{"id":"https://openalex.org/W4388092633","doi":"https://doi.org/10.48550/arxiv.2310.18586","title":"Optimal Transport for Kernel Gaussian Mixture Models","display_name":"Optimal Transport for Kernel Gaussian Mixture Models","publication_year":2023,"publication_date":"2023-10-28","ids":{"openalex":"https://openalex.org/W4388092633","doi":"https://doi.org/10.48550/arxiv.2310.18586"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2310.18586","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.18586","pdf_url":"https://arxiv.org/pdf/2310.18586","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2310.18586","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078855608","display_name":"Jung Hun Oh","orcid":"https://orcid.org/0000-0001-8791-2755","observed_orcids":["https://orcid.org/0000-0001-8791-2755"]},"institutions":[{"id":"https://openalex.org/I1334819555","display_name":"Memorial Sloan Kettering Cancer Center","ror":"https://ror.org/02yrq0923","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1334819555"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Oh, Jung Hun","raw_affiliation_strings":["Department of Medical Physics , Memorial Sloan Kettering Cancer Center , New York , NY , USA","ORG"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Medical Physics , Memorial Sloan Kettering Cancer Center , New York , NY , USA","institution_ids":["https://openalex.org/I1334819555"]},{"raw_affiliation_string":"ORG","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054676655","display_name":"Rena Elkin","orcid":"https://orcid.org/0000-0003-2435-3399","observed_orcids":["https://orcid.org/0000-0003-2435-3399"]},"institutions":[{"id":"https://openalex.org/I1334819555","display_name":"Memorial Sloan Kettering Cancer Center","ror":"https://ror.org/02yrq0923","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1334819555"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elkin, Rena","raw_affiliation_strings":["Department of Medical Physics , Memorial Sloan Kettering Cancer Center , New York , NY , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Medical Physics , Memorial Sloan Kettering Cancer Center , New York , NY , USA","institution_ids":["https://openalex.org/I1334819555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036310617","display_name":"Anish K. Simhal","orcid":"https://orcid.org/0000-0001-7848-3565","observed_orcids":["https://orcid.org/0000-0001-7848-3565"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simhal, Anish Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Zhu, Jiening","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhu, Jiening","raw_affiliation_strings":["Departments of Computer Science and Applied Mathematics & Statistics , Stony Brook University , Stony Brook , NY , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Computer Science and Applied Mathematics & Statistics , Stony Brook University , Stony Brook , NY , USA","institution_ids":["https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026159944","display_name":"Joseph O. Deasy","orcid":"https://orcid.org/0000-0002-9437-266X","observed_orcids":["https://orcid.org/0000-0002-9437-266X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Deasy, Joseph O","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012935165","display_name":"Allen Tannenbaum","orcid":"https://orcid.org/0000-0002-0567-5256","observed_orcids":["https://orcid.org/0000-0002-0567-5256"]},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tannenbaum, Allen","raw_affiliation_strings":["Departments of Computer Science and Applied Mathematics & Statistics , Stony Brook University , Stony Brook , NY , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Computer Science and Applied Mathematics & Statistics , Stony Brook University , Stony Brook , NY , USA","institution_ids":["https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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":0.8041999936103821,"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":0.8041999936103821,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.048700001090765,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.02590000070631504,"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/optimal-transport","display_name":"optimal transport","score":0.9240000247955322},{"id":"https://openalex.org/keywords/wasserstein-distance","display_name":"Wasserstein distance","score":0.9449999928474426},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"reproducing kernel Hilbert space","score":0.9890000224113464},{"id":"https://openalex.org/keywords/kernel-trick","display_name":"kernel trick","score":0.9660000205039978},{"id":"https://openalex.org/keywords/gaussian-mixture-model","display_name":"Gaussian mixture model","score":0.5759999752044678},{"id":"https://openalex.org/keywords/distance-between-probability-distributions","display_name":"distance between probability distributions","score":0.7039999961853027}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.849175214767456},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.7395113110542297},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.6945208311080933},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5680311322212219},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5407185554504395},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.5361093878746033},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.5198596119880676},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4938271939754486},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.49075350165367126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4857788383960724},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.47259077429771423},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.46054312586784363},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.45524874329566956},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4448775351047516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4445110857486725},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.419586181640625},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.4122031629085541},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3785463869571686},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3666127920150757},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3599191904067993},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.20401370525360107},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14309227466583252},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.1226363480091095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09994050860404968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08521431684494019},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06546980142593384},{"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},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2310.18586","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.18586","pdf_url":"https://arxiv.org/pdf/2310.18586","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2310.18586","doi":"https://doi.org/10.48550/arxiv.2310.18586","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2310.18586","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2310.18586","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.18586","pdf_url":"https://arxiv.org/pdf/2310.18586","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G24641535","display_name":null,"funder_award_id":"BCRF-17-193","funder_id":"https://openalex.org/F4320306260","funder_display_name":"Breast Cancer Research Foundation"},{"id":"https://openalex.org/G36446433","display_name":null,"funder_award_id":"FA9550-20-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3978591521","display_name":null,"funder_award_id":"CA008748","funder_id":"https://openalex.org/F4320306260","funder_display_name":"Breast Cancer Research Foundation"},{"id":"https://openalex.org/G4102770861","display_name":null,"funder_award_id":"CA008748","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"},{"id":"https://openalex.org/G4727317247","display_name":"Glymphatic function in a transgenic rat model of Alzheimer's disease","funder_award_id":"R01AG048769","funder_id":"https://openalex.org/F4320337337","funder_display_name":"National Institute on Aging"},{"id":"https://openalex.org/G4757223689","display_name":null,"funder_award_id":"W911NF-22-1-0292","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5729145195","display_name":null,"funder_award_id":"FA9550-20","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7228553140","display_name":null,"funder_award_id":"FA9550-20-1-0029","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G782458776","display_name":null,"funder_award_id":"P30CA008748","funder_id":"https://openalex.org/F4320306260","funder_display_name":"Breast Cancer Research Foundation"},{"id":"https://openalex.org/G9000003249","display_name":null,"funder_award_id":"CA008748","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G9000856728","display_name":"Cancer Center Support Grant","funder_award_id":"P30CA008748","funder_id":"https://openalex.org/F4320337351","funder_display_name":"National Cancer Institute"}],"funders":[{"id":"https://openalex.org/F4320306260","display_name":"Breast Cancer Research Foundation","ror":"https://ror.org/0348ff195"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337337","display_name":"National Institute on Aging","ror":"https://ror.org/049v75w11"},{"id":"https://openalex.org/F4320337351","display_name":"National Cancer Institute","ror":"https://ror.org/040gcmg81"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388092633.pdf","grobid_xml":"https://content.openalex.org/works/W4388092633.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4394639000","https://openalex.org/W2963181447","https://openalex.org/W4416301798","https://openalex.org/W3136732307","https://openalex.org/W2905054156","https://openalex.org/W2919087791","https://openalex.org/W3001421962","https://openalex.org/W4404374918","https://openalex.org/W4306294982","https://openalex.org/W3111589478"],"abstract_inverted_index":{"The":[0],"Wasserstein":[1],"distance":[2,23,107],"from":[3],"optimal":[4],"mass":[5],"transport":[6],"(OMT)":[7],"is":[8,79],"a":[9,18,69,91,101,113],"powerful":[10],"mathematical":[11],"tool":[12],"with":[13],"numerous":[14],"applications":[15],"that":[16],"provides":[17],"natural":[19],"measure":[20],"of":[21,51,56],"the":[22,49,65,76,83,96,106,116],"between":[24,108],"two":[25,109],"probability":[26],"distributions.":[27],"Several":[28],"methods":[29],"to":[30,47,81,85,104],"incorporate":[31],"OMT":[32,66],"into":[33,90],"widely":[34],"used":[35],"probabilistic":[36],"models,":[37],"such":[38],"as":[39],"Gaussian":[40,42,110,121],"or":[41],"mixture,":[43],"have":[44,63],"been":[45],"developed":[46],"enhance":[48],"capability":[50],"modeling":[52],"complex":[53],"multimodal":[54],"densities":[55],"real":[57],"datasets.":[58],"However,":[59],"very":[60],"few":[61],"studies":[62],"explored":[64],"problems":[67],"in":[68,112],"reproducing":[70],"kernel":[71,77,117,120],"Hilbert":[72],"space":[73],"(RKHS),":[74],"wherein":[75],"trick":[78],"utilized":[80],"avoid":[82],"need":[84],"explicitly":[86],"map":[87],"input":[88],"data":[89],"high-dimensional":[92],"feature":[93],"space.":[94],"In":[95],"current":[97],"study,":[98],"we":[99],"propose":[100],"Wasserstein-type":[102],"metric":[103],"compute":[105],"mixtures":[111],"RKHS":[114],"via":[115],"trick,":[118],"i.e.,":[119],"mixture":[122],"models.":[123]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2023-11-01T00:00:00"}
