Single-trial motor imagery electroencephalogram intention recognition by optimal discriminant hyperplane and interpretable discriminative rectangle mixture model.

Spatial filtering is widely used in brain-computer interface (BCI) systems to augmented signal characteristics of electroencephalogram (EEG) signals. In this study, a spatial domain filtering based EEG feature extraction method, optimal discriminant hyperplane-common spatial subspace decomposition (ODH-CSSD) is proposed. Specifically, the multi-dimensional EEG features were extracted from the original EEG signals by common space subspace decomposition (CSSD) algorithm, and the optimal feature criterion was established to find the multi-dimensional optimal projection space. A classic method of data dimension optimizing is using the eigenvectors of a lumped covariance matrix corresponding to the maximum eigenvalues. Then, the cost function is defined as the extreme value of the discriminant criterion, and the orthogonal N discriminant vectors corresponding to the N extreme value of the criterion are solved and constructed into the N-dimensional optimal feature space. Finally, the multi-dimensional EEG features are projected into the N-dimensional optimal projection space to obtain the optimal N-dimensional EEG features. Moreover, this study involves the extraction of two-dimensional and three-dimensional optimal EEG features from motor imagery EEG datasets, and the optimal EEG features are identified using the interpretable discriminative rectangular mixture model (DRMM). Experimental results show that the accuracy of DRMM to identify two-dimensional optimal features is more than 0.91, and the highest accuracy even reaches 0.975. Meanwhile, DRMM has the most stable recognition accuracy for two-dimensional optimal features, and its average clustering accuracy reaches 0.942, the gap between the accuracy of the DRMM with the accuracy of the FCM and K-means can reach 0.26. And the optimal three-dimensional features, for most subjects, the clustering accuracy of DRMM is higher than that of FCM and K-means. In general, the decision rectangle obtained by DRMM can clearly explain the difference of each cluster, notably, the optimization of multidimensional EEG features by optimal projection is superior to Fisher's ratio, and this method provides an alternative for the application of BCI. Supplementary Information: The online version contains supplementary material available at 10.1007/s11571-021-09768-w.