Refined Composite Multiscale Dispersion Entropy: A Fast Measure of Complexity

Multiscale entropy (MSE) was proposed to overcome the deficiencies of conventional entropy methods when quantifying the complexity of time series. However, MSE is not fast enough for real-time applications because of the use of sample entropy (SampEn). Here, we introduce multiscale DisEn (MDE) as a very fast and powerful method to quantify the complexity of signals. MDE is based on our recently developed DisEn, which has a computation cost of O(N), compared with O(N) for SampEn. We also propose the refined composite MDE (RCMDE) to improve the reliability and stability of MDE, especially for short signals. To evaluate the proposed methods, we employ white Gaussian and 1/f noises to discriminate the concept of irregularity from complexity. Moreover, we use logistic map to understand the ability of MDE and RCMDE to detect changes from periodicity to non-periodic nonlinearity. We also employ two publicly-available datasets to illustrate the application of our method to real-world signals. The results show a similar behaviour of RCMSE and RCMDE, although the latter is significantly faster. The results also show more stability and reliability of RCMDE than MDE, especially for short signals. Thus, this novel measure is expected to be useful for the analysis of real signals thanks to its ability to distinguish different types of dynamics.