A Deep Dynamic Latent Block Model for the Co-Clustering of Zero-Inflated Data Matrices

Abstract

The simultaneous clustering of observations and features of data sets (a.k.a. co-clustering) has recently emerged as a central machine learning task to summarize massive data sets. However, most existing models focus on stationary scenarios, where cluster assignments do not evolve in time. This work introduces a novel latent block model for the dynamic co-clustering of data matrices with high sparsity. The data are assumed to follow dynamic mixtures of block-dependent zero-inflated distributions. Moreover, the sparsity parameter as well as the cluster proportions are assumed to be driven by dynamic systems, whose parameters must be estimated. The inference of the model parameters relies on an original variational EM algorithm whose maximization step trains fully connected neural networks that approximate the dynamic systems. Due to the model ability to work with empty clusters, the selection of the number of clusters can be done in a (computationally) parsimonious way. Numerical experiments on simulated and real world data sets demonstrate the effectiveness of the proposed methodology in the context of count data.