Kullback-Leibler Penalized Sparse Discriminant Analysis for Event-Related Potential Classification

A brain computer interface (BCI) is a system which provides direct communication between the mind of a person and the outside world by using only brain activity (EEG). The event-related potential (ERP)-based BCI problem consists of a binary pattern recognition. Linear discriminant analysis (LDA) is widely used to solve this type of classification problems, but it fails when the number of features is large relative to the number of observations. In this work we propose a penalized version of the sparse discriminant analysis (SDA), called Kullback-Leibler penalized sparse discriminant analysis (KLSDA). This method inherits both the discriminative feature selection and classification properties of SDA and it also improves SDA performance through the addition of Kullback-Leibler class discrepancy information. The KLSDA method is design to automatically select the optimal regularization parameters. Numerical experiments with two real ERP-EEG datasets show that this new method outperforms standard SDA.