Complexity Analysis of Electroencephalographic Data

Abstract

This project investigates whether it is possible to correlate changes in the EEG structure with changes in the complexity of the original signal. Based on the assumption that the complexity of the EEG is due to the non-linear interaction of a few degrees of freedom, dynamical embedding of the EEG is performed to capture the dynamics of local sections of the underlying manifold, which are smooth non-linear fitting surfaces. Singular value decomposition (SVD) projects these sections of the manifold onto orthogonal axes that retain maximum variance, thereby identifying the degrees of freedom associated with the original EEG signal. Furthermore we assume that any change in the interaction of these degrees of freedom indicates a change in the brain state of the subject. We model this interaction by applying two measures of complexity, (i) entropy and (ii) Fisher’s information content. Finally we performed experiments to see if changes in complexity corresponded to changes in the structure of the EEG and compared the performance of the two measures.