Discriminant Analysis Based On Common Spatial Patterns—Euler Representation And Cross-frequency Coupling

In the field of electroencephalogram(EEG)-based brain–computer interfaces(BCIs),the technique of common spatial patterns(CSP)is a widely used method in the field of feature extraction of electroencephalogram(EEG)signals.Motivated by the fact that a cosine distance can enlarge the distance between samples of different classes,we propose the Euler CSP(e-CSP)for the feature extraction of EEG signals,and it is then used for EEG classification.The e-CSP is essentially the conventional CSP with the Euler representation.It includes the following two stages: each sample value is first mapped into a complex space by using the Euler representation,and then the conventional CSP is performed in the Euler space.Thus,the e-CSP is equivalent to applying the Euler representation as a kernel function to the input of the CSP.It is computationally as straightforward as the CSP.However,it extracts more discriminative features from the EEG signals.Extensive experimental results illustrate the discrimination ability of the e-CSP.The Euler common spatial patterns optimizes the CSP method from the aspect of distance metric.For the objective function of CSP,the calculation of covariance matrix is a very critical step,which is another optimization aspect we consider.Cross-frequency coupling(CFC)represents the interaction between different frequency bands,which can better control the complex brain network than a single frequency band and provides a new idea for research on EEG signals.In this paper,we apply amplitude–amplitude coupling(AAC)to reformulate the covariance matrices in e-CSP;as a result,the AAC-modulated e-CSP is proposed.With the proposed method,the extracted features are more detailed and more advantageous for subsequent task recognition.The proposed method is validated based on the Cho’s dataset.The experimental results illustrate the discrimination ability of the proposed method.In order to further improve the performance of the method,inspired by the theory of microstate analysis and proposes the construction of a microstate-based dynamic spatial model.In this section,the analysis of microstates based on motor imagery(MI)is investigated,and the classification experiments under each microstate label are carried out separately based on the analysis results.The experiments are all conducted based on the Cho dataset,and the experimental results show that the classification accuracy of the CFC-e CSP method is improved in the framework of microstates,and extracted spatial patterns that were more beneficial for the recognition of motor imagery tasks.We improve the CSP algorithm mainly based on two aspects,Euler representation and cross-frequency coupling,and validate all three methods on the public dataset of the BCI competition as well as the Cho dataset,and the classification accuracy of the algorithm is improved.We consider the relevance to the motor imagery task in terms of signal characteristics,and make the features extracted by the methods more detailed and recognizable while conducting intensive research on the CSP algorithm improvements.