Orthogonal Series Density Estimation and the Kernel Eigenvalue Problem

Kernel principal component analysis has been introduced as a method of extracting a set of orthonormal nonlinear features from multi-variate data and many impressive applications are being reported within the literature. This paper presents the view that the eigenvalue decomposition of a kernel matrix can also provide the discrete expansion coefficients required for a non-parametric orthogonal series density estimator. In addition to providing novel insights into non-parametric density estimation this paper provides an intuitively appealing interpretation for the nonlinear features extracted from data using kernel principal component analysis.