Davenport, Mark A.Baraniuk, Richard G.Scott, Clayton D.2007-10-312007-10-312006-09-012006-09-01M. A. Davenport, R. G. Baraniuk and C. D. Scott, "Learning minimum volume sets with support vector machines," 2006.https://hdl.handle.net/1911/19833Conference PaperGiven a probability law P on d-dimensional Euclidean space, the minimum volume set (MV-set) with mass beta , 0 < beta < 1, is the set with smallest volume enclosing a probability mass of at least beta. 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.engConference paperhttp://dx.doi.org/10.1109/MLSP.2006.275565