Dimensionality reduction of sample covariance matrices by graph fourier transform for motor imagery brain-machine interface

An efficient method for dimensionality reduction in classification of multi-class electroencephalogram (EEG) during motor imagery (MI) aiming at brain-machine interfacing is proposed. In this method, the reduction of dimensions is achieved by spectral decomposition of a given graph, which is defined by a geometrical distribution of electrodes on the head surface. The resulting subspace reduces the dimension of EEG signals, and therefore, the size of the sample co-variance matrix (SCM) of EEG can also be reduced. The reduction method is combined with a differential geometry-based approach called tangent space mapping (TSM) that can map a SCM in a Riemannian manifold onto an element in an Euclidean space called a tangent space. Thus, any machine learning algorithm that works in the Euclidean space can be applied. Results of two-class and four-class classification of EEG during MI show that the proposed method of dimensionality reduction increases the recognition accuracy even in the case of a training dataset having a small number of elements.