The Stability of Kernel Principal Components Analysis and its Relation to the Process Eigenspectrum

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Christopher Williams, John Shawe-taylor


In this paper we analyze the relationships between the eigenvalues of the m x m Gram matrix K for a kernel k(ยท, .) corresponding to a sample Xl, ... ,Xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the dif(cid:173) ferences between the two spectra and provide a performance bound on kernel peA.