Probabilistic analysis of kernel principal components

This paper presents a probabilistic analysis of kernel principal compo-nents by unifying the theory of probabilistic principal component analy-
sis and kernel principal component analysis. It is shown that, while the
kernel component enhances the nonlinear modeling power, the proba-
bilistic structure offers (i) a mixture model for nonlinear data structure
containing nonlinear sub-structures, and (ii) an effective classification
scheme. It turns out that the original loading matrix is replaced by a
newly defined empirical loading matrix. The expectation/maximization
algorithm for learning parameters of interest is also presented.