Learning optimal spatial filters by discriminant analysis for brain–computer-interface

Common Spatial Pattern (CSP) is one of the most widespread methods for Brain–Computer Interfaces (BCI), which is capable of enhancing the separability of the brain signals such as multi-channel electroencephalogram (EEG). CSP attempts to strengthen the separability by maximizing the variance of the spatially filtered signal of one class while minimizing it for another class. A straightforward way to improve the CSP is to employ the Fisher–Rao linear discriminant analysis (FLDA). But for the two-class scenario in BCI, FLDA merely result in as small as one filter. Experimental results have shown that the number of spatial filter is too small to achieve satisfying classification accuracy. Therefore, more than one filter is expected to get better performance. To deal with this difficulty, in this paper we propose to divide each class into many sub-classes (clusters) and formulate the problem in a re-designed graph embedding framework where the vertexes are cluster centers. We also reformulate the traditional FLDA in our graph embedding framework, which helps developing and understanding the proposed method. Experimental results demonstrate the advantages of the proposed method.