Lp-norm-based Local Temporal Common Spatial Patterns

Common spatial patterns(CSP),as one of the effective feature extraction methods,is widely used for classification of electroencephalogram(EEG)-based brain-compute interface(BCI)system.However,CSP is prone to be affected by the appearance of singula value,outliers and noise in EEG signals.As an extension of CSP,local temporal correlation common spatial patterns(LTCCSP)can extract more discriminative features by introducing the local temporal correlation information into the covariance modelling of the classical CSP algorithm.But the L2-norm-based mathematical expression of these methods implies that it is sensitive to the presence of outliers.Moreover,the lack of neural phase synchronization leads to the worse performance of these methods.In order to further improve the robustness of the classification,in this paper,we generalize the LTCCSP algorithm by replacing the L2-norm with Lp(0<p<2)-norm in the objective function,called Lp-norm-based LTCCSP(LTCCSP-Lp).Meanwhile,an elegant iterative algorithm is designed under the framework of minorization-maximization(MM)optimization algorithm to solve the optimal spatial filters of LTCCSP-Lp.The iterative solution is justified in theory and the effectiveness of our novel proposed method is verified by experimental results on a 2-D artifical dataset and three publicly available real EEG datasets of BCI competitions.Besides,the study proposes a phase synchronization CSP algorithm namely local temporal phase locking value common spatial patterns(LTPCSP)by introducing the synchronizing information of nerual activity into the covariance modelling of the classical CSP algorithm.Then the study further proposes the Lp-norm-based LTPCSP(LTPCSP-Lp)by generalizing the LTPCSP algorithm with well performance and thereby owns more neurophysiological interpretation.