On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel-PCA.

In this paper, the relationships between the eigenvalues of the m × m Gram matrix K for a kernel k(.,.) corresponding to a sample x1,ߪ,xm, drawn from a density p(x) and the igenvalues 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. [ABSTRACT FROM AUTHOR]