The stability of kernel principal components analysis and its relation to the process eigenspectrum

In this paper we analyze the relationships between the eigenvalues of the mxm Gram matrix K for a kernel k (·,.) corresponding to a sample Xl,..., Xm drawn from a density p (x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the dif (cid: 173) ferences between the two spectra and provide a performance bound on kernel peA.