Assessing the Number of Components in Mixture Models: a Review.

Despite the widespread application of finite mixture models, the decision of how many classes are required to adequately represent the data is, according to many authors, an important, but unsolved issue. This work aims to review, describe and organize the available approaches designed to help the selection of the adequate number of mixture components (including Monte Carlo test procedures, information criteria and classification-based criteria); we also provide some published simulation results about their relative performance, with the purpose of identifying the scenarios where each criterion is more effective (adequate).