Lp/q-Norm Based Common Spatial Patterns

Brain-computer interface(BCI)can collect and analyze signals generated by the brain,and translates these signals into machine commands that are transmitted to devices to control them to perform specific tasks.Common spatial pattern(CSP)is a pure data-driven multi-channel spatial filtering method,which minimizes one class of variance while maximizing another class of variance.In the brain-computer interface system based on electroencephalogram(EEG)signals,CSP has a better effect in signal feature extraction,so it has been a research hotspot in the classification of EEG based on motor imagination(MI).However,the objective function of CSP can be regarded as a form based on the L2-norm,this method is susceptible to noises,so it is impossible to obtain an accurate estimation of the covariance matrix.In addition,the CSP only calculates the global spatial covariance matrix to solve the spatial filter,and does not include the local temporal information in the EEG data.To reduce the influence of outliers on CSP and obtain a robust EEG feature extraction method,common spatial pattern with mixed Lp-and Lq-norms(CSP-Lp/q)is proposed.This method is based on CSP and introduces the concept of mixed norms for modeling.That is,the differences between the classes are fully considered when defining the divergence of the data,and the variances of the two classes are calculated by using the method based on Lp-and Lq-norms(0 < p,q <2).Theoretically,the model based on mixed Lp/q-norm has better stability and robustness.This paper also proposes an iterative algorithm to solve the spatial filtering vector of CSP-Lp/q,and verifies the effectiveness of this iterative algorithm.To solve the lack of local temporal information in CSP,local temporal joint recurrence common spatial pattern(LTJRCSP)is proposed,which considers local temporal information.In theory,LTJRCSP introduces joint recurrence rate(JRR)of local time,which has better interpretation of neurophysiology.Considering the concepts of local temporal information and mixed norms to improve CSP,local temporal joint recurrence common spatial pattern with mixed Lp-and Lq-norms(LTJRCSP-Lp/q)is proposed.This method introduces the mixed norm and joint recurrence rate while performing covariance estimation to obtain features that contain more discriminative information.Linear discriminant analysis(LDA)is used to classify the extracted features.On three datasets of BCI competition of EEG based on motor imagination,experiments are performed on the three proposed methods for comparison.The experimental results prove that CSP-Lp/q,LTJRCSP and LTJRCSP-Lp/q proposed in this paper are robust,and can obtain better spatial filtering vectors which can extract more discriminative features.