Cluster analysis of biological samples using gene expression measurements is
a common task which aids the discovery of heterogeneous biological
sub-populations having distinct mRNA profiles. Several model-based clustering
algorithms have been proposed in which the distribution of gene expression
values within each sub-group is assumed to be Gaussian. In the presence of
noise and extreme observations, a mixture of Gaussian densities may over-fit
and overestimate the true number of clusters. Moreover, commonly used
model-based clustering algorithms do not generally provide a mechanism to
quantify the relative contribution of each gene to the final partitioning of
the data. We propose a penalised mixture of Student's t distributions for
model-based clustering and gene ranking. Together with a bootstrap procedure,
the proposed approach provides a means for ranking genes according to their
contributions to the clustering process. Experimental results show that the
algorithm performs well comparably to traditional Gaussian mixtures in the
presence of outliers and longer tailed distributions. The algorithm also
identifies the true informative genes with high sensitivity, and achieves
improved model selection. An illustrative application to breast cancer data is
also presented which confirms established tumor subclasses.