Detecting group effects in sequences reveals team strategies in football
Uncovering higher-order interactions from memory in observed dynamics
Social and Information Networks
Summary
Many complex systems feature interactions among groups, not just pairs, but it's hard to tell if observed behavior truly reflects these group interactions or can be explained by simple pairs. The authors developed a method using hidden Markov models to analyze sequences of observed activity without needing labels for groups, identifying when higher-order group interactions are necessary to explain the data. They confirmed their method works on both computer-generated examples and real football match data, where it identified meaningful team formations.
What this means in practice
- •For sports analytics teams: Reveal underlying group tactics directly from player movement data without predefined group labels to inform coaching strategies.
- •For network engineers: Identify when communications or data flows depend on groups of nodes rather than pairs, improving network design and monitoring.
Authors
Arthur Rondeau, Alain Barrat, Roland Bouffanais
Abstract
Many complex systems involve group interactions, which can readily be represented by higher-order structures such as hypergraphs. However, when observing a system's dynamical evolution, establishing whether that evolution actually results from higher-order interactions, or whether pairwise interactions suffice to explain the data, remains a challenge. Even in the simple case of a temporal sequence of nodes visited during a diffusion process, such a task is intricate. Indeed, group interactions leave their traces as memory on the observed nodes, while path dependence in a purely pairwise process can mimic that same footprint without any group structure. To resolve this, we propose an inference pipeline based on a hidden Markov model (HMM) that tests, directly from an observed sequence of nodes carrying no group labels, whether higher-order interactions are required to describe the dynamics. The HMM latent states represent higher-order interactions, seen as hyperedges of an unobserved hypergraph, so that their detection becomes a model selection problem between the HMM class and a class of null models without higher-order interactions. We first validate this approach on synthetic node sequences generated from random walks on graphs and hypergraphs, showing that it recovers both the number and the composition of the underlying hyperedges, while correctly rejecting them when the generating process is pairwise. As a second step, we consider a validation based on empirical data, namely empirical trajectories of ball possession in football matches. This application shows that the pipeline goes beyond providing statistical evidence of the presence of higher-order interactions, and yields interpretable underlying structures: the recovered hyperedges map directly onto recognizable tactical team formations.