Refined composite multivariate multiscale fuzzy dispersion entropy: Theoretical analysis and applications

Multivariate multiscale sample entropy (mvMSE) is a popular method to quantify the irregularity of multi-channel time series. However, mvMSE generates either undefined or unreliable results for short-length signals and has a high computational cost. To address these issues, multivariate multiscale dispersion entropy (mvMDE) was recently developed, but it depends on its parameters and overlooks some data information. To address these limitations, we herein propose an extension of fuzzy dispersion entropy (FDE) by incorporating fuzzy set theory, multidimensional embedding reconstruction theory, and dispersion patterns. This leads to the multivariate multiscale FDE (mvMFDE) and refined composite mvMFDE (RCmvMFDE) measures. (RC)mvMFDE is the first multivariate analysis based on Shannon entropy that uses the fuzzification concept. Some sets of time series have been synthesized and analyzed using several concepts in multivariate signal processing to evaluate the advantages of our introduced mvMFDE and RCmvMFDE. The results indicated that the proposed methods are less sensitive to their parameters, signal length, and noise, providing more stable results compared to the existing approaches mvMSE and mvMDE. On multi-channel noise signals and bivariate autoregressive processes, mvMSE, mvMDE, and mvMFDE produced similar finding although mvMFDE exhibited superior discriminative capabilities. When applied to one physiological dataset and two mechanical datasets, RCmvMFDE distinguished the diverse dynamics of multichannel signals exceptionally well.