Probabilistic Analysis of Kernel Principal Components

This paper presents a probabilistic analysis of kernel prin cipal components by unifying the theory of probabilistic principal com ponent analysis and kernel principal component analysis. It is shown tha t, while the kernel component enhances the nonlinear modeling power, th probabilistic structure offers (i) a mixture model for nonlinear data structure containing nonlinear sub-structures, and (ii) an effectiv e classification scheme. It turns out that the original loading matrix is repl aced by a newly defined empirical loading matrix. The expectation/ma xi ization algorithm for learning parameters of interest is also prese nted.