A Kernel PCA Radial Basis Function Neural Networks and Application

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Abstract

This paper reviewed the classical principal components analysis methods for multivariate data analysis and feature extraction in pattern classification. A kernel-based extension to the classical PCA models was discussed to cope with nonlinear data dependencies. Kernel PCA was implicitly performing a linear PCA in some high-dimensional kernel feature space that was nonlinearly related to input space by using a suitable nonlinear kernel function mapping. And then, the conjunction of kernel PCA method and RBF neural networks was proposed in practical and algorithmic considerations. Finally, we illustrate the usefulness of kernel PCA algorithms by discussing kernel PCA RBF neural networks application in handwritten digit classification

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