Latent Block Model for Contingency Table

Gérard Govaert (1) , Mohamed Nadif (2)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 CRIP5 - EA 2517 - Centre de Recherche en Informatique de Paris 5

Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, variables, there are other methods, called block clustering methods, which simultaneously consider the two sets and organize the data into homogeneous blocks. This kind of method has practical importance in a wide variety of applications such as text and market basket data analysis. Typically, the data that arise in these applications are arranged as a 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 provided. 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.

Mots clés: Block clustering; Block Poisson mixture model; CEM algorithm; Contingency table; EM algorithm.; EM algorithm

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Gérard Govaert, Mohamed Nadif. Latent Block Model for Contingency Table. Communications in Statistics - Theory and Methods, 2010, 39 (3), pp.416 - 425. ⟨10.1080/03610920903140197⟩. ⟨hal-00447792⟩