Variable Selection for Mixed Data Clustering: Application in Human Population Genomics

Model-based clustering of human population genomic data, composed of 1,318 individuals arisen from western Central Africa and 160,470 markers, is considered. This challenging analysis leads us to develop a new methodology for variable selection in clustering. To explain the differences between subpopulations and to increase the accuracy of the estimates, variable selection is done simultaneously to clustering. We proposed two approaches for selecting variables when clustering is managed by the latent class model (i.e., mixture considering independence within components). The first method simultaneously performs model selection and parameter inference. It optimizes the Bayesian Information Criterion with a modified version of the standard expectation-maximization algorithm. The second method performs model selection without requiring parameter inference by maximizing the Maximum Integrated Complete-data Likelihood criterion. Although the application considers categorical data, the proposed methods are introduced in the general context of mixed data (data composed of different types of features). As the first step, the interest of both proposed methods is shown on simulated and several benchmark real data. Then, we apply the clustering method to the human population genomic data which permits to detect the most discriminative genetic markers. The proposed method implemented in the R package VarSelLCM is available on CRAN.