{"id":"https://openalex.org/W4412594107","doi":"https://doi.org/10.3390/axioms14080551","title":"Comparative Evaluation of Nonparametric Density Estimators for Gaussian Mixture Models with Clustering Support","display_name":"Comparative Evaluation of Nonparametric Density Estimators for Gaussian Mixture Models with Clustering Support","publication_year":2025,"publication_date":"2025-07-23","ids":{"openalex":"https://openalex.org/W4412594107","doi":"https://doi.org/10.3390/axioms14080551"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14080551","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080551","pdf_url":"https://www.mdpi.com/2075-1680/14/8/551/pdf?version=1753258931","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/8/551/pdf?version=1753258931","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006845983","display_name":"Tomas Ruzgas","orcid":"https://orcid.org/0000-0002-2292-9852"},"institutions":[{"id":"https://openalex.org/I172574986","display_name":"Kaunas University of Technology","ror":"https://ror.org/01me6gb93","country_code":"LT","type":"education","lineage":["https://openalex.org/I172574986"]}],"countries":["LT"],"is_corresponding":true,"raw_author_name":"Tomas Ruzgas","raw_affiliation_strings":["Department of Applied Mathematics, Kaunas University of Technology, LT-51368 Kaunas, Lithuania"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Kaunas University of Technology, LT-51368 Kaunas, Lithuania","institution_ids":["https://openalex.org/I172574986"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039743499","display_name":"Gintaras Stankevi\u010dius","orcid":"https://orcid.org/0009-0004-0029-1829"},"institutions":[{"id":"https://openalex.org/I172574986","display_name":"Kaunas University of Technology","ror":"https://ror.org/01me6gb93","country_code":"LT","type":"education","lineage":["https://openalex.org/I172574986"]}],"countries":["LT"],"is_corresponding":false,"raw_author_name":"Gintaras Stankevi\u010dius","raw_affiliation_strings":["Department of Applied Mathematics, Kaunas University of Technology, LT-51368 Kaunas, Lithuania"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Kaunas University of Technology, LT-51368 Kaunas, Lithuania","institution_ids":["https://openalex.org/I172574986"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065206508","display_name":"Birut\u0117 Narijauskait\u0117","orcid":"https://orcid.org/0000-0002-9042-7168"},"institutions":[{"id":"https://openalex.org/I172574986","display_name":"Kaunas University of Technology","ror":"https://ror.org/01me6gb93","country_code":"LT","type":"education","lineage":["https://openalex.org/I172574986"]}],"countries":["LT"],"is_corresponding":false,"raw_author_name":"Birut\u0117 Narijauskait\u0117","raw_affiliation_strings":["Department of Applied Mathematics, Kaunas University of Technology, LT-51368 Kaunas, Lithuania"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Kaunas University of Technology, LT-51368 Kaunas, Lithuania","institution_ids":["https://openalex.org/I172574986"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5119051830","display_name":"Jurgita Arnastauskait\u0117 Zencevi\u010dien\u0117","orcid":null},"institutions":[{"id":"https://openalex.org/I172574986","display_name":"Kaunas University of Technology","ror":"https://ror.org/01me6gb93","country_code":"LT","type":"education","lineage":["https://openalex.org/I172574986"]}],"countries":["LT"],"is_corresponding":false,"raw_author_name":"Jurgita Arnastauskait\u0117 Zencevi\u010dien\u0117","raw_affiliation_strings":["Department of Computer Sciences, Kaunas University of Technology, LT-51368 Kaunas, Lithuania"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Kaunas University of Technology, LT-51368 Kaunas, Lithuania","institution_ids":["https://openalex.org/I172574986"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006845983"],"corresponding_institution_ids":["https://openalex.org/I172574986"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08765278,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"8","first_page":"551","last_page":"551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9994999766349792,"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":0.9994999766349792,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9793999791145325,"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/T10552","display_name":"Colorectal Cancer Screening and Detection","score":0.9678000211715698,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.6971008777618408},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6930675506591797},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6813860535621643},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.5402417182922363},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.507574200630188},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.42818158864974976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42550498247146606},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4215197265148163},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39982882142066956},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3347189724445343},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11998984217643738}],"concepts":[{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.6971008777618408},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6930675506591797},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6813860535621643},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.5402417182922363},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.507574200630188},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.42818158864974976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42550498247146606},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4215197265148163},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39982882142066956},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3347189724445343},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11998984217643738},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14080551","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080551","pdf_url":"https://www.mdpi.com/2075-1680/14/8/551/pdf?version=1753258931","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:ktu.edu:elaba:243377858","is_oa":true,"landing_page_url":"https://vb.ktu.edu/KTU:ELABAPDB243377858&prefLang=en_US","pdf_url":null,"source":{"id":"https://openalex.org/S4406922255","display_name":"KTUePubl (Repository of Kaunas University of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN 2075-1680","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:52dd8c4381c54e2480c4075694ab10a9","is_oa":true,"landing_page_url":"https://doaj.org/article/52dd8c4381c54e2480c4075694ab10a9","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 8, p 551 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14080551","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080551","pdf_url":"https://www.mdpi.com/2075-1680/14/8/551/pdf?version=1753258931","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412594107.pdf","grobid_xml":"https://content.openalex.org/works/W4412594107.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W1489950266","https://openalex.org/W1584961538","https://openalex.org/W1893983002","https://openalex.org/W1964724001","https://openalex.org/W1969253213","https://openalex.org/W1974193774","https://openalex.org/W1976047659","https://openalex.org/W1977137874","https://openalex.org/W1984499217","https://openalex.org/W1993333947","https://openalex.org/W1995514448","https://openalex.org/W1996057210","https://openalex.org/W2021467330","https://openalex.org/W2022884727","https://openalex.org/W2036599383","https://openalex.org/W2042770382","https://openalex.org/W2044739400","https://openalex.org/W2046031028","https://openalex.org/W2050980654","https://openalex.org/W2051218140","https://openalex.org/W2060688732","https://openalex.org/W2071408611","https://openalex.org/W2076738088","https://openalex.org/W2085463531","https://openalex.org/W2091233563","https://openalex.org/W2097671030","https://openalex.org/W2103824897","https://openalex.org/W2105725268","https://openalex.org/W2108447811","https://openalex.org/W2110385718","https://openalex.org/W2111548551","https://openalex.org/W2116718775","https://openalex.org/W2130444042","https://openalex.org/W2137337733","https://openalex.org/W2138988968","https://openalex.org/W2161831609","https://openalex.org/W2165382912","https://openalex.org/W2403035479","https://openalex.org/W3099801582","https://openalex.org/W3141459278","https://openalex.org/W4213328631","https://openalex.org/W4290973580","https://openalex.org/W4308207480","https://openalex.org/W4403456837","https://openalex.org/W6636921640","https://openalex.org/W6646760471","https://openalex.org/W6676580204","https://openalex.org/W6812386298","https://openalex.org/W6820936193","https://openalex.org/W6888847025","https://openalex.org/W7026715130"],"related_works":["https://openalex.org/W4243114048","https://openalex.org/W2529605301","https://openalex.org/W4237896776","https://openalex.org/W4231665652","https://openalex.org/W1837630526","https://openalex.org/W2000242494","https://openalex.org/W2335589441","https://openalex.org/W2111545434","https://openalex.org/W4381052368","https://openalex.org/W1578916557"],"abstract_inverted_index":{"The":[0,39,89,191,209],"article":[1,210],"investigates":[2],"the":[3,50,56,98,127,151,158,163,170,188,194],"accuracy":[4,69,94,114],"of":[5,46,105,196,203],"nonparametric":[6,207],"univariate":[7],"density":[8,30,66,99,110],"estimation":[9,26,93,111,154],"methods":[10,179],"applied":[11],"to":[12,65,228],"various":[13,86],"Gaussian":[14,61],"mixture":[15,62],"models.":[16],"A":[17],"comprehensive":[18],"comparative":[19],"analysis":[20,168],"is":[21,41,52,70,130],"performed":[22],"for":[23,85,115,148,214],"four":[24],"popular":[25],"approaches:":[27],"adaptive":[28,199],"kernel":[29,166],"estimation,":[31,35],"projection":[32],"pursuit,":[33],"log-spline":[34],"and":[36,75,103,117,177,201,221,231],"wavelet-based":[37],"estimation.":[38,67],"study":[40],"extended":[42],"with":[43,78,212],"modified":[44],"versions":[45],"these":[47],"methods,":[48],"where":[49],"sample":[51,87,101,219],"first":[53],"clustered":[54],"using":[55,73,197],"EM":[57],"algorithm":[58],"based":[59,156,217],"on":[60,97,157,187,218],"components":[63],"prior":[64],"Estimation":[68],"quantitatively":[71],"evaluated":[72],"MAE":[74],"MAPE":[76],"criteria,":[77],"simulation":[79,139],"experiments":[80],"conducted":[81],"over":[82],"100,000":[83,138],"replications":[84],"sizes.":[88],"results":[90],"show":[91],"that":[92],"strongly":[95],"depends":[96],"structure,":[100],"size,":[102],"degree":[104],"component":[106],"overlap.":[107],"Clustering":[108],"before":[109],"significantly":[112],"improves":[113],"multimodal":[116],"asymmetric":[118],"densities.":[119],"Although":[120],"no":[121],"formal":[122],"statistical":[123,160],"tests":[124],"are":[125,146],"conducted,":[126],"performance":[128,185],"improvement":[129],"validated":[131],"through":[132],"non-overlapping":[133],"confidence":[134],"intervals":[135],"obtained":[136],"from":[137],"replications.":[140],"In":[141],"addition,":[142],"several":[143],"decision-making":[144,233],"systems":[145],"compared":[147],"automatically":[149],"selecting":[150],"most":[152],"appropriate":[153],"method":[155,204,215],"sample\u2019s":[159],"features.":[161],"Among":[162],"tested":[164],"systems,":[165],"discriminant":[167],"yielded":[169],"lowest":[171],"error":[172],"rates,":[173],"while":[174],"neural":[175],"networks":[176],"hybrid":[178],"showed":[180],"competitive":[181],"but":[182],"more":[183],"variable":[184],"depending":[186],"evaluation":[189],"criterion.":[190],"findings":[192],"highlight":[193],"importance":[195],"structurally":[198],"estimators":[200],"automation":[202],"selection":[205,216],"in":[206],"statistics.":[208],"concludes":[211],"recommendations":[213],"characteristics":[220],"outlines":[222],"future":[223],"research":[224],"directions,":[225],"including":[226],"extensions":[227],"multivariate":[229],"settings":[230],"real-time":[232],"systems.":[234]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}