On the eigenspectrum of the Gram matrix and the generalization error of kernel-PCA

John Shawe-Taylor, Christopher KI Williams, Nello Cristianini, Jaz Kandola

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper the relationships between the eigenvalues of the m × m Gram matrix K for a kernel κ(·, ·) corresponding to a sample x1,..., xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem is analysed. The differences between the two spectra are bounded and a performance bound on kernel PCA is provided showing that good performance can be expected even in very high dimensional feature spaces provided the sample eigenvalues fall sufficiently quickly
Original languageEnglish
Pages (from-to)2510-2522
Number of pages13
JournalIEEE Transactions on Information Theory
Volume51
Issue number7
DOIs
Publication statusPublished - 2005

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