Model-Based Classification with High-Dimensional Data

                           Geoff McLachlan
   Department of Mathematics and Institute for Molecular Bioscience
                      University of Queensland


Finite mixture models are being increasingly used to model the
distributions of a wide variety of random phenomena.  In this talk,
we consider the use of mixture distributions to provide a model-based
approach to classification with high-dimensional data.  The need to
be able to classify such data arises in many applications ranging from
biology to image processing.  For the unsupervised classification problem
(cluster analysis), we consider the use of mixtures of factor analyzers.
This approach enables a normal mixture model to be fitted to data which
have high dimension relative to the number of data points to be clustered.
The number of free parameters is controlled through the dimension of the
latent factor space.  By working in this reduced space, it allows an
interpolation in model complexities from isotropic to full covariance
structures without any restrictions.  We also consider the case of supervised 
classification (discriminant analysis).  The methodology is illustrated 
by applications in the context of cancer diagnosis and treatment.  One
problem concerns classifiying a relatively small number of tumour tissue 
samples containing the expression data on very many (possibly thousands) 
of genes from microarray experiments.