Inference of dynamic hypergraph representations in temporal interaction data

A range of systems across the social and natural sciences generate data sets consisting of interactions between two distinct categories of items at various instances in time. Online shopping, for example, generates purchasing events of the form (user, product, time of purchase), and mutualistic interactions in plant-pollinator systems generate pollination events of the form (insect, plant, time of pollination). These data sets can be meaningfully modeled as temporal hypergraph snapshots in which multiple items within one category (i.e., online shoppers) share a hyperedge if they interacted with a common item in the other category (i.e., purchased the same product) within a given time window, allowing for the application of hypergraph analysis techniques. However, it is often unclear how to choose the number and duration of these temporal snapshots, which have a strong influence on the final hypergraph representations. Here we propose a principled nonparametric solution to this problem by extracting temporal hypergraph snapshots that optimally capture structural regularities in temporal event data according to the minimum description length principle. We demonstrate our methods on real and synthetic data sets, finding that they can recover planted artificial hypergraph structure in the presence of considerable noise and reveal meaningful activity fluctuations in human mobility data.