Online prediction model based on Reduced Kernel Principal Component Analysis

This paper proposes a new technique for online identification of a nonlinear system modeled on reproducing kernel Hilbert space (RKHS) using kernel method. This new method uses the reduced kernel principal component analysis (RKPCA) to update the principal component which represent the observations selected by the kernel principal component analysis method (KPCA). The KPCA is a nonlinear extension of principal component analysis (PCA) to RKHS as it transforms the input data by a nonlinear mapping from the input space into a high dimensional feature space to which the PCA is performed. The proposed technique may be very helpful to design an adaptive control strategy of nonlinear systems.