On the eigenspectrum of the Gram matrix and the generalization error of kernel-PCA
IEEE Transactions on Information Theory, 51 (7):
2510--2522 (2005)Abstract
In this paper, the relationships between the eigenvalues of the m*m Gram matrix K for a kernel corresponding to a sample x_1,...,x_m drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem is analyzed. The differences between the two spectra are bounded and a performance bound on kernel principal component analysis (PCA) is provided showing that good performance can be expected even in very-high-dimensional feature spaces provided the sample eigenvalues fall sufficiently quickly.