Higher-order Temporal Network Prediction

Abstract

Temporal networks, like physical contact networks, are networks whose topology changes over time. However, this representation does not account for group interactions, when people gather in groups of more than two people, that can be represented as higher-order events of a temporal network. The prediction of these higher-order events is usually overlooked in traditional temporal network prediction methods, where each higher-order event of a group is regarded as a set of pairwise interactions between every pair of individuals within the group. However, pairwise interactions only allow to partially capture interactions among constituents of a system. Therefore, we want to be able to predict the occurrence of such higher-order interactions one step ahead, based on the higher-order topology observed in the past, and to understand which types of interactions are the most influential for the prediction. We find that the similarity in network topology is relatively high at two time steps with a small time lag between them and that this similarity decreases when the time lag increases. This motivates us to propose a memory-based model that can predict a higherorder temporal network at the next time step based on the network observed in the past. In particular, the occurrence of a group event will be predicted based on the past activity of this target group and of other groups that form a subset or a superset of the target group. Our model is network-based, so it has a relatively low computational cost and allows for a good interpretation of its underlying mechanisms. We propose as a baseline the memory-based method for the traditional pairwise network prediction problem. In this baseline model, the predicted higher-order events at a prediction time step are then deduced from the predicted pairwise network at the same prediction time step. We evaluate the prediction quality of all models in eight real-world physical contact networks and find that our model outperforms the baseline model. We also analyze the contribution of group events of different orders to the prediction quality. We find that the past activity of the target group is the most important factor for the prediction. Moreover, the past activity of groups of a larger size has, in general, a lower impact on the prediction of events of an arbitrary size than groups of a smaller size.