Multivariate Multiscale Entropy Analysis

TL;DR: This work first introduces multivariate sample entropy (MSampEn) and evaluates it over multiple time scales to perform the multivariate multiscale entropy (MMSE) analysis, which makes it possible to assess structural complexity of multivariate physical or physiological systems, together with more degrees of freedom and enhanced rigor in the analysis.

Abstract: Multivariate physical and biological recordings are common and their simultaneous analysis is a prerequisite for the understanding of the complexity of underlying signal generating mechanisms. Traditional entropy measures are maximized for random processes and fail to quantify inherent long-range dependencies in real world data, a key feature of complex systems. The recently introduced multiscale entropy (MSE) is a univariate method capable of detecting intrinsic correlations and has been used to measure complexity of single channel physiological signals. To generalize this method for multichannel data, we first introduce multivariate sample entropy (MSampEn) and evaluate it over multiple time scales to perform the multivariate multiscale entropy (MMSE) analysis. This makes it possible to assess structural complexity of multivariate physical or physiological systems, together with more degrees of freedom and enhanced rigor in the analysis. Simulations on both multivariate synthetic data and real world postural sway analysis support the approach.