Analyzing Collective Motion Using Graph Fourier Analysis

TL;DR

This paper introduces a novel framework using graph Fourier analysis to uncover hidden structures in collective animal motion, integrating topological and signal processing methods for enhanced analysis.

Contribution

It presents a new approach that combines computational topology and graph signal processing to analyze and interpret collective motion in animal groups.

Findings

Reveals hidden structures in swarm states

Provides a flexible analysis framework

Unifies topological and signal processing methods

Abstract

Collective motion in animal groups, such as swarms of insects, flocks of birds, and schools of fish, are some of the most visually striking examples of emergent behavior. Empirical analysis of these behaviors in experiment or computational simulation primarily involves the use of "swarm-averaged" metrics or order parameters such as velocity alignment and angular momentum. Recently, tools from computational topology have been applied to the analysis of swarms to further understand and automate the detection of fundamentally different swarm structures evolving in space and time. Here, we show how the field of graph signal processing can be used to fuse these two approaches by collectively analyzing swarm properties using graph Fourier harmonics that respect the topological structure of the swarm. This graph Fourier analysis reveals hidden structure in a number of common swarming states and forms the basis of a flexible analysis framework for collective motion.