Multiplex Dirichlet stochastic block model for clustering multidimensional compositional networks

Network data often represent multiple types of relations, which can also denote exchanged quantities, and are typically encompassed in a weighted multiplex. Such data frequently exhibit clustering structures, however, traditional clustering methods are not well-suited for multiplex networks. Additionally, standard methods treat edge weights in their raw form, potentially biasing clustering towards a node's total weight capacity rather than reflecting cluster-related interaction patterns. To address this, we propose transforming edge weights into a compositional format, enabling the analysis of connection strengths in relative terms and removing the impact of nodes' total weights. We introduce a multiplex Dirichlet stochastic block model designed for multiplex networks with compositional layers. This model accounts for sparse compositional networks and enables joint clustering across different types of interactions. We validate the model through a simulation study and apply it to the international export data from the Food and Agriculture Organization of the United Nations.

A Dirichlet stochastic block model for composition-weighted networks

Network data are observed in various applications where the individual entities of the system interact with or are connected to each other, and often these interactions are defined by their associated strength or importance. Clustering is a common task in network analysis that involves finding groups of nodes displaying similarities in the way they interact with the rest of the network. However, most clustering methods use the strengths of connections between entities in their original form, ignoring the possible differences in the capacities of individual nodes to send or receive edges. This often leads to clustering solutions that are heavily influenced by the nodes' capacities. One way to overcome this is to analyse the strengths of connections in relative rather than absolute terms, expressing each edge weight as a proportion of the sending (or receiving) capacity of the respective node. This, however, induces additional modelling constraints that most existing clustering methods are not designed to handle. In this work we propose a stochastic block model for composition-weighted networks based on direct modelling of compositional weight vectors using a Dirichlet mixture, with the parameters determined by the cluster labels of the sender and the receiver nodes. Inference is implemented via an extension of the classification expectation-maximisation algorithm that uses a working independence assumption, expressing the complete data likelihood of each node of the network as a function of fixed cluster labels of the remaining nodes. A model selection criterion is derived to aid the choice of the number of clusters. The model is validated using simulation studies, and showcased on network data from the Erasmus exchange program and a bike sharing network for the city of London.