We propose minimum volume ellipsoids (MVE) clustering as an alternate clustering technique to k-means clustering for Gaussian data points and explore its value and practicality. MVE clustering allocates data points into clusters that minimizes the total volumes of each cluster's covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and unequal clusters, and our ability to formulate it as a mixed-integer semidefinite programming problem that can be solved to global optimality. We present some preliminary empirical results that illustrate MVE clustering as an appropriate method for clustering data from mixtures of Gaussian distributions and compare its performance with the k-means clustering algorithm.
Research Report CORR 2005--12, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada, May 2005.