On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel-PCA
John S. Shawe-Taylor, Chris K. Williams, Nello Cristianini, Jaz Kandola · IEEE Transactions on Information Theory · 2005
In this paper, the relationships between the eigenvalues of the m/spl times/m Gram matrix K for a kernel /spl kappa/(/spl middot/,/spl middot/) corresponding to a sample x/sub 1/,...,x/sub 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.