{"id":"https://openalex.org/W7141601389","doi":"https://doi.org/10.1016/j.patcog.2026.113616","title":"Balancing tails when comparing distributions: Comprehensive equity index (CEI) with application to bias evaluation in operational face biometrics","display_name":"Balancing tails when comparing distributions: Comprehensive equity index (CEI) with application to bias evaluation in operational face biometrics","publication_year":2026,"publication_date":"2026-03-27","ids":{"openalex":"https://openalex.org/W7141601389","doi":"https://doi.org/10.1016/j.patcog.2026.113616"},"language":"en","primary_location":{"id":"doi:10.1016/j.patcog.2026.113616","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.patcog.2026.113616","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.patcog.2026.113616","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113407870","display_name":"Imanol Solano","orcid":null},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]},{"id":"https://openalex.org/I86843133","display_name":"University of Pamplona","ror":"https://ror.org/04dfr7a85","country_code":"CO","type":"education","lineage":["https://openalex.org/I86843133"]}],"countries":["CO","ES"],"is_corresponding":true,"raw_author_name":"Imanol Solano","raw_affiliation_strings":["BiometricsAI, Universidad Autonoma de Madrid, Spain","Veridas, Pamplona, Spain"],"raw_orcid":"https://orcid.org/0009-0004-1463-4511","affiliations":[{"raw_affiliation_string":"BiometricsAI, Universidad Autonoma de Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]},{"raw_affiliation_string":"Veridas, Pamplona, Spain","institution_ids":["https://openalex.org/I86843133"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130793274","display_name":"Julian Fierrez","orcid":null},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Julian Fierrez","raw_affiliation_strings":["BiometricsAI, Universidad Autonoma de Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-6343-5656","affiliations":[{"raw_affiliation_string":"BiometricsAI, Universidad Autonoma de Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007904250","display_name":"\u00c1ngela Morales","orcid":null},"institutions":[{"id":"https://openalex.org/I119635470","display_name":"Universidad de Las Palmas de Gran Canaria","ror":"https://ror.org/01teme464","country_code":"ES","type":"education","lineage":["https://openalex.org/I119635470"]},{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Aythami Morales","raw_affiliation_strings":["BiometricsAI, Universidad Autonoma de Madrid, Spain","Department of Mathematics, Universidad de Las Palmas de Gran Canaria, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7268-4785","affiliations":[{"raw_affiliation_string":"BiometricsAI, Universidad Autonoma de Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]},{"raw_affiliation_string":"Department of Mathematics, Universidad de Las Palmas de Gran Canaria, Spain","institution_ids":["https://openalex.org/I119635470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101705195","display_name":"Alejandro Pe\u00f1a","orcid":"https://orcid.org/0000-0001-6907-5826"},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alejandro Pe\u00f1a","raw_affiliation_strings":["BiometricsAI, Universidad Autonoma de Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"BiometricsAI, Universidad Autonoma de Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009955709","display_name":"Rub\u00e9n Tolosana","orcid":"https://orcid.org/0000-0002-9393-3066"},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ruben Tolosana","raw_affiliation_strings":["BiometricsAI, Universidad Autonoma de Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9393-3066","affiliations":[{"raw_affiliation_string":"BiometricsAI, Universidad Autonoma de Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003560190","display_name":"Francisco Zamora-Mart\u00ednez","orcid":null},"institutions":[{"id":"https://openalex.org/I86843133","display_name":"University of Pamplona","ror":"https://ror.org/04dfr7a85","country_code":"CO","type":"education","lineage":["https://openalex.org/I86843133"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Francisco Zamora-Martinez","raw_affiliation_strings":["Veridas, Pamplona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Veridas, Pamplona, Spain","institution_ids":["https://openalex.org/I86843133"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130797074","display_name":"Javier San Agustin","orcid":null},"institutions":[{"id":"https://openalex.org/I86843133","display_name":"University of Pamplona","ror":"https://ror.org/04dfr7a85","country_code":"CO","type":"education","lineage":["https://openalex.org/I86843133"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Javier San Agustin","raw_affiliation_strings":["Veridas, Pamplona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Veridas, Pamplona, Spain","institution_ids":["https://openalex.org/I86843133"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113407870","https://openalex.org/A5130793274"],"corresponding_institution_ids":["https://openalex.org/I63634437","https://openalex.org/I86843133"],"apc_list":{"value":2850,"currency":"USD","value_usd":2850},"apc_paid":{"value":2850,"currency":"USD","value_usd":2850},"fwci":7.2205,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.96417172,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"179","issue":null,"first_page":"113616","last_page":"113616"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11448","display_name":"Face recognition and analysis","score":0.73580002784729,"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/T11448","display_name":"Face recognition and analysis","score":0.73580002784729,"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/T10828","display_name":"Biometric Identification and Security","score":0.2070000022649765,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.01850000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/biometrics","display_name":"Biometrics","score":0.7896000146865845},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5698000192642212},{"id":"https://openalex.org/keywords/equity","display_name":"Equity (law)","score":0.5242999792098999},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.4207000136375427},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.41830000281333923},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.35190001130104065}],"concepts":[{"id":"https://openalex.org/C184297639","wikidata":"https://www.wikidata.org/wiki/Q177765","display_name":"Biometrics","level":2,"score":0.7896000146865845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6869000196456909},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5698000192642212},{"id":"https://openalex.org/C199728807","wikidata":"https://www.wikidata.org/wiki/Q2578557","display_name":"Equity (law)","level":2,"score":0.5242999792098999},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.44929999113082886},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4442000091075897},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.4207000136375427},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.40459999442100525},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3862000107765198},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3467000126838684},{"id":"https://openalex.org/C2780898871","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Performance metric","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C31510193","wikidata":"https://www.wikidata.org/wiki/Q1192553","display_name":"Facial recognition system","level":3,"score":0.32260000705718994},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26179999113082886}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.patcog.2026.113616","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.patcog.2026.113616","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.patcog.2026.113616","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.patcog.2026.113616","pdf_url":null,"source":{"id":"https://openalex.org/S414566","display_name":"Pattern Recognition","issn_l":"0031-3203","issn":["0031-3203","1873-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Recognition","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.4122603237628937}],"awards":[],"funders":[{"id":"https://openalex.org/F4320329682","display_name":"Gobierno de Navarra","ror":"https://ror.org/025qq4838"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2106234275","https://openalex.org/W2122098412","https://openalex.org/W2793708128","https://openalex.org/W2953522645","https://openalex.org/W3018301625","https://openalex.org/W3181414820","https://openalex.org/W3192864012","https://openalex.org/W3198878858","https://openalex.org/W3199041638","https://openalex.org/W3212169258","https://openalex.org/W4220908375","https://openalex.org/W4379745834","https://openalex.org/W4390075275","https://openalex.org/W4414155288","https://openalex.org/W4414197517"],"related_works":[],"abstract_inverted_index":{"\u2022":[0,20,40],"A":[1,146],"new":[2],"metric":[3,88,153],"is":[4,201],"proposed":[5,174],"to":[6,30,69,90,133],"compare":[7],"statistical":[8,194],"distributions,":[9],"with":[10,67],"a":[11,32,86,104,163],"focus":[12,106],"on":[13,46,107],"detecting":[14],"disparities":[15,71],"in":[16,36,54,72,183,187,196,203],"the":[17,73,76,81,152,205],"distribution":[18,114,206],"tails.":[19,207],"The":[21,41,173],"method":[22],"separately":[23],"analyzes":[24,96],"genuine":[25,97],"and":[26,48,98,126,157,165],"impostor":[27,99],"score":[28,77,100],"distributions":[29,101,195],"provide":[31],"view":[33],"of":[34,75,151],"bias":[35,53,181],"high-performance":[37,55],"biometric":[38],"systems.":[39],"proposal":[42],"was":[43],"tested":[44],"extensively":[45],"real-world,":[47],"large-scale":[49],"operational":[50,169],"scenarios.":[51],"Demographic":[52],"face":[56,184],"recognition":[57],"(FR)":[58],"systems":[59],"often":[60],"eludes":[61],"detection":[62],"by":[63],"existing":[64],"metrics,":[65],"especially":[66],"respect":[68],"subtle":[70],"tails":[74],"distribution.":[78],"We":[79],"introduce":[80],"Comprehensive":[82],"Equity":[83],"Index":[84],"(CEI),":[85],"novel":[87],"designed":[89],"address":[91],"this":[92],"limitation.":[93],"CEI":[94,145,161],"uniquely":[95],"separately,":[102],"enabling":[103],"configurable":[105],"tail":[108],"probabilities":[109],"while":[110],"also":[111],"considering":[112],"overall":[113],"shapes.":[115],"Our":[116],"extensive":[117],"experiments":[118],"(evaluating":[119],"state-of-the-art":[120],"FR":[121,170],"systems,":[122],"intentionally":[123],"biased":[124],"models,":[125],"diverse":[127],"datasets)":[128],"confirm":[129],"CEI\u2019s":[130],"superior":[131],"ability":[132],"detect":[134],"nuanced":[135],"biases":[136],"where":[137,199],"previous":[138],"methods":[139,175],"fall":[140],"short.":[141],"Furthermore,":[142],"we":[143],"present":[144],",":[147],"an":[148],"automated":[149],"version":[150],"that":[154],"enhances":[155],"objectivity":[156],"simplifies":[158],"practical":[159],"application.":[160],"provides":[162],"robust":[164],"sensitive":[166],"tool":[167],"for":[168,180,192],"fairness":[171],"assessment.":[172],"have":[176],"been":[177],"developed":[178],"particularly":[179],"evaluation":[182],"biometrics":[185],"but,":[186],"general,":[188],"they":[189],"are":[190],"applicable":[191],"comparing":[193],"any":[197],"problem":[198],"one":[200],"interested":[202],"analyzing":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-03-28T00:00:00"}
