Model-based clustering with gene ranking using penalized mixtures of heavy-tailed distributions

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 penalized mixture of Student's t distributions for model-based clustering and gene ranking. Together with a resampling 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 sub-classes.