The stochastic approximation method for adaptive Bayesian classifiers: Towards online brain-computer interfaces

Recent developments of brain-computer interfaces (BCIs) bring forward some challenging problems to the machine learning community, of which classification of time-varying electrophysiological signals is a crucial one. Constructing adaptive classifiers is a promising approach to deal with this problem. In this paper, Bayesian classifiers with Gaussian mixture models (GMMs) are adopted to classify electroencephalogram (EEG) signals online. We propose to use the stochastic approximation method (SAM) as the specific gradient descent method for parameter update and systematically derive the instantaneous gradient formulas with respect to mean values and covariance matrices in the distributions of a GMM. With SAM, the parameters of mean values and covariance matrices embodied in the Bayesian classifiers can be simultaneously updated in a batch mode. The online simulation of EEG classification tasks in a BCI shows the effectiveness of the proposed SAM.