Multichannel EEG Signal Classification -A Geometric Approach

Abstract

<p> The study of the different sleep stages of a patient using his/her recorded EEG signals falls in the area of signal classification. In general, this involves extracting from the EEG signals, a signal feature on which the classification is performed. In this thesis, we apply the techniques of signal classification to the analysis of the sleep of a patient. The feature we use is the power spectral density (PSD) matrices of a multi-channel EEG signal. This not only allows us to examine the power spectrum contents of each signal which complies with what clinical experts use in their visual judgement of EEG signals, but also allows the correlation between the multi-channel signals to be studied. To establish a metric facilitating the classification, we analyze the structure as well as exploit the specific geometric properties of the space of PSD matrices. Specifically, we study this space from the viewpoint of Riemannian manifolds. We apply a Riemannian metric and, with the aid of fibre bundle theory, develop intrinsic (geodesic) distance measures for the PSD matrix manifold. To utilize such new distance measures effectively for EEG signal classification, we need to find a suitable weighting matrix for the PSD matrices so that the distances between similar features are minimized while those between dissimilar features are maximized. A closed form expression for this weighting matrix is obtained by solving an equivalent convex optimization problem. The effectiveness of using these novel weighted distance measures is verified by applying them to the sleep pattern classification of a collection of recorded EEG signals using the k-nearest neighbor decision algorithm with excellent results. </p>