Hussain, Z; Shawe-Taylor, J; (2009) Theory of matching pursuit. In: Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference. (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  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.
|Title:||Theory of matching pursuit|
|UCL classification:||UCL > School of BEAMS > Faculty of Engineering Science > Computer Science|
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