%0 Journal Article %J NIPS %D 2004 %T Probabilistic analysis of kernel principal components %A Zhou, S. %A Chellapa, Rama %A Moghaddam, B. %X 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. %B NIPS %8 2004/// %G eng