Variable selection for model-based clustering using the integrated complete-data likelihood

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-o between the clustering accuracy and the number of selected variables by using a lasso-type penalty. How-ever, the calibration of the penalty term can suer from criticisms. Model selection methods are an ecient alternative, yet they require a dicult optimization of an information criterion which involves combinatorial problems. First, most of these op-timization algorithms are based on a suboptimal procedure (e.g. stepwise method). Second, the algorithms are often greedy because they need multiple calls of EM algo-rithms. Here we propose to use a new information criterion based on the integrated complete-data likelihood. It does not require any estimate and its maximization is simple and computationally ecient. The original contribution of our approach is to perform the model selection without requiring any parameter estimation. Then, pa-rameter inference is needed only for the unique selected model. This approach is used for the variable selection of a Gaussian mixture model with conditional independence assumption. The numerical experiments on simulated and benchmark datasets show that the proposed method often outperforms two classical approaches for variable selection