{"id":"https://openalex.org/W2587634198","doi":"https://doi.org/10.1109/tbme.2017.2664105","title":"Bubble Entropy: An Entropy Almost Free of Parameters","display_name":"Bubble Entropy: An Entropy Almost Free of Parameters","publication_year":2017,"publication_date":"2017-02-07","ids":{"openalex":"https://openalex.org/W2587634198","doi":"https://doi.org/10.1109/tbme.2017.2664105","mag":"2587634198","pmid":"https://pubmed.ncbi.nlm.nih.gov/28182552"},"language":"en","primary_location":{"id":"doi:10.1109/tbme.2017.2664105","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tbme.2017.2664105","pdf_url":null,"source":{"id":"https://openalex.org/S5240358","display_name":"IEEE Transactions on Biomedical Engineering","issn_l":"0018-9294","issn":["0018-9294","1558-2531"],"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 Biomedical Engineering","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/A5028559566","display_name":"George Manis","orcid":null},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"George Manis","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Ioannina, Ioannina, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Ioannina, Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064961287","display_name":"Md Aktaruzzaman","orcid":"https://orcid.org/0000-0003-0349-1434"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Md Aktaruzzaman","raw_affiliation_strings":["Dipartimento di InformaticaUniversit\u00e0 degli Studi di Milano"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di InformaticaUniversit\u00e0 degli Studi di Milano","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039803457","display_name":"Roberto Sassi","orcid":"https://orcid.org/0000-0001-9729-2641"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Roberto Sassi","raw_affiliation_strings":["Dipartimento di InformaticaUniversit\u00e0 degli Studi di Milano"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di InformaticaUniversit\u00e0 degli Studi di Milano","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028559566"],"corresponding_institution_ids":["https://openalex.org/I194019607"],"apc_list":null,"apc_paid":null,"fwci":6.8953,"has_fulltext":false,"cited_by_count":150,"citation_normalized_percentile":{"value":0.97768877,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"64","issue":"11","first_page":"2711","last_page":"2718"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10745","display_name":"Heart Rate Variability and Autonomic Control","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10745","display_name":"Heart Rate Variability and Autonomic Control","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10429","display_name":"EEG and Brain-Computer Interfaces","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6043307185173035},{"id":"https://openalex.org/keywords/min-entropy","display_name":"Min entropy","score":0.5064634084701538},{"id":"https://openalex.org/keywords/bubble","display_name":"Bubble","score":0.48693597316741943},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.4819333553314209},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4749841094017029},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.457133412361145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4540295898914337},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.4291017949581146},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.42641234397888184},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.4224443733692169},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37931913137435913},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36155736446380615},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3045880198478699},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.3027573823928833},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.26148468255996704},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13527822494506836},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09000489115715027}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6043307185173035},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.5064634084701538},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.48693597316741943},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.4819333553314209},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4749841094017029},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.457133412361145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4540295898914337},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.4291017949581146},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.42641234397888184},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.4224443733692169},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37931913137435913},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36155736446380615},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3045880198478699},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.3027573823928833},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.26148468255996704},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13527822494506836},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09000489115715027},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000328","descriptor_name":"Adult","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000328","descriptor_name":"Adult","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000328","descriptor_name":"Adult","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000368","descriptor_name":"Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D004562","descriptor_name":"Electrocardiography","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004562","descriptor_name":"Electrocardiography","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004562","descriptor_name":"Electrocardiography","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006333","descriptor_name":"Heart Failure","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D006333","descriptor_name":"Heart Failure","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D006333","descriptor_name":"Heart Failure","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D006339","descriptor_name":"Heart Rate","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006339","descriptor_name":"Heart Rate","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006339","descriptor_name":"Heart Rate","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008875","descriptor_name":"Middle Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008875","descriptor_name":"Middle Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008875","descriptor_name":"Middle Aged","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","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":true},{"descriptor_ui":"D019277","descriptor_name":"Entropy","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":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tbme.2017.2664105","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tbme.2017.2664105","pdf_url":null,"source":{"id":"https://openalex.org/S5240358","display_name":"IEEE Transactions on Biomedical Engineering","issn_l":"0018-9294","issn":["0018-9294","1558-2531"],"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 Biomedical Engineering","raw_type":"journal-article"},{"id":"pmid:28182552","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28182552","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 bio-medical engineering","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6800000071525574,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1259078","https://openalex.org/W1492154839","https://openalex.org/W1535668527","https://openalex.org/W1980474897","https://openalex.org/W1991033480","https://openalex.org/W1998711164","https://openalex.org/W2014683958","https://openalex.org/W2017091714","https://openalex.org/W2077204677","https://openalex.org/W2085009317","https://openalex.org/W2087978863","https://openalex.org/W2095067567","https://openalex.org/W2096209718","https://openalex.org/W2115734410","https://openalex.org/W2118183148","https://openalex.org/W2119152851","https://openalex.org/W2157881370","https://openalex.org/W2162800060","https://openalex.org/W2318640187","https://openalex.org/W2322045482","https://openalex.org/W2348036828","https://openalex.org/W2549302251","https://openalex.org/W6629309747","https://openalex.org/W6677105841"],"related_works":["https://openalex.org/W862060148","https://openalex.org/W2139507220","https://openalex.org/W2898188192","https://openalex.org/W2955910739","https://openalex.org/W2026360404","https://openalex.org/W2034921015","https://openalex.org/W2884476384","https://openalex.org/W2242607083","https://openalex.org/W2038174233","https://openalex.org/W2910493821"],"abstract_inverted_index":{"Objective:":[0],"A":[1],"critical":[2],"point":[3],"in":[4,20,55,191],"any":[5],"definition":[6,26,42,134],"of":[7,12,27,34,76,95,139,168,187],"entropy":[8,28,94,111,189],"is":[9,47,136,162,170],"the":[10,13,32,40,53,56,63,68,74,93,128,146,151,159,166,184,208,218,223,233,236,239,242],"selection":[11],"parameters":[14,198,209],"employed":[15],"to":[16,30,123],"obtain":[17],"an":[18],"estimate":[19],"practice.":[21],"We":[22,38,61],"propose":[23],"a":[24,86],"new":[25,41],"aiming":[29],"reduce":[31],"significance":[33,228],"this":[35,96],"selection.":[36],"Methods:":[37],"call":[39],"Bubble":[43,45],"Entropy.":[44],"Entropy":[46],"based":[48],"on":[49],"permutation":[50],"entropy,":[51],"where":[52],"vectors":[54],"embedding":[57,152],"space":[58],"are":[59,145,210],"ranked.":[60],"use":[62,186],"bubble":[64,110],"sort":[65],"algorithm":[66],"for":[67,79,196],"ordering":[69],"procedure":[70],"and":[71,90,104,115,119,150,165,179,214,221,241,244],"count":[72],"instead":[73],"number":[75],"swaps":[77],"performed":[78],"each":[80],"vector.":[81],"Doing":[82],"so,":[83],"we":[84],"create":[85],"more":[87],"coarse-grained":[88],"distribution":[89],"then":[91],"compute":[92],"distribution.":[97],"Results:":[98],"Experimental":[99],"results":[100],"with":[101],"both":[102],"real":[103],"synthetic":[105],"HRV":[106],"signals":[107],"showed":[108],"that":[109],"presents":[112,176],"remarkable":[113],"stability":[114,178],"exhibits":[116],"increased":[117,177],"descriptive":[118,224],"discriminating":[120,180],"power":[121],"compared":[122],"all":[124],"other":[125],"definitions,":[126],"including":[127],"most":[129,142],"popular":[130],"ones.":[131],"Conclusion:":[132],"The":[133,141,173],"proposed":[135,174],"almost":[137],"free":[138],"parameters.":[140],"common":[143],"ones":[144],"scale":[147,160],"factor":[148,161],"r":[149],"dimension":[153],"m":[154,169],".":[155],"In":[156],"our":[157],"definition,":[158],"totally":[163],"eliminated":[164],"importance":[167],"significantly":[171],"reduced.":[172],"method":[175,237],"power.":[181,225],"Significance:":[182],"After":[183],"extensive":[185],"some":[188],"measures":[190],"physiological":[192],"signals,":[193],"typical":[194],"values":[195],"their":[197,227],"have":[199],"been":[200],"suggested,":[201],"or":[202,229],"at":[203],"least,":[204],"widely":[205],"used.":[206],"However,":[207],"still":[211],"there,":[212],"application":[213],"dataset":[215],"dependent,":[216],"influencing":[217],"computed":[219],"value":[220],"affecting":[222],"Reducing":[226],"eliminating":[230,245],"them":[231],"alleviates":[232],"problem,":[234],"decoupling":[235],"from":[238],"data":[240],"application,":[243],"subjective":[246],"factors.":[247]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4}],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-10-10T00:00:00"}