On the convergence of eigenspaces in kernel principal component analysis

This paper presents a non-asymptotic statistical analysis of Kernel-PCA with a focus different from the one proposed in previous work on this topic. Here instead of considering the reconstruction error of KPCA we are interested in approximation error bounds for the eigenspaces them-selves. We prove an upper bound depending on the spacing between eigenvalues but not on the dimensionality of the eigenspace. As a conse-quence this allows to infer stability results for these estimated spaces. 1 Introduction. Principal Component Analysis (PCA for short in the sequel) is a widely used tool for data dimensionality reduction. It consists in nding the most relevant lower-dimension projec-tion of some data in the sense that the projection should keep as much of the variance of the original data as possible. If the target dimensionality of the projected data is xed i