{"id":"https://openalex.org/W3004924329","doi":"https://doi.org/10.1109/ijcnn48605.2020.9207630","title":"Wasserstein Exponential Kernels","display_name":"Wasserstein Exponential Kernels","publication_year":2020,"publication_date":"2020-07-01","ids":{"openalex":"https://openalex.org/W3004924329","doi":"https://doi.org/10.1109/ijcnn48605.2020.9207630","mag":"3004924329"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn48605.2020.9207630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn48605.2020.9207630","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/671297","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059511710","display_name":"Henri De Plaen","orcid":"https://orcid.org/0000-0003-3397-068X"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Henri De Plaen","raw_affiliation_strings":["Department of Electrical Engineering, KU Leuven, Leuven, Belgium","Katholieke Universiteit Leuven"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071057567","display_name":"Micha\u00ebl Fanuel","orcid":"https://orcid.org/0000-0002-7438-0005"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Michael Fanuel","raw_affiliation_strings":["Department of Electrical Engineering, KU Leuven, Leuven, Belgium","Katholieke Universiteit Leuven"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078854904","display_name":"Johan A. K. Suykens","orcid":"https://orcid.org/0000-0002-8846-6352"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Johan A. K. Suykens","raw_affiliation_strings":["Department of Electrical Engineering, KU Leuven, Leuven, Belgium","Katholieke Universiteit Leuven"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Katholieke Universiteit Leuven","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059511710"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.0981,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.36457522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9871000051498413,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9871000051498413,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9837999939918518,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9653000235557556,"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/mathematics","display_name":"Mathematics","score":0.7336416244506836},{"id":"https://openalex.org/keywords/positive-definiteness","display_name":"Positive definiteness","score":0.6708125472068787},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6308683753013611},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.593556821346283},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5493535399436951},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5376526117324829},{"id":"https://openalex.org/keywords/wasserstein-metric","display_name":"Wasserstein metric","score":0.508206844329834},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4688820540904999},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.4672425091266632},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4390029013156891},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43053147196769714},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.42252209782600403},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37157392501831055},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.35795867443084717},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3429277539253235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2681830823421478},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.23292487859725952},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.18040966987609863},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14594286680221558},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.12441548705101013},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09360611438751221},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.08896347880363464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7336416244506836},{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.6708125472068787},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6308683753013611},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.593556821346283},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5493535399436951},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5376526117324829},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.508206844329834},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4688820540904999},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.4672425091266632},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4390029013156891},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43053147196769714},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.42252209782600403},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37157392501831055},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.35795867443084717},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3429277539253235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2681830823421478},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.23292487859725952},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18040966987609863},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14594286680221558},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.12441548705101013},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09360611438751221},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.08896347880363464},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/ijcnn48605.2020.9207630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn48605.2020.9207630","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/671297","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/671297","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"2020 International Joint Conference on Neural Networks (IJCNN), Glasgow, Scotland, 19-24 July 2020","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2002.01878","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.01878","pdf_url":"https://arxiv.org/pdf/2002.01878","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":"","raw_type":"text"},{"id":"mag:3004924329","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2002.01878.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2002.01878","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2002.01878","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/671297","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/671297","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"2020 International Joint Conference on Neural Networks (IJCNN), Glasgow, Scotland, 19-24 July 2020","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1150901635","display_name":"Exploring Duality for Future Data-driven Modelling","funder_award_id":"787960","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1431749042","display_name":null,"funder_award_id":"KUL0076","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G3092313991","display_name":null,"funder_award_id":"KUL0076","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4956428346","display_name":null,"funder_award_id":"Horizon 2020 research and innovatio","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5036817778","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innov","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8633428685","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innovat","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G907169927","display_name":null,"funder_award_id":"GOA4917N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320319128","display_name":"Vlaams Supercomputer Centrum","ror":null},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W179694669","https://openalex.org/W385466589","https://openalex.org/W1496317909","https://openalex.org/W1560724230","https://openalex.org/W1596717185","https://openalex.org/W1746819321","https://openalex.org/W2100659887","https://openalex.org/W2123818990","https://openalex.org/W2158131535","https://openalex.org/W2170308301","https://openalex.org/W2520536546","https://openalex.org/W2626898927","https://openalex.org/W2793477525","https://openalex.org/W2796051023","https://openalex.org/W2913783817","https://openalex.org/W2951637053","https://openalex.org/W2963766931","https://openalex.org/W2970112944","https://openalex.org/W3039256091","https://openalex.org/W6682962330","https://openalex.org/W6712094938","https://openalex.org/W6738958611","https://openalex.org/W6759401939","https://openalex.org/W6764650314"],"related_works":["https://openalex.org/W3091152815","https://openalex.org/W3013505032","https://openalex.org/W3001788823","https://openalex.org/W2787871992","https://openalex.org/W2803171681","https://openalex.org/W2474499646","https://openalex.org/W2952072569","https://openalex.org/W2037271062","https://openalex.org/W2919087791","https://openalex.org/W2962818398","https://openalex.org/W1176528776","https://openalex.org/W3150094433","https://openalex.org/W2759934021","https://openalex.org/W2106784859","https://openalex.org/W2097973429","https://openalex.org/W2963668836","https://openalex.org/W3039537761","https://openalex.org/W1823600381","https://openalex.org/W2111181349","https://openalex.org/W2111121652"],"abstract_inverted_index":{"In":[0,62],"the":[1,6,14,23,26,45,67,75],"context":[2],"of":[3,69,119],"kernel":[4,15,29],"methods,":[5],"similarity":[7],"between":[8,48],"data":[9],"points":[10],"is":[11,18,30],"encoded":[12],"by":[13],"function":[16],"which":[17],"often":[19],"defined":[20,72],"thanks":[21,73],"to":[22,74,110,122],"Euclidean":[24,126],"distance;":[25],"squared":[27,105],"exponential":[28,70,106],"a":[31],"common":[32],"example.":[33],"Recently,":[34],"other":[35],"distances":[36],"relying":[37],"on":[38,115],"optimal":[39],"transport":[40],"theory":[41],"-":[42,51],"such":[43],"as":[44],"Wasserstein":[46,77,88,104],"distance":[47,78],"probability":[49],"distributions":[50],"have":[52],"shown":[53,109],"their":[54,81,93],"practical":[55],"relevance":[56],"for":[57,95],"different":[58],"machine":[59],"learning":[60,97],"techniques.":[61],"this":[63],"paper,":[64],"we":[65,86],"study":[66],"use":[68],"kernels":[71,107],"regularized":[76],"and":[79,91,101],"discuss":[80],"positive":[82],"definiteness.":[83],"More":[84],"specifically,":[85],"define":[87],"feature":[89],"maps":[90],"illustrate":[92],"interest":[94],"supervised":[96],"problems":[98],"involving":[99],"shapes":[100],"images.":[102],"Empirically,":[103],"are":[108],"yield":[111],"smaller":[112],"classification":[113],"errors":[114],"small":[116],"training":[117],"sets":[118],"shapes,":[120],"compared":[121],"analogous":[123],"classifiers":[124],"using":[125],"distances.":[127]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-10-10T00:00:00"}