Latent Block Regression Model

Abstract When dealing with high dimensional sparse data, such as in recommender systems,co-clustering turns out to be more beneficial than one-sided clustering, even if one is interested in clustering along one dimension only. Thereby, co-clusterwise is a natural extension of clusterwise. Unfortunately, all of the existing approaches do not consider covariates on both dimensions of a data matrix. In this paper, we propose a Latent Block Regression Model (LBRM) overcoming this limit. For inference, we propose an algorithm performing simultaneously co-clustering and regression where a linear regression model characterizes each block. Placing the estimate of the model parameters under the maximum likelihood approach, we derive a Variational Expectation–Maximization (VEM) algorithm for estimating the model’s parameters. The finality of the proposed VEM-LBRM is illustrated through simulated datasets.