Efficient synchronization estimation for complex time series using refined cross-sample entropy measure

Efficient and robust synchronization estimation, namely refined cross-sample entropy (RCSE) measure, is presented in this study to analyze complex time series. Unlike the original cross-sample entropy (CSE) that relies on a fixed tolerance r , the proposed RCSE is based on a concept called the cumulative histogram method (CHM) to gain a range of entropy values with different r selections in a certain range. Moreover, the dissimilarity measure in RCSE is redefined, rather than the distance function used in the CSE. Trials are conducted over both simulated and real-world data for providing a comparative study. The original CSE is introduced as a comparison to testify that the proposed RCSE is capable of drawing more specific relationships from time series, and it is also a superior method to describe the synchronization between them. The results show that the new method is capable of distinguishing different kinds of time series and possesses robustness in the noise test. It is suggest that the proposed RCSE may potentially become a new reliable method for synchronization estimation of complex time series. (C) 2020 Elsevier B.V. All rights reserved.