Multivariate Multiscale Variations Dispersion Entropy and Multivariate Multiscale Variations Fuzzy Dispersion Entropy for Time-Series Analysis

Entropy serves as an effective nonlinear dynamic indicator of time series complexity. A number of multivariate entropy methods exist and are effectively used in signal analysis. Existing multivariate entropy methods are, however, limited in capturing cross-channel and within-channel information. In order to address these limitations and represent a wide range of scale information, we propose multivariate multiscale variations dispersion entropy (mvMVDE); moreover, to reduce the loss of signal information of mvMVDE, we develop multivariate multiscale variations fuzzy dispersion entropy (mvMVFDE) based on fuzzy membership functions. Experiments with simulated signals indicate that the proposed methods can better detect nonlinear dynamic changes in signals and exhibit reduced sensitivity to parameters, signal length, and noise, yielding more stable outcomes than mvMSE and mvMDE. Real-world experiments on electroencephalogram (EEG) signals, furthermore, show that mvMVDE and mvMVFDE demonstrate a notable advantage in discerning the distinct dynamics of multichannel signals, and the accuracy of mvMVDE and mvMVFDE is higher than that of the popular mvMSE and mvMDE. In this study, we propose two valuable signal detection methods, each with its own performance advantages: the mvMVDE is fast, while the mvMVFDE has high accuracy.