{"id":"https://openalex.org/W2340447012","doi":"https://doi.org/10.1109/tnnls.2015.2436064","title":"Improper Complex-Valued Bhattacharyya Distance","display_name":"Improper Complex-Valued Bhattacharyya Distance","publication_year":2015,"publication_date":"2015-06-10","ids":{"openalex":"https://openalex.org/W2340447012","doi":"https://doi.org/10.1109/tnnls.2015.2436064","mag":"2340447012","pmid":"https://pubmed.ncbi.nlm.nih.gov/26068880"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2015.2436064","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2436064","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 and Learning Systems","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/A5058253407","display_name":"Arash Mohammadi","orcid":"https://orcid.org/0000-0003-1972-7923"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Arash Mohammadi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059152392","display_name":"Konstantinos N. Plataniotis","orcid":"https://orcid.org/0000-0003-3647-5473"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Konstantinos N. Plataniotis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058253407"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":2.0103,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.8802472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"5","first_page":"1049","last_page":"1064"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9973000288009644,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9950000047683716,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9916999936103821,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bhattacharyya-distance","display_name":"Bhattacharyya distance","score":0.988936722278595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6644828915596008},{"id":"https://openalex.org/keywords/statistical-distance","display_name":"Statistical distance","score":0.5789303779602051},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5443221926689148},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5340624451637268},{"id":"https://openalex.org/keywords/triangle-inequality","display_name":"Triangle inequality","score":0.5271843671798706},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4685400724411011},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4670763313770294},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.46416524052619934},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4538716673851013},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.43463587760925293},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4340210556983948},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4141744077205658},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3607289493083954},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34856805205345154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3091939687728882},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.24724334478378296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.17376390099525452}],"concepts":[{"id":"https://openalex.org/C24145651","wikidata":"https://www.wikidata.org/wiki/Q2901249","display_name":"Bhattacharyya distance","level":2,"score":0.988936722278595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6644828915596008},{"id":"https://openalex.org/C58948655","wikidata":"https://www.wikidata.org/wiki/Q7604392","display_name":"Statistical distance","level":3,"score":0.5789303779602051},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5443221926689148},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5340624451637268},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.5271843671798706},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4685400724411011},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4670763313770294},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.46416524052619934},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4538716673851013},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.43463587760925293},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4340210556983948},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4141744077205658},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3607289493083954},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34856805205345154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3091939687728882},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.24724334478378296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.17376390099525452},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2015.2436064","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2436064","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 and Learning Systems","raw_type":"journal-article"},{"id":"pmid:26068880","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26068880","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 and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W142384176","https://openalex.org/W639989723","https://openalex.org/W1496856925","https://openalex.org/W1503003940","https://openalex.org/W1553616913","https://openalex.org/W1560089794","https://openalex.org/W1963871118","https://openalex.org/W1965536289","https://openalex.org/W1965555277","https://openalex.org/W1987307056","https://openalex.org/W1993285324","https://openalex.org/W2015245929","https://openalex.org/W2016757156","https://openalex.org/W2022504879","https://openalex.org/W2033178790","https://openalex.org/W2046059763","https://openalex.org/W2047852416","https://openalex.org/W2057590097","https://openalex.org/W2067489830","https://openalex.org/W2070264454","https://openalex.org/W2071779346","https://openalex.org/W2079690285","https://openalex.org/W2080392569","https://openalex.org/W2098337110","https://openalex.org/W2103632679","https://openalex.org/W2106431294","https://openalex.org/W2108288396","https://openalex.org/W2112014348","https://openalex.org/W2125105520","https://openalex.org/W2129078811","https://openalex.org/W2130418280","https://openalex.org/W2131049662","https://openalex.org/W2143410296","https://openalex.org/W2144723957","https://openalex.org/W2146166496","https://openalex.org/W2146399213","https://openalex.org/W2149197198","https://openalex.org/W2149338142","https://openalex.org/W2150581408","https://openalex.org/W2152586694","https://openalex.org/W2153244858","https://openalex.org/W2157305948","https://openalex.org/W2159071216","https://openalex.org/W2159894619","https://openalex.org/W2162548352","https://openalex.org/W2163090509","https://openalex.org/W2166288622","https://openalex.org/W2476841360","https://openalex.org/W2949071206","https://openalex.org/W3100792434","https://openalex.org/W3143528639","https://openalex.org/W4211251910","https://openalex.org/W4249489015","https://openalex.org/W6629759753","https://openalex.org/W6633232462","https://openalex.org/W6662016103","https://openalex.org/W6676085441","https://openalex.org/W6676904260","https://openalex.org/W6683775918","https://openalex.org/W7009903362"],"related_works":["https://openalex.org/W2149197198","https://openalex.org/W2138467869","https://openalex.org/W139051966","https://openalex.org/W2150461503","https://openalex.org/W2239343357","https://openalex.org/W2340447012","https://openalex.org/W2246287460","https://openalex.org/W3121898367","https://openalex.org/W2031848671","https://openalex.org/W2115924925"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"application":[2,229],"of":[3,39,89,108,122,130,157,160,166,180,186,209,230],"complex-valued":[4,32,110],"signal":[5],"processing":[6],"techniques":[7],"in":[8,50,55,155,183],"statistical":[9,44,140,187],"pattern":[10,56],"recognition,":[11,57],"classification,":[12],"and":[13,58,133,149,163,238],"Gaussian":[14,33,111],"mixture":[15],"(GM)":[16],"modeling,":[17],"this":[18,116],"paper":[19,114],"derives":[20],"analytical":[21],"expressions":[22],"for":[23,46,59,142,220,235],"computing":[24,143],"the":[25,40,71,79,87,90,106,120,123,128,131,144,153,158,161,167,178,184,199,203,210,228,231],"Bhattacharyya":[26],"coefficient/distance":[27],"(BC/BD)":[28],"between":[29,92],"two":[30,222,240],"improper":[31,109],"distributions.":[34],"The":[35,64,170,190],"BC/BD":[36,91,233],"is":[37,75,95,192],"one":[38],"most":[41],"widely":[42],"used":[43,175],"measures":[45,234],"evaluating":[47],"class":[48],"separability":[49],"classification":[51],"problems,":[52],"feature":[53,84],"extraction":[54],"GM":[60],"reduction":[61],"(GMR)":[62],"purposes.":[63],"BC":[65,191],"provides":[66],"an":[67,214],"upper":[68,148],"bound":[69],"on":[70,152],"Bayes":[72],"error,":[73],"which":[74,126],"commonly":[76],"known":[77],"as":[78],"best":[80],"criterion":[81],"to":[82,105,176,197],"evaluate":[83],"sets.":[85],"Although":[86],"computation":[88],"real-valued":[93],"signals":[94],"a":[96],"well-known":[97],"result,":[98],"it":[99,136,195],"has":[100],"not":[101],"yet":[102],"been":[103],"extended":[104],"case":[107],"densities.":[112,169],"This":[113],"addresses":[115],"gap.":[117],"We":[118,146],"analyze":[119],"role":[121],"pseudocovariance":[124,164],"matrix,":[125],"characterizes":[127],"noncircularity":[129],"signal,":[132],"show":[134],"that":[135],"carries":[137],"critical":[138],"second-order":[139],"information":[141],"BC/BD.":[145],"derive":[147],"lower":[150],"bounds":[151,172],"BD":[154],"terms":[156],"eigenvalues":[159],"covariance":[162],"matrices":[165],"underlying":[168],"theoretical":[171],"are":[173],"then":[174],"introduce":[177],"concept":[179],"\u03b2":[181],"-dominance":[182],"context":[185],"distance":[188,205,218],"measures.":[189],"pseudometric,":[193],"since":[194],"fails":[196],"satisfy":[198],"triangle":[200],"inequality.":[201],"Using":[202],"Matusita":[204],"(a":[206],"full-metric":[207],"variant":[208],"BC),":[211],"we":[212,226],"propose":[213],"intuitively":[215],"pleasing":[216],"indirect":[217],"measure":[219],"comparing":[221],"general":[223],"GMs.":[224],"Finally,":[225],"investigate":[227],"proposed":[232],"GMR":[236,242],"purposes":[237],"develop":[239],"BC-based":[241],"algorithms.":[243]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
