Feature extraction and denoising using kernel PCA

Abstract

Kernel PCA methodology, an elegant nonlinear generalization of the linear PCA, is illustrated by considering the examples of (i) denoising chaotic time series and, (ii) prediction of properties of polymer nanocomposites developed in our laboratory. Kernel PCA captures the dominant nonlinear features of the original data by transforming it to a high dimensional feature space. An appropriately defined kernel function allows the computations to be performed in the original input space and facilitates extraction of substantially higher number of principal components enabling excellent denoising and feature extraction capabilities. Use of simple matrix algebra in simulations makes the method an attractive alternative to some hard optimization based methodologies.