Statistical properties of kernel principal component analysis

摘要

The main goal of this paper is to prove inequalities on the reconstruction error for kernel principal component analysis. With respect to previous work on this topic, our contribution is twofold: (1) we give bounds that explicitly take into account the empirical centering step in this algorithm, and (2) we show that a “localized” approach allows to obtain more accurate bounds. In particular, we show faster rates of convergence towards the minimum reconstruction error; more precisely, we prove that the convergence rate can typically be faster than n −1/2. We also obtain a new relative bound on the error.