Optimizing Spatial Filters for BCI: Margin- and Evidence-Maximization Approaches.

We present easy-to-use alternatives to the often-used two-stage Common Spatial Pattern + classifier approach for spatial filtering and classification of Event-Related Desynchronization signals in BCI. We report two algorithms that aim to optimize the spatial filters according to a criterion more directly related to the ability of the algorithms to generalize to unseen data. Both are based upon the idea of treating the spatial filter coefficients as hyperparameters of a kernel or covariance function. We then optimize these hyper-parameters directly along side the normal classifier parameters with respect to our chosen learning objective function. The two objectives considered are margin maximization as used in Support-Vector Machines and the evidence maximization framework used in Gaussian Processes. Our experiments assessed generalization error as a function of the number of training points used, on 9 BCI competition data sets and 5 offline motor imagery data sets measured in Tubingen. Both our approaches sho w consistent improvements relative to the commonly used CSP+linear classifier combination. Strikingly, the improvement is most significant in the higher noise cases, when either few trails are used for training, or with the most poorly performing subjects. This a reversal of the usual "rich get richer" effect in the development of CSP extensions, which tend to perform best when the signal is strong enough to accurately find their additional parameters. This makes our approach particularly suitable for clinical application where high levels of noise are to be expected.