# Physically-interpretable classification of biological network dynamics for complex collective motions

## TL;DR

This paper introduces a physically-interpretable, data-driven spectral analysis method for classifying complex biological network dynamics, revealing key physical and contextual features that distinguish collective motions.

## Contribution

It applies graph dynamic mode decomposition to classify collective motions, integrating physical properties with contextual information for improved understanding.

## Key findings

- Identified critical physical and contextual features for classification.
- Discovered label-specific spectral relationships among agents.
- Enhanced understanding of biological network dynamics through nonlinear systems analysis.

## Abstract

Understanding biological network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network properties often transiently and complexly change. A fundamental question addressed here pertains to the classification of collective motion network based on physically-interpretable dynamical properties. Here we apply a data-driven spectral analysis called graph dynamic mode decomposition, which obtains the dynamical properties for collective motion classification. Using a ballgame as an example, we classified the strategic collective motions in different global behaviours and discovered that, in addition to the physical properties, the contextual node information was critical for classification. Furthermore, we discovered the label-specific stronger spectra in the relationship among the nearest agents, providing physical and semantic interpretations. Our approach contributes to the understanding of principles of biological complex network dynamics from the perspective of nonlinear dynamical systems.