Block models for multipartite networks.Applications in ecology and ethnobiology

TL;DR

This paper introduces a novel stochastic block model designed for multipartite networks, enabling clustering of individuals across multiple interconnected networks, with applications demonstrated in ecology and ethnobiology.

Contribution

It extends existing block models to handle multipartite networks and provides a variational EM estimation method for clustering in complex multi-network data.

Findings

Successfully applied to ecological and ethnobiological datasets

Effective in uncovering latent structures across multiple networks

Model selection guided by Integrated Completed Likelihood criterion

Abstract

Modeling relations between individuals is a classical question in social sciences, ecology, etc. In order to uncover a latent structure in the data, a popular approach consists in clustering individuals according to the observed patterns of interactions. To do so, Stochastic block models (SBM) and Latent Block models (LBM) are standard tools for clustering the individuals with respect to their comportment in a unique network. However, when adopting an integrative point of view, individuals are not involved in a unique network but are part of several networks, resulting into a potentially complex multipartite network. In this contribution, we propose a stochastic block model able to handle multipartite networks, thus supplying a clustering of the individuals based on their connection behavior in more than one network. Our model is an extension of the latent block models (LBM) and stochastic block model (SBM). The parameters -- such as the marginal probabilities of assignment to blocks and the matrix of probabilities of connections between blocks -- are estimated through a variational Expectation-Maximization procedure. The numbers of blocks are chosen with the Integrated Completed Likelihood criterion, a penalized likelihood criterion. The pertinence of our methodology is illustrated on two datasets issued from ecology and ethnobiology.