Multiclass Common Spatial Patterns and Information

We address two shortcomings of the common spa- tial patterns (CSP) algorithm for spatial filtering in the context of brain-computer interfaces (BCIs) based on electroencephalogra- phy/magnetoencephalography (EEG/MEG): First, the question of optimality of CSP in terms of the minimal achievable classification error remains unsolved. Second, CSP has been initially proposed for two-class paradigms. Extensions to multiclass paradigms have been suggested, but are based on heuristics. We address these short- comings in the framework of information theoretic feature extrac- tion (ITFE). We show that for two-class paradigms, CSP maximizes an approximation of mutual information of extracted EEG/MEG components and class labels. This establishes a link between CSP and the minimal classification error. For multiclass paradigms, we point out that CSP by joint approximate diagonalization (JAD) is equivalent to independent component analysis (ICA), and provide am ethod to choose those independent components (ICs) that ap- proximately maximize mutual information of ICs and class labels. This eliminates the need for heuristics in multiclass CSP, and al- lows incorporating prior class probabilities. The proposed method is applied to the dataset IIIa of the third BCI competition, and is shown to increase the mean classification accuracy by 23.4% in comparison to multiclass CSP.