display_name":"National Institute of Biomedical Imaging and Bioengineering"},{"id":"https://openalex.org/G6384593338","display_name":null,"funder_award_id":"W911NF-20-1-0076","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320337363","display_name":"National Institute of Biomedical Imaging and Bioengineering","ror":"https://ror.org/00372qc85"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W385466589","https://openalex.org/W1519654970","https://openalex.org/W1526636590","https://openalex.org/W1585160083","https://openalex.org/W1598140581","https://openalex.org/W1742512077","https://openalex.org/W1965359844","https://openalex.org/W1972801555","https://openalex.org/W1994154911","https://openalex.org/W2001141328","https://openalex.org/W2046104068","https://openalex.org/W2053186076","https://openalex.org/W2053985176","https://openalex.org/W2061681393","https://openalex.org/W2077180490","https://openalex.org/W2094100343","https://openalex.org/W2096413780","https://openalex.org/W2097308346","https://openalex.org/W2100495367","https://openalex.org/W2117863806","https://openalex.org/W2132442278","https://openalex.org/W2132883347","https://openalex.org/W2154249783","https://openalex.org/W2156838815","https://openalex.org/W2160850888","https://openalex.org/W2211336473","https://openalex.org/W2240450848","https://openalex.org/W2267271843","https://openalex.org/W2509518867","https://openalex.org/W2534420330","https://openalex.org/W2607074821","https://openalex.org/W2735418187","https://openalex.org/W2889326414","https://openalex.org/W2902652978","https://openalex.org/W2963693826","https://openalex.org/W2978329087","https://openalex.org/W3101920124","https://openalex.org/W3197713830","https://openalex.org/W3217527333","https://openalex.org/W4206471589","https://openalex.org/W4213367101","https://openalex.org/W4245253888","https://openalex.org/W4248500611","https://openalex.org/W4255839052","https://openalex.org/W4310895557","https://openalex.org/W4395086252"],"related_works":["https://openalex.org/W2375574759","https://openalex.org/W3088634662","https://openalex.org/W3162910294","https://openalex.org/W2539700568","https://openalex.org/W1995622179","https://openalex.org/W1484111231","https://openalex.org/W2383239174","https://openalex.org/W117517268","https://openalex.org/W2166963679","https://openalex.org/W2573981081"],"abstract_inverted_index":{".In":[0],"this":[1],"paper,":[2],"we":[3,83],"propose":[4],"Wasserstein":[5,37,42],"Isometric":[6],"Mapping":[7],"(Wassmap),":[8],"a":[9,50,78,86,102],"nonlinear":[10,23],"dimensionality":[11,24,139],"reduction":[12,25],"technique":[13],"that":[14,57,85,126],"provides":[15],"solutions":[16],"to":[17,48,62,105,112],"some":[18,67],"drawbacks":[19],"in":[20,27,36],"existing":[21],"global":[22,134],"algorithms":[26,119],"imaging":[28],"applications.":[29],"Wassmap":[30,127],"represents":[31],"images":[32],"via":[33],"probability":[34],"measures":[35,47,99],"space,":[38],"then":[39],"uses":[40],"pairwise":[41],"distances":[43],"between":[44],"the":[45,58,90,117],"associated":[46],"produce":[49],"low-dimensional,":[51],"approximately":[52],"isometric":[53],"embedding.":[54],"We":[55],"show":[56,84],"algorithm":[59,91],"is":[60],"able":[61],"exactly":[63],"recover":[64],"parameters":[65,93],"of":[66,77,89,116],"image":[68,122],"manifolds,":[69],"including":[70],"those":[71],"generated":[72,96],"by":[73,100],"translations":[74],"or":[75],"dilations":[76],"fixed":[79],"generating":[80],"measure.":[81],"Additionally,":[82],"discrete":[87,98,113],"version":[88],"retrieves":[92],"from":[94,97,109],"manifolds":[95,124],"providing":[101],"theoretical":[103],"bridge":[104],"transfer":[106],"recovery":[107],"results":[108],"functional":[110],"data":[111,123],"data.":[114],"Testing":[115],"proposed":[118],"on":[120],"various":[121],"shows":[125],"yields":[128],"good":[129],"embeddings":[130],"compared":[131],"with":[132],"other":[133],"and":[135],"local":[136],"techniques.Keywordsmanifold":[137],"learningnonlinear":[138],"reductionoptimal":[140],"transportWasserstein":[141],"spaceIsomapMSC":[142],"codes68T1049Q22":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
