Identifying manifolds underlying group motion in Vicsek agents

TL;DR

This paper introduces a new model-free framework to identify and analyze the low-dimensional manifolds underlying collective group motion, using a novel metric and dimensionality reduction, validated on Vicsek model simulations.

Contribution

It presents a novel metric and a simple agent mapping method to characterize and distinguish underlying manifolds in collective motion, applicable across species.

Findings

Successfully identified switching manifolds in simulated Vicsek models.

Demonstrated the method's ability to detect changes in speed, coordination, and structure.

Provides a model-free approach for analyzing collective animal behavior.

Abstract

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.