{"id":"https://openalex.org/W2159963587","doi":"https://doi.org/10.1162/08997660460734029","title":"Asymptotic Properties of the Fisher Kernel","display_name":"Asymptotic Properties of the Fisher Kernel","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2159963587","doi":"https://doi.org/10.1162/08997660460734029","mag":"2159963587","pmid":"https://pubmed.ncbi.nlm.nih.gov/15006026"},"language":"en","primary_location":{"id":"doi:10.1162/08997660460734029","is_oa":false,"landing_page_url":"https://doi.org/10.1162/08997660460734029","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5070597006","display_name":"Koji Tsuda","orcid":"https://orcid.org/0000-0002-4288-1606"},"institutions":[{"id":"https://openalex.org/I4210112925","display_name":"Max Planck Institute for Biological Cybernetics","ror":"https://ror.org/026nmvv73","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210112925"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Koji Tsuda","raw_affiliation_strings":["Max Planck Institute for Biological Cybernetics, 72076 T\u00fcbingen, Germany, and AIST Computational Biology Research Center, Koto-ku, Tokyo, 135-0064, Japan,"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Biological Cybernetics, 72076 T\u00fcbingen, Germany, and AIST Computational Biology Research Center, Koto-ku, Tokyo, 135-0064, Japan,","institution_ids":["https://openalex.org/I4210112925"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080238107","display_name":"Shotaro Akaho","orcid":"https://orcid.org/0000-0002-4623-2718"},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shotaro Akaho","raw_affiliation_strings":["AIST Neuroscience Research Institute, Tsukuba, 305-8568, Japan,"],"affiliations":[{"raw_affiliation_string":"AIST Neuroscience Research Institute, Tsukuba, 305-8568, Japan,","institution_ids":["https://openalex.org/I73613424"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004328317","display_name":"Motoaki Kawanabe","orcid":null},"institutions":[{"id":"https://openalex.org/I4923324","display_name":"Fraunhofer Society","ror":"https://ror.org/05hkkdn48","country_code":"DE","type":"funder","lineage":["https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Motoaki Kawanabe","raw_affiliation_strings":["Fraunhofer FIRST, 12489 Berlin, Germany,"],"affiliations":[{"raw_affiliation_string":"Fraunhofer FIRST, 12489 Berlin, Germany,","institution_ids":["https://openalex.org/I4923324"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107838719","display_name":"Klaus\u2010Robert M\u00fcller","orcid":null},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Klaus-Robert M\u00fcller","raw_affiliation_strings":["Fraunhofer FIRST, 12489 Berlin, Germany, and University of Potsdam, 14482 Potsdam, Germany,"],"affiliations":[{"raw_affiliation_string":"Fraunhofer FIRST, 12489 Berlin, Germany, and University of Potsdam, 14482 Potsdam, Germany,","institution_ids":["https://openalex.org/I176453806"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5004328317","https://openalex.org/A5070597006","https://openalex.org/A5080238107","https://openalex.org/A5107838719"],"corresponding_institution_ids":["https://openalex.org/I176453806","https://openalex.org/I4210112925","https://openalex.org/I4923324","https://openalex.org/I73613424"],"apc_list":null,"apc_paid":null,"fwci":6.0077,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.96138727,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"1","first_page":"115","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9991000294685364,"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/T10057","display_name":"Face and Expression Recognition","score":0.9983999729156494,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9965000152587891,"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/fisher-kernel","display_name":"Fisher kernel","score":0.6919697523117065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6387798190116882},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.5287691354751587},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.52622389793396},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.44978296756744385},{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.4469899535179138},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.4269108772277832},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4118836522102356},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35523277521133423},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34361228346824646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33013367652893066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27990788221359253},{"id":"https://openalex.org/keywords/kernel-fisher-discriminant-analysis","display_name":"Kernel Fisher discriminant analysis","score":0.24791878461837769},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.10692211985588074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09847226738929749}],"concepts":[{"id":"https://openalex.org/C207798031","wikidata":"https://www.wikidata.org/wiki/Q8563425","display_name":"Fisher kernel","level":5,"score":0.6919697523117065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6387798190116882},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.5287691354751587},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.52622389793396},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.44978296756744385},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.4469899535179138},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.4269108772277832},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4118836522102356},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35523277521133423},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34361228346824646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33013367652893066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27990788221359253},{"id":"https://openalex.org/C181367576","wikidata":"https://www.wikidata.org/wiki/Q6394184","display_name":"Kernel Fisher discriminant analysis","level":4,"score":0.24791878461837769},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.10692211985588074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09847226738929749}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":8,"locations":[{"id":"doi:10.1162/08997660460734029","is_oa":false,"landing_page_url":"https://doi.org/10.1162/08997660460734029","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:15006026","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/15006026","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.3.3161","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3161","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ida.first.fhg.de/publications/TsuAkaKawMue03.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.5888","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.5888","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.informatik.hu-berlin.de/Forschung_Lehre/wm/journalclub/pdf2268.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:232663","is_oa":false,"landing_page_url":"http://edoc.mpg.de/232663","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Neural Computation, v.16, 115-137 (2004)","raw_type":"Article"},{"id":"pmh:oai:fraunhofer.de:N-37676","is_oa":false,"landing_page_url":"http://publica.fraunhofer.de/documents/N-37676.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer FIRST","raw_type":"Journal Article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/205603","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/205603","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"journal article"},{"id":"pmh:oai:pure.mpg.de:item_1792096","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0013-DA51-B","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Neural computation","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1512558044","https://openalex.org/W1528905581","https://openalex.org/W1545344782","https://openalex.org/W1563088657","https://openalex.org/W1564947197","https://openalex.org/W1572659166","https://openalex.org/W1573082642","https://openalex.org/W1574877594","https://openalex.org/W1601740268","https://openalex.org/W1603339577","https://openalex.org/W1692895552","https://openalex.org/W1984929054","https://openalex.org/W1994720204","https://openalex.org/W2037761619","https://openalex.org/W2038390905","https://openalex.org/W2042161430","https://openalex.org/W2068448872","https://openalex.org/W2079782346","https://openalex.org/W2085536277","https://openalex.org/W2090614046","https://openalex.org/W2106868411","https://openalex.org/W2108146080","https://openalex.org/W2108995755","https://openalex.org/W2114281975","https://openalex.org/W2120217353","https://openalex.org/W2123152930","https://openalex.org/W2136112386","https://openalex.org/W2140409019","https://openalex.org/W2148603752","https://openalex.org/W2150796457","https://openalex.org/W2150872430","https://openalex.org/W2156909104","https://openalex.org/W2158529569","https://openalex.org/W2161813919","https://openalex.org/W2165758113","https://openalex.org/W2166473218","https://openalex.org/W2345813284","https://openalex.org/W2767905780","https://openalex.org/W3023786531","https://openalex.org/W4243392806"],"related_works":["https://openalex.org/W2610521515","https://openalex.org/W2079825755","https://openalex.org/W1509134351","https://openalex.org/W2105121207","https://openalex.org/W2132005946","https://openalex.org/W2048352225","https://openalex.org/W2035337734","https://openalex.org/W2046363782","https://openalex.org/W1503372842","https://openalex.org/W2522249745"],"abstract_inverted_index":{"This":[0],"letter":[1,147],"analyzes":[2],"the":[3,25,37,49,53,65,74,91,96,100,115,131,142,150],"Fisher":[4,13,54,101,143,151],"kernel":[5,14,102,152],"from":[6],"a":[7,16,22,135,158,162],"statistical":[8,50,164,168],"point":[9,112],"of":[10,24,32,36,52,90,99],"view.":[11],"The":[12],"is":[15,42,69,120,138],"particularly":[17],"interesting":[18],"method":[19],"for":[20],"constructing":[21],"model":[23,68],"posterior":[26,67],"probability":[27],"that":[28,64,114,149],"makes":[29],"intelligent":[30],"use":[31],"unlabeled":[33,105],"data":[34,39,106],"(i.e.,":[35,71],"underlying":[38],"density).":[40],"It":[41],"important":[43],"to":[44,80,108],"analyze":[45],"and":[46,103],"ultimately":[47],"understand":[48],"properties":[51],"kernel.":[55,144],"To":[56],"this":[57,146],"end,":[58],"we":[59,84],"first":[60],"establish":[61],"sufficient":[62],"conditions":[63],"constructed":[66],"realizable":[70],"it":[72],"contains":[73],"true":[75],"distribution).":[76],"Realizability":[77],"immediately":[78],"leads":[79],"consistency":[81],"results.":[82],"Subsequently,":[83],"focus":[85],"on":[86],"an":[87],"asymptotic":[88],"analysis":[89],"generalization":[92],"error,":[93],"which":[94],"elucidates":[95],"learning":[97],"curves":[98],"how":[104],"contribute":[107],"learning.":[109],"We":[110],"also":[111],"out":[113],"squared":[116],"or":[117],"log":[118],"loss":[119],"theoretically":[121],"preferable-because":[122],"both":[123],"yield":[124],"consistent":[125],"estimators-to":[126],"other":[127],"losses":[128],"such":[129],"as":[130,157,161],"exponential":[132],"loss,":[133],"when":[134],"linear":[136],"classifier":[137],"used":[139],"together":[140],"with":[141,166],"Therefore,":[145],"underlines":[148],"should":[153],"be":[154],"viewed":[155],"not":[156],"heuristics":[159],"but":[160],"powerful":[163],"tool":[165],"well-controlled":[167],"properties.":[169]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
