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Theory of matching pursuit
"... We analyse matching pursuit for kernel principal components analysis (KPCA) by proving that the sparse subspace it produces is a sample compression scheme. We show that this bound is tighter than the KPCA bound of ShaweTaylor et al [7] and highly predictive of the size of the subspace needed to cap ..."
Abstract

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We analyse matching pursuit for kernel principal components analysis (KPCA) by proving that the sparse subspace it produces is a sample compression scheme. We show that this bound is tighter than the KPCA bound of ShaweTaylor et al [7] and highly predictive of the size of the subspace needed to capture most of the variance in the data. We analyse a second matching pursuit algorithm called kernel matching pursuit (KMP) which does not correspond to a sample compression scheme. However, we give a novel bound that views the choice of subspace of the KMP algorithm as a compression scheme and hence provide a VC bound to upper bound its future loss. Finally we describe how the same bound can be applied to other matching pursuit related algorithms. 1