Latent Block Model for Contingency Table

Although many clustering procedures aim 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. This kind of methods has practical importance in a wide of variety of applications such as text and market basket data analysis. Typically, the data that arises in these applications is arranged as two-way contingency table. Using Poisson distributions, a latent block model for these data is proposed and, setting it under the maximum likelihood approach and the classification maximum likelihood approach, various algorithms are proposed. Their performances are evaluated and compared to a simple use of EM or CEM applied separately on the rows and columns of the contingency table.