{"id":"https://openalex.org/W2034182200","doi":"https://doi.org/10.3390/e16063273","title":"On Clustering Histograms with k-Means by Using Mixed \u03b1-Divergences","display_name":"On Clustering Histograms with k-Means by Using Mixed \u03b1-Divergences","publication_year":2014,"publication_date":"2014-06-17","ids":{"openalex":"https://openalex.org/W2034182200","doi":"https://doi.org/10.3390/e16063273","mag":"2034182200"},"language":"en","primary_location":{"id":"doi:10.3390/e16063273","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16063273","pdf_url":"https://www.mdpi.com/1099-4300/16/6/3273/pdf?version=1424785490","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/16/6/3273/pdf?version=1424785490","any_repository_has_fulltext":true},"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":["Polytechnique, 91128 Palaiseau Cedex, France","Sony Computer Science Laboratories, Inc, Tokyo 141-0022, Japan"],"affiliations":[{"raw_affiliation_string":"Polytechnique, 91128 Palaiseau Cedex, France","institution_ids":[]},{"raw_affiliation_string":"Sony Computer Science Laboratories, Inc, Tokyo 141-0022, Japan","institution_ids":["https://openalex.org/I4210122684"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082414223","display_name":"Richard Nock","orcid":"https://orcid.org/0000-0001-8384-9621"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"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"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Richard Nock","raw_affiliation_strings":["NICTA and The Australian National University, Locked Bag 9013, Alexandria NSW 1435, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA and The Australian National University, Locked Bag 9013, Alexandria NSW 1435, Australia","institution_ids":["https://openalex.org/I42894916","https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055812530","display_name":"\u0428\u0443\u043d-\u0438\u0447\u0438 \u0410\u043c\u0430\u0440\u0438","orcid":"https://orcid.org/0000-0001-8860-8675"},"institutions":[{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shun-ichi Amari","raw_affiliation_strings":["RIKEN Brain Science Institute, 2-1 Hirosawa Wako City, Saitama 351-0198, Japan"],"affiliations":[{"raw_affiliation_string":"RIKEN Brain Science Institute, 2-1 Hirosawa Wako City, Saitama 351-0198, Japan","institution_ids":["https://openalex.org/I2800939219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061293973"],"corresponding_institution_ids":["https://openalex.org/I4210122684"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9885,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.80161263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"16","issue":"6","first_page":"3273","last_page":"3301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9986000061035156,"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":0.9986000061035156,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9879999756813049,"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/T10689","display_name":"Remote-Sensing Image Classification","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/cluster-analysis","display_name":"Cluster analysis","score":0.7505613565444946},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5363963842391968},{"id":"https://openalex.org/keywords/categorization","display_name":"Categorization","score":0.5139967799186707},{"id":"https://openalex.org/keywords/histogram","display_name":"Histogram","score":0.5100453495979309},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.47347891330718994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43825921416282654},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.42901864647865295},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4151005148887634},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.38504719734191895},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.34612569212913513},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33027711510658264},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.13939008116722107}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7505613565444946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5363963842391968},{"id":"https://openalex.org/C94124525","wikidata":"https://www.wikidata.org/wiki/Q912550","display_name":"Categorization","level":2,"score":0.5139967799186707},{"id":"https://openalex.org/C53533937","wikidata":"https://www.wikidata.org/wiki/Q185020","display_name":"Histogram","level":3,"score":0.5100453495979309},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.47347891330718994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43825921416282654},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.42901864647865295},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4151005148887634},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.38504719734191895},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.34612569212913513},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33027711510658264},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.13939008116722107},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e16063273","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16063273","pdf_url":"https://www.mdpi.com/1099-4300/16/6/3273/pdf?version=1424785490","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:67bab809f23a4f98ae31c50a1cd6b3e6","is_oa":true,"landing_page_url":"https://doaj.org/article/67bab809f23a4f98ae31c50a1cd6b3e6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 16, Iss 6, Pp 3273-3301 (2014)","raw_type":"article"},{"id":"pmh:oai:irdb.nii.ac.jp:00953:0006739219","is_oa":false,"landing_page_url":"https://teikyo-u.repo.nii.ac.jp/records/2024127","pdf_url":null,"source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"journal article"},{"id":"pmh:oai:mdpi.com:/1099-4300/16/6/3273/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e16063273","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 16; Issue 6; Pages: 3273-3301","raw_type":"Text"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/98885","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/98885","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":"Entropy","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.3390/e16063273","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16063273","pdf_url":"https://www.mdpi.com/1099-4300/16/6/3273/pdf?version=1424785490","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6194240451","display_name":"National ICT Australia","funder_award_id":"NICTA","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320315885","display_name":"Australian Government","ror":"https://ror.org/0314h5y94"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2034182200.pdf","grobid_xml":"https://content.openalex.org/works/W2034182200.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W75235505","https://openalex.org/W152055444","https://openalex.org/W1533484961","https://openalex.org/W1570212550","https://openalex.org/W1573082642","https://openalex.org/W1592842123","https://openalex.org/W1594951899","https://openalex.org/W1644149629","https://openalex.org/W1975731806","https://openalex.org/W1986121825","https://openalex.org/W2006048942","https://openalex.org/W2030524974","https://openalex.org/W2040335539","https://openalex.org/W2042587503","https://openalex.org/W2045405869","https://openalex.org/W2051657238","https://openalex.org/W2064580901","https://openalex.org/W2068558963","https://openalex.org/W2073459066","https://openalex.org/W2085854859","https://openalex.org/W2088866137","https://openalex.org/W2091046407","https://openalex.org/W2096765209","https://openalex.org/W2105777181","https://openalex.org/W2110905836","https://openalex.org/W2110956982","https://openalex.org/W2121133842","https://openalex.org/W2125133553","https://openalex.org/W2132512523","https://openalex.org/W2137340484","https://openalex.org/W2140750317","https://openalex.org/W2150593711","https://openalex.org/W2159139259","https://openalex.org/W2162995444","https://openalex.org/W2321045369","https://openalex.org/W2523170955","https://openalex.org/W2532478580","https://openalex.org/W2950552949","https://openalex.org/W3021105684","https://openalex.org/W3101699127","https://openalex.org/W3127518054","https://openalex.org/W4210741401","https://openalex.org/W6674201379","https://openalex.org/W6680103276","https://openalex.org/W6700584362"],"related_works":["https://openalex.org/W1498259939","https://openalex.org/W1983610137","https://openalex.org/W2097458023","https://openalex.org/W2990472155","https://openalex.org/W2181817726","https://openalex.org/W2901148276","https://openalex.org/W2750350980","https://openalex.org/W3140013985","https://openalex.org/W3024593842","https://openalex.org/W1966028303"],"abstract_inverted_index":{"Clustering":[0],"sets":[1],"of":[2,11,15,33,37,68,77],"histograms":[3],"has":[4],"become":[5],"popular":[6],"thanks":[7],"to":[8,51,80,89],"the":[9,12,31,41,62,66,86],"success":[10],"generic":[13],"method":[14],"bag-of-X":[16],"used":[17],"in":[18,22,56],"text":[19],"categorization":[20,24],"and":[21,92],"visual":[23],"applications.":[25],"In":[26],"this":[27],"paper,":[28],"we":[29,60,72,84,99],"investigate":[30],"use":[32],"a":[34,74,94,101],"parametric":[35],"family":[36],"distortion":[38],"measures,":[39],"called":[40],"\u03b1-divergences,":[42],"for":[43,105],"clustering":[44,79,103],"histograms.":[45],"Since":[46],"it":[47],"usually":[48],"makes":[49],"sense":[50],"deal":[52],"with":[53],"symmetric":[54],"divergences":[55],"information":[57],"retrieval":[58],"systems,":[59],"symmetrize":[61],"\u03b1":[63],"-divergences":[64],"using":[65],"concept":[67],"mixed":[69,81,90,106],"divergences.":[70,82],"First,":[71],"present":[73],"novel":[75],"extension":[76],"k-means":[78],"Second,":[83],"extend":[85],"k-means++":[87],"seeding":[88],"\u03b1-divergences":[91],"report":[93],"guaranteed":[95],"probabilistic":[96],"bound.":[97],"Finally,":[98],"describe":[100],"soft":[102],"technique":[104],"\u03b1-divergences.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}