Multivariate improved weighted multiscale permutation entropy and its application on EEG data

Abstract

This paper introduces an entropy based method that measures complexity in non-stationary multivariate signals. This method, called Mutivariate Improved Weighted Multiscale Permutation Entropy (mvIWMPE), has two main advantages: (i) it shows lower variance for the results when applied on a wide range of multivariate signals; (ii) it has good accuracy quantifying complexity of different recorded states in signals and hence discriminating them. mvIWMPE is based on two previously introduced permutation entropy algorithms, Improved Multiscale Permutation Entropy (IMPE) and Multivariate Weighted Multiscale Permutation Entropy (mvWMPE). It combines the concept of coarse graining from IMPE and the introduction of the weight of amplitudes of the signals from mvWMPE. mvIWMPE was validated on both synthetic and human electroencephalographic (EEG) signals. Several synthetic signals were simulated: mixtures of white Gaussian noise (WGN) and pink noise, chaotic and convergent Lorenz system signals, stochastic and deterministic signals. As for real signals, resting-state EEG recorded in healthy and epileptic children during eyes closed and eyes open sessions were analyzed. Our method was compared to multivariate multiscale, multivariate weighted multiscale and multivariate improved multiscale permutation entropy methods. Performance on synthetic as well as on EEG signals showed more undeviating results and higher ability for mvIWMPE discriminating different states of signals (chaotic vs convergent, WGN vs pink noise, stochastic vs deterministic simulated signals, and eyes open vs eyes closed EEG signals). We herein proposed an efficient method to measure the complexity of multivariate non-stationary signals. Experimental results showed the accuracy and the robustness (in terms of variance) of the method.