Random matrix theory analysis of EEG data

Abstract

In this study, we first construct the empirical cross-correlation matrices in the EEG signals by the Pearsons correlation coefficient. Then, we apply random matrix theory (RMT) investigate the statistical properties of cross-correlations in EEG data. The EEG signals of Alzheimer's disease (AD) subjects are chosen as the research objects. Here, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues. Meanwhile, we identify the deterministic or stochastic dynamics of the EEG system based on RMT. The correlation matrix of a Wishart matrix or a Gaussian Wigner matrix in random matrix theory has a structure similar to that of EEG data. For a noisy signal, its eigenvalue statistics are closely those of random matrix ensembles. The results show that the EEG signals are different from the stochastic time series.