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.
Keywords: Poincaré plot; distribution entropy; nonextensive; sector ring subinterval.