The Dynamic Latent Block Model for Sparse and Evolving Count Matrices

Giulia Marchello (1, 2, 3, 4) , Marco Corneli (1, 5, 3, 4) , Charles Bouveyron (1, 2, 3, 4)

1 UniCA - Université Côte d'Azur
2 CNRS - Centre National de la Recherche Scientifique
3 LJAD - Laboratoire Jean Alexandre Dieudonné
4 MAASAI - Modèles et algorithmes pour l’intelligence artificielle
5 MSI - Maison de la Modélisation, de la Simulation et des Interactions [Sophia-Antipolis]

We consider here the problem of co-clustering count matrices with a high level of missing values that may evolve along the time. We introduce a generative model, named dynamic latent block model (dLBM), to handle this situation and which extends the classical binary latent block model (LBM) to the dynamic case. The modeling of the dynamic time framework in a continuous time relies on a non-homogeneous Poisson process, with a latent partition of time intervals. The continuous time is handled by a time partition over the whole considered time period, where the interactions are aggregated on the time intervals of such partition obtaining a sequence of static matrices that allows us to identify meaningful time clusters. We proposed to use the SEM-Gibbs algorithm for model inference and the ICL criterion for model selection. Finally, an application with real-world data is proposed.

Domaines: Statistiques [math.ST]; Mathématiques [math]

Giulia Marchello, Marco Corneli, Charles Bouveyron. The Dynamic Latent Block Model for Sparse and Evolving Count Matrices. ICML Workskshop Artemiss, Jul 2020, Nice / Virtual, France. ⟨hal-02971127⟩