L21-Norm Based Common Spatial Patterns

With the development of intelligent technology and the deepening of brain science research,electroencephalography(EEG),which is dedicated to the mining of brain functional information,has quickly gained its place in the field of brain-computer interface(BCI)systems due to its low management cost and high time resolution.The accurate recognition of motor imagination(MI)task based on brain-computer interface(BCI)is always a key issue in intelligent rehabilitation.As one of the most commonly used feature extraction methods,common spatial patterns(CSP)have good performance in the classification of multi-channel EEG signals.However,the objective function expression of the traditional CSP algorithm is based on the square of Euclidean distance,which makes the performance of the method easily affected by outliers and noise.Therefore,finding more robust and sparse CSP improvement methods has become a research hotspot in recent years.In this paper,L21-norm based common spatial patterns(CSP-L21)algorithm is proposed to measure the covariance matrix of EEG data by using L21-norm instead of the divergence expression of L2-norm.The influence of noise and outliers is suppressed,and the geometric structure of data can be described well.At the same time,this paper proposes a non-greedy iterative algorithm by constructing auxiliary functions,and using the subgradient algorithm and Armijo line search method to solve the optimization problem of the objective function of the CSP-L21 algorithm.The convergence of the iterative algorithm is proved theoretically.And experiments are carried out on one simulated data set and three public real EEG-based BCI competition datasets respectively.The results verify the effectiveness of the proposed algorithm.To solve the overfitting problem of the algorithm in the case of small samples,this paper adds a penalty term with L21-norm to the CSP-L21 algorithm.It is called regularized common spatial patterns with the L21-norm(RCSP-L21)algorithm.Based on the combination of group sparsity and regularization,this paper redefines the optimization problem of classical CSP method,realizes the idea of sparse and robust modeling at the same time.Besides,an effective iterative algorithm is designed to solve the proposed non-smooth and non-convex optimization problem.In order to further improve the robustness of the algorithm classification,this paper also considers the upper bound operation of the L21-norm.The proposed capped L21-norm based common spatial patterns(CCSP-L21)algorithm is designed to mitigate the effects of some extreme outliers which signal amplitude is much higher than that of the normal signal.The model with better stability and robustness is obtained.Linear discriminant analysis(LDA)is used as a classifier in this paper to compare the above three methods and some classical extensions on the three real EEG datasets of BCI competitions.The results show that the three methods proposed in this paper can obtain more discriminant features and improve the recognition rate of classification.