Identifying manifolds underlying group motion in Vicsek agents
This provides a model-free framework for analyzing collective behavior across animal species, though it is incremental as it builds on existing Vicsek models and dimensionality reduction techniques.
The paper tackled the problem of identifying low-dimensional manifolds underlying collective motion changes in animal groups, introducing a novel metric and mapping method that successfully revealed distinct manifolds in simulated Vicsek model scenarios.
Collective motion of animal groups often undergoes changes due to perturbations. In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents. To characterize such manifolds, first we introduce a simple mapping of agents between time-steps. Then, we construct a novel metric which is susceptible to variations in the collective motion, thus revealing distinct underlying manifolds. The method is validated through three sample scenarios simulated using a Vicsek model, namely switching of speed, coordination, and structure of a group. Combined with a dimensionality reduction technique that is used to infer the dimensionality of the embedding manifold, this approach provides an effective model-free framework for the analysis of collective behavior across animal species.