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Theory of matching pursuit

Hussain, Z; Shawe-Taylor, J; (2009) Theory of matching pursuit. In: (pp. pp. 721-728).

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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 Shawe-Taylor 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.

Type: Proceedings paper
Title: Theory of matching pursuit
ISBN-13: 9781605609492
UCL classification: UCL > School of BEAMS
UCL > School of BEAMS > Faculty of Engineering Science
URI: http://discovery.ucl.ac.uk/id/eprint/79207
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