School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
Sensors (Basel). 2022 Aug 21;22(16):6283. doi: 10.3390/s22166283.
As a novel form of visual analysis technique, the Poincaré 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, Poincaré plot nonextensive distribution entropy (NDE) is proposed to solve the problem of insufficient discrimination ability of Poincaré plot distribution entropy (DE) in analyzing fractional Brownian motion time series with different Hurst indices. More specifically, firstly, the reasons for the failure of Poincaré 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 Poincaré 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 Poincaré plot NDE can effectively reflect different sleep stages. The obtained results for the two classes of time series demonstrate that the Poincaré plot NDE provides a prospective tool for single-channel EEG time series analysis.
作为一种新颖的可视化分析技术，庞加莱图已被用于识别传统分析方法无法检测到的时间序列中的相关模式。在这项工作中，基于 EEG 的非广延性，提出了庞加莱图非广延分布熵（NDE），以解决庞加莱图分布熵（DE）在分析具有不同赫斯特指数的分数布朗运动时间序列时区分能力不足的问题。更具体地说，首先，分析了庞加莱图 DE 在分析分数布朗运动时失败的原因；其次，针对 EEG 的非广延性，引入了非广延参数，即原点与扇区环子区间之间的距离，以突出每个扇区环子区间在系统中的不同作用。为了验证该方法的有效性，使用庞加莱图 NDE 对具有不同赫斯特指数的分数布朗运动的模拟时间序列进行了分析，并进一步解释了确定相关参数的过程。此外，还对已发表的睡眠 EEG 数据集进行了分析，结果表明，庞加莱图 NDE 可以有效地反映不同的睡眠阶段。对这两类时间序列的研究结果表明，庞加莱图 NDE 为单通道 EEG 时间序列分析提供了一种有前景的工具。
