Variable selection in model-based clustering using multilocus genotype data

We propose a variable selection procedure in model-based clustering multilocus genotype data. Indeed, it may happen that some loci are not relevant for clustering into statistically different populations. Inferring the number K of clusters and the relevant clustering subset S of loci is regarded as a model selection problem. The competing models are compared using penalized maximum likelihood criteria. Under weak assumptions on the penalty function, we prove the consistency of the resulting estimator ( K̂n, Ŝn ) . An associated algorithm named Mixture Model for Genotype Data (MixMoGenD) was implemented using c + + programming language and is available on www.math.u-psud.fr/~toussile. To avoid an exhaustive research of the optimum model, we propose an adaptation of the Backward-Stepwise algorithm, which enables a better research of the optimum model among all possible cardinalities of S. We present numerical experiments on simulated and real datasets that highlight the interest of our loci selection procedure.