{"id":"https://openalex.org/W2095738857","doi":"https://doi.org/10.3390/e18010022","title":"Increment Entropy as a Measure of Complexity for Time Series","display_name":"Increment Entropy as a Measure of Complexity for Time Series","publication_year":2016,"publication_date":"2016-01-08","ids":{"openalex":"https://openalex.org/W2095738857","doi":"https://doi.org/10.3390/e18010022","mag":"2095738857"},"language":"en","primary_location":{"id":"doi:10.3390/e18010022","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010022","pdf_url":"https://www.mdpi.com/1099-4300/18/1/22/pdf?version=1460534792","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/18/1/22/pdf?version=1460534792","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100359300","display_name":"Xiaofeng Liu","orcid":"https://orcid.org/0000-0003-1310-6739"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]},{"id":"https://openalex.org/I4210108723","display_name":"Changzhou Institute of Technology","ror":"https://ror.org/020mrfq61","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210108723"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaofeng Liu","raw_affiliation_strings":["Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China","College of IOT Engineering, Hohai University, Changzhou 213022, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China","institution_ids":["https://openalex.org/I4210108723"]},{"raw_affiliation_string":"College of IOT Engineering, Hohai University, Changzhou 213022, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028119374","display_name":"Aimin Jiang","orcid":"https://orcid.org/0000-0002-9181-934X"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]},{"id":"https://openalex.org/I4210108723","display_name":"Changzhou Institute of Technology","ror":"https://ror.org/020mrfq61","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210108723"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aimin Jiang","raw_affiliation_strings":["Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China","College of IOT Engineering, Hohai University, Changzhou 213022, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China","institution_ids":["https://openalex.org/I4210108723"]},{"raw_affiliation_string":"College of IOT Engineering, Hohai University, Changzhou 213022, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113354555","display_name":"Ning Xu","orcid":"https://orcid.org/0000-0002-2554-4309"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]},{"id":"https://openalex.org/I4210108723","display_name":"Changzhou Institute of Technology","ror":"https://ror.org/020mrfq61","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210108723"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ning Xu","raw_affiliation_strings":["Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China","College of IOT Engineering, Hohai University, Changzhou 213022, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Changzhou Key Laboratory of Robotics and Intelligent Technology, Changzhou 213022, China","institution_ids":["https://openalex.org/I4210108723"]},{"raw_affiliation_string":"College of IOT Engineering, Hohai University, Changzhou 213022, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031934171","display_name":"Jianru Xue","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianru Xue","raw_affiliation_strings":["Institute of Artificial Intelligence and Robotics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China","Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence and Robotics, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100359300"],"corresponding_institution_ids":["https://openalex.org/I163340411","https://openalex.org/I4210108723"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":11.423,"has_fulltext":false,"cited_by_count":70,"citation_normalized_percentile":{"value":0.97911588,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"18","issue":"1","first_page":"22","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9922000169754028,"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"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9922000169754028,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9833999872207642,"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"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9703999757766724,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6482713222503662},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.52361661195755},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5012290477752686},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.4892825782299042},{"id":"https://openalex.org/keywords/transfer-entropy","display_name":"Transfer entropy","score":0.4879409968852997},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.48317447304725647},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.464485228061676},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45654961466789246},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4305875897407532},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.359637975692749},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.3163115382194519},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23517408967018127},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.18080666661262512},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1789952516555786},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11481130123138428}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6482713222503662},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.52361661195755},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5012290477752686},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.4892825782299042},{"id":"https://openalex.org/C182049051","wikidata":"https://www.wikidata.org/wiki/Q17147155","display_name":"Transfer entropy","level":3,"score":0.4879409968852997},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.48317447304725647},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.464485228061676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45654961466789246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4305875897407532},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.359637975692749},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3163115382194519},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23517408967018127},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.18080666661262512},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1789952516555786},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11481130123138428},{"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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e18010022","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010022","pdf_url":"https://www.mdpi.com/1099-4300/18/1/22/pdf?version=1460534792","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.01053","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.01053","pdf_url":"https://arxiv.org/pdf/1503.01053","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:2a198e4bb54f4b838925990e19024c60","is_oa":true,"landing_page_url":"https://doaj.org/article/2a198e4bb54f4b838925990e19024c60","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 18, Iss 1, p 22 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/18/1/22/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e18010022","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 18; Issue 1; Pages: 22","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e18010022","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010022","pdf_url":"https://www.mdpi.com/1099-4300/18/1/22/pdf?version=1460534792","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W1586227619","https://openalex.org/W1776514298","https://openalex.org/W1841099355","https://openalex.org/W1862394037","https://openalex.org/W1964000773","https://openalex.org/W1966835677","https://openalex.org/W1969072025","https://openalex.org/W1978683658","https://openalex.org/W1978909760","https://openalex.org/W1985978480","https://openalex.org/W1999518678","https://openalex.org/W2014683958","https://openalex.org/W2017091714","https://openalex.org/W2018876117","https://openalex.org/W2027321393","https://openalex.org/W2036613247","https://openalex.org/W2036988740","https://openalex.org/W2041935121","https://openalex.org/W2046945477","https://openalex.org/W2050196023","https://openalex.org/W2052466231","https://openalex.org/W2061448580","https://openalex.org/W2071044018","https://openalex.org/W2075694080","https://openalex.org/W2075899699","https://openalex.org/W2077204677","https://openalex.org/W2077770566","https://openalex.org/W2085743383","https://openalex.org/W2090414491","https://openalex.org/W2093266575","https://openalex.org/W2095067567","https://openalex.org/W2096209718","https://openalex.org/W2102244548","https://openalex.org/W2102319935","https://openalex.org/W2105220282","https://openalex.org/W2114499604","https://openalex.org/W2116578201","https://openalex.org/W2118183148","https://openalex.org/W2119557840","https://openalex.org/W2130253467","https://openalex.org/W2138190513","https://openalex.org/W2141514928","https://openalex.org/W2147211064","https://openalex.org/W2157881370","https://openalex.org/W2164102251","https://openalex.org/W2164366998","https://openalex.org/W2164454345","https://openalex.org/W2262095545","https://openalex.org/W2317201179","https://openalex.org/W2318640187","https://openalex.org/W2322045482","https://openalex.org/W4242358482","https://openalex.org/W4285719527","https://openalex.org/W6638355978","https://openalex.org/W6639343545","https://openalex.org/W6677760164","https://openalex.org/W6683948454"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2009218479","https://openalex.org/W2387011115","https://openalex.org/W1966203994","https://openalex.org/W3041490575","https://openalex.org/W2970690932","https://openalex.org/W2150055352","https://openalex.org/W2356475741","https://openalex.org/W2075237332","https://openalex.org/W1993345826"],"abstract_inverted_index":{"Entropy":[0],"has":[1],"been":[2],"a":[3,14,38],"common":[4],"index":[5],"to":[6,24,45,52,113],"quantify":[7],"the":[8,26,46,49,53,61,65,87],"complexity":[9,27],"of":[10,16,28,40,64,81,86,98],"time":[11,29,106],"series":[12,30],"in":[13,31],"variety":[15],"fields.":[17],"Here,":[18],"we":[19],"introduce":[20],"an":[21],"increment":[22,34],"entropy":[23,56,63],"measure":[25],"which":[32],"each":[33],"is":[35,58],"mapped":[36],"onto":[37],"word":[39],"two":[41],"letters,":[42],"one":[43],"corresponding":[44,51],"sign":[47],"and":[48,71,108],"other":[50],"magnitude.":[54],"Increment":[55],"(IncrEn)":[57],"defined":[59],"as":[60],"Shannon":[62],"words.":[66],"Simulations":[67],"on":[68,73,105],"synthetic":[69],"data":[70],"tests":[72],"epileptic":[74],"electroencephalogram":[75],"(EEG)":[76],"signals":[77],"demonstrate":[78],"its":[79],"ability":[80],"detecting":[82],"abrupt":[83],"changes,":[84],"regardless":[85],"energetic":[88],"(e.g.,":[89],"spikes":[90],"or":[91,93],"bursts)":[92],"structural":[94],"changes.":[95],"The":[96],"computation":[97],"IncrEn":[99],"does":[100],"not":[101],"make":[102],"any":[103],"assumption":[104],"series,":[107],"it":[109],"can":[110],"be":[111],"applicable":[112],"arbitrary":[114],"real-world":[115],"data.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}