Analysis of EEG data using a geometric-based ICA algorithm

Electroencephalographic (EEG) signals are used as a non-invasive clinical tool for the diagnosis and treatment of brain deaseases. However, they are often disturbed by artifacts which limit the possibility to interpret the data. Independent Component Analysis (ICA) is able to recover n independent sources [s\vec](t) which are linearly mixed by an unknown mixing process [x\vec](t) = A [s\vec](t). Various ICA-algorithms have been successfully applied for discovering the artifacts in the EEG data and correcting the signals. We propose a geometric algorithm for the detection of artifacts in the EEG signals. The set of all probability distributions of the mixtures [x\vec]i(t) forms a hyperparallelepiped in the observation space. By taking n vectors [w\vec]i each one located at the edges of the cone that contains the mixing space, as column vectors of a matrix W, we obtain a matrix similar to the mixing matrix A. Considering n vectors [e\vec]1,...,[e\vec]n their angular proximity gn is given by gn = ai = 1n-1 aj = i+1n cos[[e\vec]i, [e\vec]j] It can be shown, that by maximizing gn the corresponding vectors [w\vec]i for the matrix W and thus the mixing matrix A can be evaluated. After using PCA in order to reduce the dimensions, the proposed algorithms were able to find up to five clearly definable artifacts which were similar to those found by different algorithms.