Parameters Estimation of Block Mixture Models

Abstract

While most of the clustering procedures are aimed to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows to embed simultaneous clustering of objects and variables in a mixture approach. We have considered this probabilistic model under the classification likelihood approach and we have developed a new algorithm for simultaneous partitioning based on the Classification EM algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. To reach this aim, we use an approximation of the likelihood and we propose an alternated-optimization algorithm to estimate the parameters, and to illustrate our approach, we study the case of binary data.