{"id":"https://openalex.org/W2623585316","doi":"https://doi.org/10.1109/lsp.2017.2712195","title":"Generalizing Skew Jensen Divergences and Bregman Divergences With Comparative Convexity","display_name":"Generalizing Skew Jensen Divergences and Bregman Divergences With Comparative Convexity","publication_year":2017,"publication_date":"2017-06-05","ids":{"openalex":"https://openalex.org/W2623585316","doi":"https://doi.org/10.1109/lsp.2017.2712195","mag":"2623585316"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2017.2712195","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2017.2712195","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},"type":"article","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/A5061293973","display_name":"Frank Nielsen","orcid":"https://orcid.org/0000-0001-5728-0726"},"institutions":[{"id":"https://openalex.org/I4210122684","display_name":"Sony Computer Science Laboratories","ror":"https://ror.org/02nc46417","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210122684"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Frank Nielsen","raw_affiliation_strings":["\u00c9cole Polytechnique, Sony Computer Science Laboratories, Inc., Tokyo, Japan","Sony Corporation (Japan)"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique, Sony Computer Science Laboratories, Inc., Tokyo, Japan","institution_ids":["https://openalex.org/I4210122684"]},{"raw_affiliation_string":"Sony Corporation (Japan)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082414223","display_name":"Richard Nock","orcid":"https://orcid.org/0000-0001-8384-9621"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I4210135110","display_name":"Centre Hospitalier Universitaire de Martinique","ror":"https://ror.org/0376kfa34","country_code":"MQ","type":"healthcare","lineage":["https://openalex.org/I4210135110"]}],"countries":["AU","MQ"],"is_corresponding":false,"raw_author_name":"Richard Nock","raw_affiliation_strings":["Data61, University of Sydney, Camperdown NSW, Australia","MEMIAD - Management, \u00e9conomie, mod\u00e9lisation, informatique et aide \u00e0 la d\u00e9cision [UR7_3] (Universit\u00e9 des Antilles - Facult\u00e9 de Droit et d\u2019Economie - B.P 7209 97275 Schoelcher Cedex - Martinique - Martinique)"],"affiliations":[{"raw_affiliation_string":"Data61, University of Sydney, Camperdown NSW, Australia","institution_ids":["https://openalex.org/I42894916","https://openalex.org/I129604602"]},{"raw_affiliation_string":"MEMIAD - Management, \u00e9conomie, mod\u00e9lisation, informatique et aide \u00e0 la d\u00e9cision [UR7_3] (Universit\u00e9 des Antilles - Facult\u00e9 de Droit et d\u2019Economie - B.P 7209 97275 Schoelcher Cedex - Martinique - Martinique)","institution_ids":["https://openalex.org/I4210135110"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061293973"],"corresponding_institution_ids":["https://openalex.org/I4210122684"],"apc_list":null,"apc_paid":null,"fwci":3.0174,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.90961082,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"24","issue":"8","first_page":"1123","last_page":"1127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9983999729156494,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9983999729156494,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9789999723434448,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8769201040267944},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.8169359564781189},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7109962701797485},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5610160827636719},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.461284339427948},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.451608270406723},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.4410324990749359},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21565884351730347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16641196608543396}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8769201040267944},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.8169359564781189},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7109962701797485},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5610160827636719},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.461284339427948},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.451608270406723},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.4410324990749359},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21565884351730347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16641196608543396},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/lsp.2017.2712195","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2017.2712195","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02083367v1","is_oa":false,"landing_page_url":"https://hal.univ-antilles.fr/hal-02083367","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters, 2017, 24 (8), pp.1123-1127. &#x27E8;10.1109/LSP.2017.2712195&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/218066","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/218066","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1494379901","https://openalex.org/W1954793731","https://openalex.org/W1998240081","https://openalex.org/W2014017874","https://openalex.org/W2033468335","https://openalex.org/W2047319650","https://openalex.org/W2048305092","https://openalex.org/W2050177177","https://openalex.org/W2070134780","https://openalex.org/W2075057405","https://openalex.org/W2081728937","https://openalex.org/W2096765209","https://openalex.org/W2110861437","https://openalex.org/W2116327295","https://openalex.org/W2121133842","https://openalex.org/W2124792803","https://openalex.org/W2129802470","https://openalex.org/W2146950091","https://openalex.org/W2162995444","https://openalex.org/W2296349740","https://openalex.org/W2321974580","https://openalex.org/W2326315219","https://openalex.org/W2485135680","https://openalex.org/W2490754630","https://openalex.org/W2963441115","https://openalex.org/W3106261784","https://openalex.org/W4210738344","https://openalex.org/W4292070096","https://openalex.org/W6674201379"],"related_works":["https://openalex.org/W2790371392","https://openalex.org/W3112976351","https://openalex.org/W2140505738","https://openalex.org/W4200078764","https://openalex.org/W1964872188","https://openalex.org/W952002620","https://openalex.org/W2187391117","https://openalex.org/W1981809986","https://openalex.org/W1988820292","https://openalex.org/W2765284782"],"abstract_inverted_index":{"Comparative":[0],"convexity":[1,7,43],"is":[2],"a":[3],"generalization":[4],"of":[5,13,38],"ordinary":[6,70],"based":[8],"on":[9,73],"abstract":[10],"means":[11],"instead":[12],"arithmetic":[14],"means.":[15],"We":[16],"introduce":[17],"the":[18,42,53],"generalized":[19],"skew":[20],"Jensen":[21],"divergences":[22,27,65,72],"and":[23,48,76],"their":[24],"corresponding":[25,54],"Bregman":[26,55,64,71],"with":[28],"respect":[29],"to":[30,68],"comparative":[31],"convexity.":[32],"To":[33],"illustrate":[34],"those":[35,62],"novel":[36],"families":[37],"divergences,":[39],"we":[40,59],"consider":[41],"induced":[44],"by":[45],"quasi-arithmetic":[46],"means,":[47],"report":[49],"explicit":[50],"formula":[51],"for":[52],"divergences.":[56],"In":[57],"particular,":[58],"show":[60],"that":[61],"new":[63],"are":[66],"equivalent":[67],"conformal":[69],"monotone":[74],"embeddings,":[75],"further":[77],"state":[78],"related":[79],"results.":[80]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
