Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system

We propose a method that combines single-trial classification and channel/basis selection in a single regularized empirical risk minimization problem. We use the linear sum of the Euclidian norms of the columns of the coefficient matrix as the regularizer. This penalty enables us to select rows and columns of the coefficient matrix, which correspond to a subset of the channels or a subset of basis functions, in a systematic manner. Moreover, the parameter learning can be performed in a convex optimization problem with second order cone constraints. The method is demonstrated on P300 speller dataset (dataset II) from the BCI competition III. The method performs reasonably well with small number of electrodes/basis functions.