{"id":"https://openalex.org/W4415178675","doi":"https://doi.org/10.1109/tkde.2025.3620468","title":"Fuzzy $k$kNN Entropy and its Anomaly Detection","display_name":"Fuzzy $k$kNN Entropy and its Anomaly Detection","publication_year":2025,"publication_date":"2025-10-14","ids":{"openalex":"https://openalex.org/W4415178675","doi":"https://doi.org/10.1109/tkde.2025.3620468"},"language":"en","primary_location":{"id":"doi:10.1109/tkde.2025.3620468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2025.3620468","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Knowledge and Data Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Chang Liu","orcid":"https://orcid.org/0000-0003-3139-8528"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chang Liu","raw_affiliation_strings":["College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0003-3139-8528","affiliations":[{"raw_affiliation_string":"College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008041028","display_name":"Zhong Yuan","orcid":"https://orcid.org/0000-0002-7456-4445"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhong Yuan","raw_affiliation_strings":["College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-7456-4445","affiliations":[{"raw_affiliation_string":"College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100334733","display_name":"Yuan Yuan","orcid":"https://orcid.org/0000-0001-7964-6514"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Yuan","raw_affiliation_strings":["School of Software Technology, Zhejiang University, Ningbo, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Software Technology, Zhejiang University, Ningbo, China","institution_ids":["https://openalex.org/I109935558","https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Hongmei Chen","orcid":"https://orcid.org/0000-0002-7225-5577"},"institutions":[{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongmei Chen","raw_affiliation_strings":["School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-7225-5577","affiliations":[{"raw_affiliation_string":"School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu, China","institution_ids":["https://openalex.org/I4800084"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027770821","display_name":"Dezhong Peng","orcid":"https://orcid.org/0000-0002-0987-8472"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dezhong Peng","raw_affiliation_strings":["College of Computer Science, Sichuan University, Chengdu, China"],"raw_orcid":"https://orcid.org/0000-0002-0987-8472","affiliations":[{"raw_affiliation_string":"College of Computer Science, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4210125143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061712374","display_name":"Xiaomin Song","orcid":"https://orcid.org/0000-0002-8256-4322"},"institutions":[{"id":"https://openalex.org/I4210140439","display_name":"Digital Video (Italy)","ror":"https://ror.org/04ge7a533","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210140439"]},{"id":"https://openalex.org/I4210156034","display_name":"Sichuan Research Center of New Materials","ror":"https://ror.org/0587q0807","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210156034"]}],"countries":["CN","IT"],"is_corresponding":false,"raw_author_name":"Xiaomin Song","raw_affiliation_strings":["Sichuan Newstrong UHD Video Technology Company, Ltd., Chengdu, China","Sichuan Newstrong UHD Video Technology Co., Ltd., Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sichuan Newstrong UHD Video Technology Company, Ltd., Chengdu, China","institution_ids":["https://openalex.org/I4210156034"]},{"raw_affiliation_string":"Sichuan Newstrong UHD Video Technology Co., Ltd., Chengdu, China","institution_ids":["https://openalex.org/I4210140439"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":4.498,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.94553332,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"38","issue":"1","first_page":"338","last_page":"351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9054999947547913,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9054999947547913,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-classification","display_name":"Fuzzy classification","score":0.6326000094413757},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6291999816894531},{"id":"https://openalex.org/keywords/fuzzy-number","display_name":"Fuzzy number","score":0.5514000058174133},{"id":"https://openalex.org/keywords/fuzzy-set-operations","display_name":"Fuzzy set operations","score":0.511900007724762},{"id":"https://openalex.org/keywords/defuzzification","display_name":"Defuzzification","score":0.5030999779701233},{"id":"https://openalex.org/keywords/fuzzy-associative-matrix","display_name":"Fuzzy associative matrix","score":0.48159998655319214},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.47029998898506165},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.4595000147819519}],"concepts":[{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.6326000094413757},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6291999816894531},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.5514000058174133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5241000056266785},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.511900007724762},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.5030999779701233},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.49140000343322754},{"id":"https://openalex.org/C144170203","wikidata":"https://www.wikidata.org/wiki/Q5511099","display_name":"Fuzzy associative matrix","level":5,"score":0.48159998655319214},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.4595000147819519},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43209999799728394},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C739882","wikidata":"https://www.wikidata.org/wiki/Q3560506","display_name":"Anomaly detection","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.39259999990463257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35019999742507935},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.3490000069141388},{"id":"https://openalex.org/C17350324","wikidata":"https://www.wikidata.org/wiki/Q7860605","display_name":"Type-2 fuzzy sets and systems","level":5,"score":0.3467999994754791},{"id":"https://openalex.org/C29470771","wikidata":"https://www.wikidata.org/wiki/Q4165150","display_name":"Neuro-fuzzy","level":4,"score":0.34209999442100525},{"id":"https://openalex.org/C100516043","wikidata":"https://www.wikidata.org/wiki/Q4455138","display_name":"Fuzzy measure theory","level":5,"score":0.33640000224113464},{"id":"https://openalex.org/C166586474","wikidata":"https://www.wikidata.org/wiki/Q5511129","display_name":"Fuzzy mathematics","level":5,"score":0.33149999380111694},{"id":"https://openalex.org/C17212007","wikidata":"https://www.wikidata.org/wiki/Q5511111","display_name":"Fuzzy clustering","level":3,"score":0.30000001192092896},{"id":"https://openalex.org/C182049051","wikidata":"https://www.wikidata.org/wiki/Q17147155","display_name":"Transfer entropy","level":3,"score":0.2770000100135803},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.2694000005722046},{"id":"https://openalex.org/C2780049643","wikidata":"https://www.wikidata.org/wiki/Q5511139","display_name":"Fuzzy rule","level":4,"score":0.26030001044273376},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2587999999523163}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tkde.2025.3620468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tkde.2025.3620468","pdf_url":null,"source":{"id":"https://openalex.org/S30698027","display_name":"IEEE Transactions on Knowledge and Data Engineering","issn_l":"1041-4347","issn":["1041-4347","1558-2191","2326-3865"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Knowledge and Data Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1984544529","display_name":null,"funder_award_id":"62306196","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2231590263","display_name":null,"funder_award_id":"62376230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2732457500","display_name":null,"funder_award_id":"62372315","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6855309028","display_name":null,"funder_award_id":"YJ202245","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1530232915","https://openalex.org/W1868203821","https://openalex.org/W1993361112","https://openalex.org/W1995443851","https://openalex.org/W1999635750","https://openalex.org/W2016006067","https://openalex.org/W2019014808","https://openalex.org/W2027654459","https://openalex.org/W2038190934","https://openalex.org/W2041193317","https://openalex.org/W2042763529","https://openalex.org/W2043051613","https://openalex.org/W2053289194","https://openalex.org/W2061240327","https://openalex.org/W2069222657","https://openalex.org/W2076034971","https://openalex.org/W2098093602","https://openalex.org/W2111011053","https://openalex.org/W2117839996","https://openalex.org/W2122127505","https://openalex.org/W2129281431","https://openalex.org/W2144182447","https://openalex.org/W2147597050","https://openalex.org/W2170314592","https://openalex.org/W2511098035","https://openalex.org/W2743621318","https://openalex.org/W2807198477","https://openalex.org/W2883355296","https://openalex.org/W2901560888","https://openalex.org/W2945876440","https://openalex.org/W2965948517","https://openalex.org/W2966689929","https://openalex.org/W2973442392","https://openalex.org/W2994497769","https://openalex.org/W2994713090","https://openalex.org/W3033256545","https://openalex.org/W3073853843","https://openalex.org/W3096652072","https://openalex.org/W3110580699","https://openalex.org/W3128944770","https://openalex.org/W3134257270","https://openalex.org/W4226060502","https://openalex.org/W4282980030","https://openalex.org/W4283726410","https://openalex.org/W4285229964","https://openalex.org/W4319337711","https://openalex.org/W4384938256","https://openalex.org/W4388967510","https://openalex.org/W4395447244","https://openalex.org/W4401024161","https://openalex.org/W4401879287","https://openalex.org/W4403791310","https://openalex.org/W4403968576","https://openalex.org/W4404576616","https://openalex.org/W4408288242"],"related_works":[],"abstract_inverted_index":{"With":[0],"the":[1,35,39,68,75,97,108,116,119,123,131,135,143,151,162,169,197],"successful":[2],"application":[3],"of":[4,12,80,146,165],"granular":[5],"computing":[6],"in":[7,38,118],"anomaly":[8,101,137,144,152,163,186],"detection,":[9],"a":[10,31,48],"variety":[11],"tools":[13],"including":[14],"fuzzy":[15,24,28],"information":[16,25,37,86,92,148],"entropy":[17,26,50,65,126,157],"can":[18],"achieve":[19],"superior":[20],"detection":[21,102,187],"results.":[22],"However,":[23],"calculates":[27],"similarity":[29],"through":[30],"global":[32],"strategy,":[33],"ignoring":[34],"local":[36],"data.":[40],"To":[41],"address":[42],"this":[43,45],"deficiency,":[44],"paper":[46],"constructs":[47],"fuzzy$k$NN":[49,61,81,125,133,147,156],"theory":[51,66],"and":[52,60,67,78,122],"applies":[53],"it":[54],"to":[55,141,160],"identify":[56],"anomalies.":[57],"Firstly,":[58],"fuzzy$k$-similarity":[59,109,117],"are":[62,72,93,181],"defined,":[63],"and$k$NN":[64],"related":[69],"information-theoretic":[70],"metrics":[71],"proposed.":[73],"Then,":[74,150],"relevant":[76],"definitions":[77],"propositions":[79],"entropy,":[82,84,87,134],"fuzzy$k$-joint":[83],"fuzzy$k$-conditional":[85],"as":[88,90],"well":[89],"fuzzy$k$-mutual":[91],"elaborated.":[94],"Based":[95,129],"on":[96,115,130,155,189],"proposed":[98,120,198],"theory,":[99,121],"an":[100],"model":[103],"is":[104,112,127,139,158,177],"constructed.":[105],"At":[106],"first,":[107],"relation":[110],"matrix":[111],"constructed":[113],"based":[114,154],"relative":[124,132],"calculated.":[128],"fuzzy$k$-relation":[136],"degree":[138,164],"defined":[140],"characterize":[142],"intensity":[145],"granules.":[149],"factor":[153],"built":[159],"represent":[161],"data":[166],"objects.":[167],"Finally,":[168],"corresponding":[170],"Fuzzy$k$NN":[171],"Entropy-based":[172],"Anomaly":[173],"Detection":[174],"algorithm":[175],"(F$k$EAD)":[176],"designed.":[178],"Comparative":[179],"experiments":[180],"conducted":[182],"with":[183],"11":[184],"state-of-the-art":[185],"methods":[188],"thirty":[190],"public":[191],"datasets.":[192],"The":[193],"results":[194],"reveal":[195],"that":[196],"method":[199],"achieves":[200],"better":[201],"performance.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-15T00:00:00"}