Higher-Order Temporal Network Prediction

TL;DR

This paper addresses predicting higher-order temporal networks by introducing a memory-based approach that forecasts the activation of group interactions one time step ahead, using past activity of the target hyperlink and its overlapping sub- and super-hyperlinks. It proposes a generalized model with cross-order influence coefficients $c_{d_i d_j}$ and a memory-decay mechanism $e^{-\tau(t-k)}$, alongside a baseline that treats higher-order events as pairwise and derives higher-order predictions from those. Across eight real-world datasets, the generalized model consistently outperforms the baseline, with strongest gains for orders 3 and 4, and reveals that sub-hyperlink activity with greater node overlap tends to boost the target event more than super-hyperlink activity. The approach provides actionable insights into how past interactions shape future higher-order events and offers a practical framework for forecasting in social contact networks, potentially aiding epidemic and misinformation mitigation.

Abstract

A social interaction (so-called higher-order event/interaction) can be regarded as the activation of the hyperlink among the corresponding individuals. Social interactions can be, thus, represented as higher-order temporal networks, that record the higher-order events occurring at each time step over time. The prediction of higher-order interactions is usually overlooked in traditional temporal network prediction methods, where a higher-order interaction is regarded as a set of pairwise interactions. We propose a memory-based model that predicts the higher-order temporal network (or events) one step ahead, based on the network observed in the past and a baseline utilizing pair-wise temporal network prediction method. In eight real-world networks, we find that our model consistently outperforms the baseline. Importantly, our model reveals how past interactions of the target hyperlink and different types of hyperlinks that overlap with the target hyperlinks contribute to the prediction of the activation of the target link in the future.

Figures (3)

• Figure 1: Jaccard similarities of a network at two time steps for each order as a function of the time lag in eight real-world physical contact networks.
• Figure 2: Precision (Ratio of true positives) of predicting events of order 3 as a function of $c_{23}$, with $c_{43}$ fixed, for all datasets.
• Figure 3: Precision (Ratio of true positives) of predicting events of a given order as a function of one coefficient, with the other coefficient fixed, for two datasets.