Robust Clustering Using Exponential Power Mixtures

Clustering is a widely used method in extracting useful information from gene expression data, where unknown

correlation structures in genes are believed to persist even after normalization. Such correlation structures pose a great

challenge on the conventional clustering methods, such as the Gaussian mixture (GM) model, k-means (KM), and partitioning

around medoids (PAM), which are not robust against general dependence within data. Here we use the exponential

power mixture model to increase the robustness of clustering against general dependence and nonnormality of the data. An

expectation–conditional maximization algorithm is developed to calculate the maximum likelihood estimators (MLEs) of the

unknown parameters in these mixtures. The Bayesian information criterion is then employed to determine the numbers of

components of the mixture. The MLEs are shown to be consistent under sparse dependence. Our numerical results indicate

that the proposed procedure outperforms GM, KM, and PAM when there are strong correlations or non-Gaussian components

in the data.