Co-clustering through Latent Bloc Model: a Review

Résumé

We present here model-based co-clustering methods, with a focus on the latent block model (LBM). We introduce several specifications of the LBM (standard, sparse, Bayesian) and review some identifiability results. We show how the complex dependency structure prevents standard maximum likelihood estimation and present alternative and popular inference methods. Those estimation methods are based on a tractable approximation of the likelihood and rely on iterative procedures, which makes them difficult to analyze. We nevertheless present some asymptotic results for consistency. The results are partial as they rely on a reasonable but still unproved condition. Likewise, available model selection tools for choosing the number of groups in rows and columns are only valid up to a conjecture. We also briefly discuss non model-based co-clustering procedures. Finally, we show how LBM can be used for bipartite graph analysis and highlight throughout this review its connection to the Stochastic Block Model.