Kernel PCA Pattern Reconstruction via Approximate Pre-Images

This work has shown that the reconstruction of patterns from their largest nonlinear principal components, a technique which is common practice in linear principal component analysis, can be performed using a kernel without explicitly working in F.

Abstract

Algorithms based on Mercer kernels construct their solutions in terms of expansions in a high-dimensional feature space F. Previous work has shown that all algorithms which can be formulated in terms of dot products in F can be performed using a kernel without explicitly working in F. The list of such algorithms includes support vector machines and nonlinear kernel principal component extraction. So far, however, it did not include the reconstruction of patterns from their largest nonlinear principal components, a technique which is common practice in linear principal component analysis. The present work proposes an idea for approximately performing this task. As an illustrative example, an application to the de-noising of data clusters is presented.