Tensor latent block model for co-clustering

With the exponential growth of collected data in different fields like recommender system (user, items), text mining (document, term), bioinformatics (individual, gene), co-clustering, which is a simultaneous clustering of both dimensions of a data matrix, has become a popular technique. Co-clustering aims to obtain homogeneous blocks leading to a straightforward simultaneous interpretation of row clusters and column clusters. Many approaches exist; in this paper, we rely on the latent block model (LBM), which is flexible, allowing to model different types of data matrices. We extend its use to the case of a tensor (3D matrix) data in proposing a Tensor LBM (TLBM), allowing different relations between entities. To show the interest of TLBM, we consider continuous, binary, and contingency tables datasets. To estimate the parameters, a variational EM algorithm is developed. Its performances are evaluated on synthetic and real datasets to highlight different possible applications.