## Abstract

Given a probability law P on d-dimensional Euclidean space, the minimum volume set (MV-set) with mass β, 0 < β < 1, is the set with smallest volume enclosing a probability mass of at least β. We examine the use of support vector machines (SVMs) for estimating an MV-set from a collection of data points drawn from P, a problem with applications in clustering and anomaly detection. We investigate both one-class and two-class methods. The two-class approach reduces the problem to Neyman-Pearson (NP) classification, where we artificially generate a second class of data points according to a uniform distribution. The simple approach to generating the uniform data suffers from the curse of dimensionality. In this paper we (1) describe the reduction of MV-set estimation to NP classification, (2) devise improved methods for generating artificial uniform data for the two-class approach, (3) advocate a new performance measure for systematic comparison of MV-set algorithms, and (4) establish a set of benchmark experiments to serve as a point of reference for future MV-set algorithms. We find that, in general, the two-class method performs more reliably.

Original language | English (US) |
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Title of host publication | Proceedings of the 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, MLSP 2006 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 301-306 |

Number of pages | 6 |

ISBN (Print) | 1424406560, 9781424406562 |

DOIs | |

State | Published - Jan 1 2006 |

Event | 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, MLSP 2006 - Maynooth, Ireland Duration: Sep 6 2006 → Sep 8 2006 |

### Other

Other | 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, MLSP 2006 |
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Country/Territory | Ireland |

City | Maynooth |

Period | 9/6/06 → 9/8/06 |

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Signal Processing