{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T05:46:28Z","timestamp":1771911988865,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,21]],"date-time":"2022-08-21T00:00:00Z","timestamp":1661040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific and Technological Innovation 2030","award":["2021ZD0204300"],"award-info":[{"award-number":["2021ZD0204300"]}]},{"name":"Scientific and Technological Innovation 2030","award":["21RGSF0018"],"award-info":[{"award-number":["21RGSF0018"]}]},{"name":"Xi\u2019an City Innovation Capability Strengthening Basic Disciplines plan","award":["2021ZD0204300"],"award-info":[{"award-number":["2021ZD0204300"]}]},{"name":"Xi\u2019an City Innovation Capability Strengthening Basic Disciplines plan","award":["21RGSF0018"],"award-info":[{"award-number":["21RGSF0018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As a novel form of visual analysis technique, the Poincar\u00e9 plot has been used to identify correlation patterns in time series that cannot be detected using traditional analysis methods. In this work, based on the nonextensive of EEG, Poincar\u00e9 plot nonextensive distribution entropy (NDE) is proposed to solve the problem of insufficient discrimination ability of Poincar\u00e9 plot distribution entropy (DE) in analyzing fractional Brownian motion time series with different Hurst indices. More specifically, firstly, the reasons for the failure of Poincar\u00e9 plot DE in the analysis of fractional Brownian motion are analyzed; secondly, in view of the nonextensive of EEG, a nonextensive parameter, the distance between sector ring subintervals from the original point, is introduced to highlight the different roles of each sector ring subinterval in the system. To demonstrate the usefulness of this method, the simulated time series of the fractional Brownian motion with different Hurst indices were analyzed using Poincar\u00e9 plot NDE, and the process of determining the relevant parameters was further explained. Furthermore, the published sleep EEG dataset was analyzed, and the results showed that the Poincar\u00e9 plot NDE can effectively reflect different sleep stages. The obtained results for the two classes of time series demonstrate that the Poincar\u00e9 plot NDE provides a prospective tool for single-channel EEG time series analysis.<\/jats:p>","DOI":"10.3390\/s22166283","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T01:56:40Z","timestamp":1661133400000},"page":"6283","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Poincar\u00e9 Plot Nonextensive Distribution Entropy: A New Method for Electroencephalography (EEG) Time Series"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3459-8920","authenticated-orcid":false,"given":"Xiaobi","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghua","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"State Key Laboratory for Manufacturing Systems Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenghang","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sicong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2165-7525","authenticated-orcid":false,"given":"Xun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhicheng","family":"Teng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/S0076-6879(04)84011-4","article-title":"Sample Entropy","volume":"384","author":"Richman","year":"2004","journal-title":"Methods Enzymol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10827-010-0262-3","article-title":"Transfer entropy\u2014A model-free measure of effective connectivity for the neurosciences","volume":"30","author":"Vicente","year":"2011","journal-title":"J. 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