Assessing the Number of Clusters of the Latent Class Model

Abstract

When partitioning the data is the main concern, it is implicitly assumed that each cluster can be approximately regarded as a sample from one component of a mixture model. Thus, the clustering problem can be viewed as an estimation problem of the parameters of the mixture. Setting this problem under the Maximum likelihood and Classification likelihood approaches, we first study the clustering of objects described by categorical attributes using the latent class model and we concentrate our attention on the problem of the number of components. To this end, we use three criteria derived within a Bayesian framework to tackle this problem. These criteria based on approximations of integrated likelihood and of integrated classification likelihood have been recently compared in Gaussian mixture. In this work, we propose to extend these comparisons to the latent class model.