PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Statistical Properties of Kernel Principal Component Analysis
Olivier Bousquet, Laurent Zwald and Gilles Blanchard
In: 17th. Conference on Learning Theory (COLT 2004), 1-4 July 2004, Banff, Canada.

Abstract

We study the properties of the eigenvalues of Gram matrices in a non-asymptotic setting. Using local Rademacher averages, we provide data-dependent and tight bounds for their convergence towards eigenvalues of the corresponding kernel operator. We perform these computations in a functional analytic framework which allows to deal implicitly with reproducing kernel Hilbert spaces of infinite dimension. This can have applications to various kernel algorithms, such as Support Vector Machines (SVM). We focus on Kernel Principal Component Analysis (KPCA) and, using such techniques, we obtain sharp excess risk bounds for the reconstruction error. In these bounds, the dependence on the decay of the spectrum and on the closeness of successive eigenvalues is made explicit.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:467
Deposited By:Gilles Blanchard
Deposited On:23 December 2004