{"id":"https://openalex.org/W1928434541","doi":"https://doi.org/10.1007/978-3-540-89689-0_57","title":"Optimal Kernel in a Class of Kernels with an Invariant Metric","display_name":"Optimal Kernel in a Class of Kernels with an Invariant Metric","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1928434541","doi":"https://doi.org/10.1007/978-3-540-89689-0_57","mag":"1928434541"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-89689-0_57","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-89689-0_57","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105269463","display_name":"Akira Tanaka","orcid":"https://orcid.org/0000-0003-0055-8234"},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Akira Tanaka","raw_affiliation_strings":["Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan"],"affiliations":[{"raw_affiliation_string":"Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077220801","display_name":"Hideyuki Imai","orcid":"https://orcid.org/0000-0002-3793-1146"},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hideyuki Imai","raw_affiliation_strings":["Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan"],"affiliations":[{"raw_affiliation_string":"Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078972540","display_name":"Mineichi Kudo","orcid":"https://orcid.org/0000-0003-1013-3870"},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mineichi Kudo","raw_affiliation_strings":["Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan"],"affiliations":[{"raw_affiliation_string":"Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060354017","display_name":"Masaaki Miyakoshi","orcid":null},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masaaki Miyakoshi","raw_affiliation_strings":["Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan"],"affiliations":[{"raw_affiliation_string":"Division of Computer Science, Graduate School of Information Science and Technology, Hokkaido University, Sapporo, 060-0814, Japan","institution_ids":["https://openalex.org/I205349734"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5105269463"],"corresponding_institution_ids":["https://openalex.org/I205349734"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.473,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.84351483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"530","last_page":"539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9925000071525574,"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/T10057","display_name":"Face and Expression Recognition","score":0.9925000071525574,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10320","display_name":"Neural Networks and Applications","score":0.982200026512146,"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/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.7755329608917236},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7574150562286377},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.7349185943603516},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.6698538661003113},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6664064526557922},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5748712420463562},{"id":"https://openalex.org/keywords/radial-basis-function-kernel","display_name":"Radial basis function kernel","score":0.5676721334457397},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.5524829030036926},{"id":"https://openalex.org/keywords/string-kernel","display_name":"String kernel","score":0.5235554575920105},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.5067103505134583},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4947647452354431},{"id":"https://openalex.org/keywords/kernel-principal-component-analysis","display_name":"Kernel principal component analysis","score":0.4892878234386444},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.48562589287757874},{"id":"https://openalex.org/keywords/representer-theorem","display_name":"Representer theorem","score":0.4508112668991089},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38579830527305603},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35439184308052063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3225668668746948},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2688552141189575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12179166078567505},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.0922277569770813}],"concepts":[{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.7755329608917236},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7574150562286377},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.7349185943603516},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.6698538661003113},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6664064526557922},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5748712420463562},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.5676721334457397},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.5524829030036926},{"id":"https://openalex.org/C55851704","wikidata":"https://www.wikidata.org/wiki/Q7623983","display_name":"String kernel","level":5,"score":0.5235554575920105},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.5067103505134583},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4947647452354431},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.4892878234386444},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.48562589287757874},{"id":"https://openalex.org/C172623408","wikidata":"https://www.wikidata.org/wiki/Q7314263","display_name":"Representer theorem","level":5,"score":0.4508112668991089},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38579830527305603},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35439184308052063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3225668668746948},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2688552141189575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12179166078567505},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0922277569770813},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-89689-0_57","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-89689-0_57","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1510073064","https://openalex.org/W1563088657","https://openalex.org/W1606411952","https://openalex.org/W1986280275","https://openalex.org/W2014158063","https://openalex.org/W2108995755","https://openalex.org/W2113530803","https://openalex.org/W2138805882","https://openalex.org/W2145586686","https://openalex.org/W2147243899","https://openalex.org/W2156909104","https://openalex.org/W4230674625","https://openalex.org/W4240369198"],"related_works":["https://openalex.org/W3013206934","https://openalex.org/W3100948281","https://openalex.org/W2005311689","https://openalex.org/W2958374823","https://openalex.org/W1836142315","https://openalex.org/W4294351650","https://openalex.org/W4247446331","https://openalex.org/W4243330733","https://openalex.org/W2172290429","https://openalex.org/W177392165"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}