Regularizing common spatial patterns to improve BCI designs: unified theory and new algorithms.

One of the most popular feature extraction algorithms for brain-computer interfaces (BCI) is common spatial patterns (CSPs). Despite its known efficiency and widespread use, CSP is also known to be very sensitive to noise and prone to overfitting. To address this issue, it has been recently proposed to regularize CSP. In this paper, we present a simple and unifying theoretical framework to design such a regularized CSP (RCSP). We then present a review of existing RCSP algorithms and describe how to cast them in this framework. We also propose four new RCSP algorithms. Finally, we compare the performances of 11 different RCSP (including the four new ones and the original CSP), on electroencephalography data from 17 subjects, from BCI competition datasets. Results showed that the best RCSP methods can outperform CSP by nearly 10% in median classification accuracy and lead to more neurophysiologically relevant spatial filters. They also enable us to perform efficient subject-to-subject transfer. Overall, the best RCSP algorithms were CSP with Tikhonov regularization and weighted Tikhonov regularization, both proposed in this paper.