The fundamentals of two kernel-based learning algorithms

which are kernel principal component analysis (KPCA) and support vector machines (SVM)

are introduced.An estimation formula of upper bound of generalization error is given to estimate the optimal kernel parameters and penalization factor of the SVM.Six-channel EEG data were recorded from four subjects while they performed three different mental tasks.A multivariate autoregressive (MVAR) model is applied to extract the features of EEG.The dimensionality of the feature vectors formed by the coefficients of MVAR models is reduced by KPCA first.Then the feature vectors with lower size are used as inputs of SVM with optimal parameters to train and test classification accuracy for three mental tasks.The classification accuracies indicate that the KPCA technique is a powerful feature selector in high-dimensional feature space

and optimal SVM can get optimal results which are significantly better than that of Radial Basis Function (RBF) network.The average classification accuracy over three mental tasks of four subjects achieves 78.6%.