Dimensionality reduction of RKHS model using Reduced Kernel Principal Component Analysis (RKPCA)

This paper deals with the problem of complexity reduction of RKHS models developed on the Reproducing Kernel Hilbert Space (RKHS) using the statistical learning theory (SLT) devoted to supervised learning problems. However, the provided RKHS model suffers from the parameter number which equals the observations used in the learning phase. In this paper we propose a new way to reduce the number of parameters of RKHS model. The proposed method titled Reduced Kernel Principal Component Analysis (RKPCA) consists on approximating the retained principal components given by the KPCA method by a set of observation vectors which point to the directions of the largest variances with the retained principal components. The proposed method has been tested on a chemical reactor and the results were successful.