Sparse cluster analysis of large-scale discrete variables with application to single nucleotide polymorphism data

Current extremely large scale genetic data presents significant challenges for cluster analysis. Most existing clustering methods are typically built on Euclidean distance and geared toward analyzing continuous response. They work well for clustering, e.g., microarray gene expression data, but often perform poorly for clustering, e.g., large scale single nucleotide polymorphism data. In this paper, we study the penalized latent class model for clustering extremely large scale discrete data. The penalized latent class model takes into account the discrete nature of the response using appropriate generalized linear models and adopts the lasso penalized likelihood approach for simultaneous model estimation and selection of important covariates. We develop very efficient numerical algorithms for model estimation based on the iterative coordinate descent approach and further develop the Expectation-Maximization algorithm to incorporate and model missing values. We use simulation studies and applications to the international HapMap single nucleotide polymorphism data to illustrate the competitive performance of the penalized latent class model.