On the Eigenspectrum of the Gram Matrix and the Generalisation Error of Kernel PCA
John Shawe-Taylor, Christopher Williams, Nello Cristianini and Jaz Kandola
IEEE Transactions on Information Theory
In this paper we analyze the relationships between the eigenvalues of the m x m Gram matrix K for a kernel ·(.;.) 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 showing that we can expect good performance even in very high dimensional feature spaces provided the sample eigenvalues fall sufficiently quickly.