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 the m × m Gram matrix K for a kernel k(.,.) corresponding to a sample x1, . . . , xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel PCA.