Supervised categorized principal component analysis for imagined speech classification via applying singular value decomposition on a symmetry matrix

Abstract

The dimension of the feature vectors for performing the imagined speech is large. Hence, it is required to reduce their dimension as well as perform the classification simultaneously. This is a categorized principal component analysis (CatPCA) problem. However, the conventional CatPCA methods are unsupervised learning methods and the design of the unitary matrix in the conventional principal component analysis (PCA) algorithms is only based on the PCA approach. Therefore, the classification performance is limited. This paper proposes a supervised CatPCA approach for performing the imagined speech classification. Also, the objective function of an optimization problem for designing the unitary matrix is formulated based on both the PCA algorithm and the k means algorithm. To find the analytical solution of the optimization problem, a property on computing the singular value decomposition (SVD) of a symmetric matrix is employed. Then, the design of the cluster centers in the k means algorithm is formulated as a quadratic programming. Finally, the above two procedures are iterated until the algorithm converges. Since the analytical solutions of these two optimization problems can be derived analytically, the required computational power for finding the solution of the optimization problem is low. To demonstrate the effectiveness of our proposed CatPCA algorithm, the Track 3 of the International brain computer interface (BCI) Competition Database is employed as the dataset for performing the performance evaluation. The computer numerical simulation results show that our proposed CatPCA algorithm yields the higher classification accuracy compared to PCA variants and the dimension reduction related algorithms. Also, the required execution time of our proposed method is lower than those of the states of the arts methods. This demonstrates the effectiveness and the efficiency of our proposed CatPCA algorithm.