Learning minimum volume sets with support vector machines

Mark A. Davenport, Richard G. Baraniuk, Clayton D. Scott

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

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 languageEnglish (US)
Title of host publicationProceedings of the 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, MLSP 2006
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages301-306
Number of pages6
ISBN (Print)1424406560, 9781424406562
DOIs
StatePublished - Jan 1 2006
Event2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, MLSP 2006 - Maynooth, Ireland
Duration: Sep 6 2006Sep 8 2006

Other

Other2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, MLSP 2006
CountryIreland
CityMaynooth
Period9/6/069/8/06

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Signal Processing

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