Dimensionality reduction with isomap algorithm for EEG covariance matrices

This paper presents new approach to braincomputer interface construction. Most algorithms for EEG classification use spatial covariance matrices, that contain information about synchronisation and desynchronisation in human brain. Suggested algorithm involves Riemannian geometry in the space of symmetric and positive-definite matrices to measure distances between covariance matrices in more accurate fashion. Then Isomap algorithm is applied to the Riemannian pairwise distances to locate manifold, corresponding to human EEG signals, and arrange points, corresponding to covariance matrices, in low-dimensional space, preserving geodesical distances. Finally, linear discriminant analysis is applied for classification. Suggested algorithm is tested on Berlin BCI dataset and compared with state-of-the-art algorithms common spatial patterns and classification in tangent space.