The use of kernel principal component analysis to model data distributions

Abstract

We describe the use of kernel principal component analysis (KPCA) to model data distributions in high-dimensional spaces. We show that a previous approach to representing non-linear data constraints using KPCA is not generally valid, and introduce a new ‘proximity to data’ measure that behaves correctly. We investigate the relation between this measure and the actual density for various low-dimensional data distributions. We demonstrate the effectiveness of the method by applying it to the higher-dimensional case of modelling an ensemble of images of handwritten digits, showing how it can be used to extract the digit information from noisy input images.