1Robust Common Spatial filters with a Maxmin Approach Motoaki Kawanabe1†∗, Wojciech Samek2†

Electroencephalographic signals are known to be non-stationary and easily affected by artifacts, therefore their analysis requires methods that can deal with noise. In this work we present a way to robustify the popular Common Spatial Patterns (CSP) algorithm under a maxmin approach. In contrast to standard CSP that maximizes the variance ratio between two conditions based on a single estimate of the class covariance matrices, we propose to robustly compute spatial filters by maximizing the minimum vari-ance ratio within a prefixed set of covariance matrices called the tolerance set. We show that this kind of maxmin optimization makes CSP robust to outliers and reduces its tendency to overfit. We also present a data driven approach to construct a tolerance set that captures the actual variability of the covariance matrices over time and show its ability to reduce non-stationarity of the extracted features and to sig-nificantly improve the classification accuracy. We test the spatial filters derived with this approach and compare them to standard CSP and to a state-of-the-art method on a real world brain-computer interface (BCI) data set in which we expect substantial fluctuations caused by environmental differences. Finally we investigate the advantages and limitations of the maxmin approach with simulations