Statistical modelling of time-stamped hypergraphs: a model-based clustering approach

Throughout the years, several statistical models have been developed to describe interactions between individuals. Those relationships can be represented as a graph, where vertices correspond to the individuals, and two vertices are joined by an edge if there is a relationship among them. A hypergraph is a generalization of a graph in which a hyperedge connects any number of vertices. In many real-world situations, hyperedges often change with time. However, existing statistical methods for hypergraphs usually ignore this temporal information. This thesis proposes an extension of the latent class analysis approach to describe the evolution of hypergraphs over time. The model parameters are estimated via the expectation-maximization algorithm. The estimation could be computationally demanding because every possible hyperedge between any nodes has to be considered part of the risk set, and its cardinality grows exponentially with the number of nodes. Case-control sampling is performed to deal with this situation.