Dimensionality reduction and generalization
Sofia Mosci, Lorenzo Rosasco and Alessandro Verri
In: ICML 2007(2007).

Abstract

In this paper we investigate the regularization property of Kernel Principal Component Analysis (KPCA), by studying its application to supervised learning problems as a preprocessing step. We show that performing KPCA and then ordinary least squares on the projected data, a procedure known as kernel principal component regression (KPCR), is equivalent to spectral cut-off regularization, the regularization parameter being exactly the number of principal components to keep. Using probabilistic estimates for integral operators we can prove error estimates for KPCR and provide a parameter choice procedure allowing to proof consistency of the algorithm.\\

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