Common Spatial Pattern with L21-Norm

As one of the most commonly used algorithms in the field of feature extraction, common spatial pattern (CSP) has a good effect on multichannel electroencephalogram (EEG) signal classification, especially for motor imagery-based signals. However, the formulation of the conventional CSP based on the L2-norm is sensitive to outliers. Whereas the L1-norm-based common spatial pattern (CSP-L1) proposed in recent years can seek robust spatial filters to effectively alleviate the impact of outliers, the L1-norm is unable to characterize the geometric structure of the data well. To further improve the robustness of CSP, in this paper, we propose a new extension to CSP called the L21-norm-based common spatial pattern (CSP-L21), which is formulated by using the L21-norm rather than the L2-norm. Moreover, CSP-L21 has the advantages of rotational invariance and geometric structure characterization. We provide a non-greedy iterative algorithm to maximize the objective function of CSP-L21. Experiments on a toy example and three popular data sets of BCI competitions illustrate that the proposed method can efficiently extract discriminative features.