On the eigenspectrum of the Gram matrix and its relationship to the operator eigenspectrum

In this paper we analyze the relationships between the eigenvalues of them х m Gram matrix K for a kernel k(·, ·) corresponding to a sample x1, . . . , xm drawn from a density p(x) and and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel PCA.