Diethe, T; Hussain, Z; (2009) Kernel Polytope Faces Pursuit. In: Buntine, W and Grobelnik, M and Mladenic, D and ShaweTaylor, J, (eds.) **MACHINE LEARNING AND KNOWLEDGE DISCOVERY IN DATABASES, PT I.** (pp. 290 - 301). SPRINGER-VERLAG BERLIN

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## Abstract

Polytope Faces Pursuit (PFP) is a greedy algorithm that approximates the sparse solutions recovered by l(1) regularised least-squares (Lasso) [4,10] in a similar vein to (Orthogonal) Matching Pursuit (OMP) [16]. The algorithm is based on the geometry of the polar polytope where at each step a basis function is chosen by finding the maximal vertex using a. path-following method. The algorithmic complexity is of a similar order to OMP whilst being able to solve problems known to be hard for (O)MP. Matching Pursuit was extended to build kernel-based solutions to machine learning problems, resulting in the sparse regression algorithm, Kernel Matching, Pursuit (KMP) [17]. We develop a new algorithm to build sparse kernel-based solutions using PFP, which we call Kernel Polytope Faces Pursuit (KPFP). We show the usefulness of this algorithm by providing a generalisation error bound [7] that takes into account a natural regression loss and experimental results on several benchmark datasets.

Type: | Proceedings paper |
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Title: | Kernel Polytope Faces Pursuit |

Event: | Joint European Conference on Machine Learning (ECML)/European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD) |

Location: | Bled, SLOVENIA |

Dates: | 2009-09-07 - 2009-09-11 |

ISBN-13: | 978-3-642-04179-2 |

Keywords: | Polytope Faces Pursuit, Orthogonal Matching Pursuit, Pseudo-dimension, Sample Compression Bounds, Regression, Kernel methods, VAPNIK-CHERVONENKIS DIMENSION |

UCL classification: | UCL > School of BEAMS > Faculty of Engineering Science > Computer Science UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science |

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