The Sparse Latent Position Model for nonnegative weighted networks

This paper introduces a new methodology to analyse bipartite and unipartite networks with nonnegative edge values. The proposed approach combines and adapts a number of ideas from the literature on latent variable network models. The resulting framework is a new type of latent position model which exhibits great flexibility, and is able to capture important features that are generally exhibited by observed networks, such as sparsity and heavy tailed degree distributions. A crucial advantage of the proposed method is that the number of latent dimensions is automatically deduced from the data in one single algorithmic framework. In addition, the model attaches a weight to each of the latent dimensions, hence providing a measure of their relative importance. A fast variational Bayesian algorithm is proposed to estimate the parameters of the model. Finally, applications of the proposed methodology are illustrated on both artificial and real datasets, and comparisons with other existing procedures are provided.