{"id":"https://openalex.org/W2158155276","doi":"https://doi.org/10.1109/tnn.2009.2030190","title":"Learning Gaussian Mixture Models With Entropy-Based Criteria","display_name":"Learning Gaussian Mixture Models With Entropy-Based Criteria","publication_year":2009,"publication_date":"2009-09-18","ids":{"openalex":"https://openalex.org/W2158155276","doi":"https://doi.org/10.1109/tnn.2009.2030190","mag":"2158155276","pmid":"https://pubmed.ncbi.nlm.nih.gov/19770090"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2009.2030190","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2009.2030190","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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 Transactions on Neural Networks","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/A5041732184","display_name":"Antonio Pe\u00f1alver","orcid":"https://orcid.org/0000-0002-3775-2623"},"institutions":[{"id":"https://openalex.org/I111262870","display_name":"Universitat de Miguel Hern\u00e1ndez d'Elx","ror":"https://ror.org/01azzms13","country_code":"ES","type":"education","lineage":["https://openalex.org/I111262870"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"A. Penalver Benavent","raw_affiliation_strings":["Departamento de Estad\u00edstica, Matem\u00e1ticas e Inform\u00e1tica, Universidad Miguel Hern\u00e1ndez, Elche 03202, Spain. a.penalver@umh.es","Departamento de Estad\u00edstica, Matem\u00e1ticas e Inform\u00e1tica, Universidad Miguel Hern\u00e1ndez de Elche, Elche, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Estad\u00edstica, Matem\u00e1ticas e Inform\u00e1tica, Universidad Miguel Hern\u00e1ndez, Elche 03202, Spain. a.penalver@umh.es","institution_ids":["https://openalex.org/I111262870"]},{"raw_affiliation_string":"Departamento de Estad\u00edstica, Matem\u00e1ticas e Inform\u00e1tica, Universidad Miguel Hern\u00e1ndez de Elche, Elche, Spain","institution_ids":["https://openalex.org/I111262870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011865589","display_name":"Francisco Escolano Ruiz","orcid":null},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"F. Escolano Ruiz","raw_affiliation_strings":["Departamento De Ciencia De La Computaci\u00f3n e Inteligencia Artificial, Universidad de Alicante, Alicante, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento De Ciencia De La Computaci\u00f3n e Inteligencia Artificial, Universidad de Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011354002","display_name":"J. M. G\u00f3rriz","orcid":"https://orcid.org/0000-0001-7069-1714"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J.M. Saez","raw_affiliation_strings":["Departamento De Ciencia De La Computaci\u00f3n e Inteligencia Artificial, Universidad de Alicante, Alicante, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento De Ciencia De La Computaci\u00f3n e Inteligencia Artificial, Universidad de Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041732184"],"corresponding_institution_ids":["https://openalex.org/I111262870"],"apc_list":null,"apc_paid":null,"fwci":6.9789,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.97025764,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"11","first_page":"1756","last_page":"1771"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","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/T11901","display_name":"Bayesian Methods and Mixture Models","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/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9624000191688538,"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/T11667","display_name":"Advanced Chemical Sensor Technologies","score":0.961899995803833,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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":0.669308066368103},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.6008948087692261},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5790873169898987},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.5472932457923889},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.530242919921875},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"Kernel density estimation","score":0.5124364495277405},{"id":"https://openalex.org/keywords/entropy-maximization","display_name":"Entropy maximization","score":0.48954519629478455},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.4890962243080139},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4654325544834137},{"id":"https://openalex.org/keywords/model-selection","display_name":"Model selection","score":0.45320773124694824},{"id":"https://openalex.org/keywords/density-estimation","display_name":"Density estimation","score":0.4274406135082245},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4026971757411957},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3974102735519409},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.366530179977417},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35717177391052246},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3446308374404907},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28387367725372314},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1642363965511322},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1037188470363617},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.10320082306861877}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.669308066368103},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.6008948087692261},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5790873169898987},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.5472932457923889},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.530242919921875},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.5124364495277405},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.48954519629478455},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.4890962243080139},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4654325544834137},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.45320773124694824},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.4274406135082245},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4026971757411957},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3974102735519409},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.366530179977417},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35717177391052246},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3446308374404907},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28387367725372314},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1642363965511322},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1037188470363617},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.10320082306861877},{"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"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":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","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":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","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":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","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},{"descriptor_ui":"D019277","descriptor_name":"Entropy","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019277","descriptor_name":"Entropy","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019277","descriptor_name":"Entropy","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnn.2009.2030190","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2009.2030190","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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 Transactions on Neural Networks","raw_type":"journal-article"},{"id":"pmid:19770090","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19770090","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":"IEEE transactions on neural networks","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W170307911","https://openalex.org/W1489119587","https://openalex.org/W1507028917","https://openalex.org/W1533169541","https://openalex.org/W1570317704","https://openalex.org/W1570876803","https://openalex.org/W1579271636","https://openalex.org/W1614659291","https://openalex.org/W1746680969","https://openalex.org/W1824865661","https://openalex.org/W1874027545","https://openalex.org/W1971784203","https://openalex.org/W1981276685","https://openalex.org/W1981367467","https://openalex.org/W1986758236","https://openalex.org/W1991851767","https://openalex.org/W1992338978","https://openalex.org/W1992536060","https://openalex.org/W1992587049","https://openalex.org/W2000545950","https://openalex.org/W2015245929","https://openalex.org/W2038885294","https://openalex.org/W2045656233","https://openalex.org/W2049169027","https://openalex.org/W2049633694","https://openalex.org/W2058815839","https://openalex.org/W2059579283","https://openalex.org/W2060677448","https://openalex.org/W2072623282","https://openalex.org/W2075839890","https://openalex.org/W2079044534","https://openalex.org/W2084812512","https://openalex.org/W2099111195","https://openalex.org/W2106110775","https://openalex.org/W2108284981","https://openalex.org/W2108301410","https://openalex.org/W2109919255","https://openalex.org/W2111842831","https://openalex.org/W2114759290","https://openalex.org/W2114771311","https://openalex.org/W2118020555","https://openalex.org/W2118292158","https://openalex.org/W2120211304","https://openalex.org/W2123649031","https://openalex.org/W2123883809","https://openalex.org/W2124369546","https://openalex.org/W2126678392","https://openalex.org/W2132425342","https://openalex.org/W2132549764","https://openalex.org/W2140136927","https://openalex.org/W2140935196","https://openalex.org/W2141893773","https://openalex.org/W2145268945","https://openalex.org/W2151454335","https://openalex.org/W2161717801","https://openalex.org/W2166698530","https://openalex.org/W2168175751","https://openalex.org/W2169026875","https://openalex.org/W2319660501","https://openalex.org/W2488678869","https://openalex.org/W2492794003","https://openalex.org/W2493977830","https://openalex.org/W2573934436","https://openalex.org/W2795528501","https://openalex.org/W2797746357","https://openalex.org/W2905505054","https://openalex.org/W3129711340","https://openalex.org/W4252386822","https://openalex.org/W6665272994","https://openalex.org/W6678819120"],"related_works":["https://openalex.org/W1482149696","https://openalex.org/W2583877436","https://openalex.org/W2144201579","https://openalex.org/W4240479520","https://openalex.org/W3123419490","https://openalex.org/W2977337932","https://openalex.org/W35193756","https://openalex.org/W2007242302","https://openalex.org/W4311428604","https://openalex.org/W1534559501"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,132],"address":[4],"the":[5,9,16,21,28,31,41,44,48,53,59,70,73,76,87,106,115,123,129,172,196],"problem":[6],"of":[7,11,30,43,55,62,72,75,89,98,108,114,126,128,198],"estimating":[8],"parameters":[10,33],"Gaussian":[12],"mixture":[13,50,92,140],"models.":[14],"Although":[15],"expectation-maximization":[17],"(EM)":[18],"algorithm":[19,118],"yields":[20],"maximum-likelihood":[22],"(ML)":[23],"solution,":[24],"its":[25],"sensitivity":[26],"to":[27,40,82,85,104,121,176],"selection":[29,203],"starting":[32],"is":[34],"well-known":[35],"and":[36,111,147,166,189],"it":[37,182],"may":[38,64],"converge":[39],"boundary":[42],"parameter":[45],"space.":[46],"Furthermore,":[47],"resulting":[49],"depends":[51],"on":[52],"number":[54,61,97,125],"selected":[56],"components,":[57],"but":[58],"optimal":[60],"kernels":[63],"be":[65],"unknown":[66],"beforehand.":[67],"We":[68,100,178],"introduce":[69],"use":[71,133],"entropy":[74,107],"probability":[77,184],"density":[78,185],"function":[79],"(pdf)":[80],"associated":[81],"each":[83,109],"kernel":[84,110,165,174],"measure":[86],"quality":[88],"a":[90,95,112,137,148,163],"given":[91],"model":[93,201],"with":[94,162],"fixed":[96],"kernels.":[99],"propose":[101],"two":[102,134],"methods":[103],"approximate":[105],"modification":[113],"classical":[116],"EM":[117,159],"in":[119,183],"order":[120,202],"find":[122],"optimum":[124],"components":[127],"mixture.":[130],"Moreover,":[131],"stopping":[135],"criteria:":[136],"novel":[138],"global":[139],"entropy-based":[141,158],"criterion":[142],"called":[143,157],"Gaussianity":[144],"deficiency":[145],"(GD)":[146],"minimum":[149],"description":[150],"length":[151],"(MDL)":[152],"principle-based":[153],"one.":[154],"Our":[155],"algorithm,":[156],"(EBEM),":[160],"starts":[161],"unique":[164],"performs":[167],"only":[168],"splitting":[169],"by":[170],"selecting":[171],"worst":[173],"attending":[175],"GD.":[177],"have":[179],"successfully":[180],"tested":[181],"estimation,":[186],"pattern":[187],"classification,":[188],"color":[190],"image":[191],"segmentation.":[192],"Experimental":[193],"results":[194],"improve":[195],"ones":[197],"other":[199],"state-of-the-art":[200],"methods.":[204]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}