Robust Mixture Modeling

• Activity Number: 35
• Type: Invited
• Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Geoffrey J. McLachlan*+
• Companies: University of Queensland
• Keywords: finite mixture models ; EM algorithm ; multiresolution kd-trees ; t-distributions ; mixtures of factor analyzers

Abstract

Finite mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster datasets. We shall focus on the use of normal mixture models to cluster datasets of continuous multivariate data. We shall consider a robust approach to clustering by modeling the data by a mixture of t-distributions. With this t-mixture model-based approach, the normal distribution for each component in the mixture model is embedded in a wider class of elliptically symmetric distributions with an additional parameter called the degrees of freedom. The advantage of the t-mixture model is that, although the number of outliers needed for breakdown is almost the same as with the normal mixture model, the outliers have to be much larger. We also consider the use of the t-distribution for the robust clustering of high-dimensional data via mixtures of factor analyzers. Finally, we consider the robust fitting of normal mixtures using multiresolution kd-trees.