Analyzing collective motion with machine learning and topology.

Area of Science:

• Complex Systems
• Computational Biology
• Data Science

Background:

• Collective motion is fundamental in biological systems, with models like D'Orsogna et al. (2006) describing agent interactions via social forces.
• Emergent behaviors such as flocking and milling arise from these nonlinear interactions, posing challenges for analysis.
• Traditional methods often rely on specific order parameters that may not capture the full complexity of these systems.

Purpose of the Study:

• To apply topological data analysis (TDA) and machine learning (ML) to classify collective motion in a biological model.
• To compare the efficacy of TDA-based features against traditional order parameters for ML analysis.
• To investigate the ability of TDA to recover model parameters from simulation data.

Main Methods:

• Utilized a seminal model of nonlinear agent interactions (D'Orsogna et al., 2006).
• Generated a large library of numerical simulations capturing diverse collective behaviors.
• Applied unsupervised and supervised machine learning algorithms.
• Extracted features using both traditional order parameters and topological measures (persistent homology).

Main Results:

• The topological approach, summarizing persistent homology, significantly outperformed traditional order parameters.
• TDA-based methods demonstrated superior performance in both unsupervised and supervised machine learning tasks.
• This indicates TDA's robustness in characterizing complex, emergent patterns without prior assumptions.

Conclusions:

• Topological data analysis offers a powerful, data-driven framework for studying collective motion.
• TDA provides richer, more comprehensive features than traditional order parameters for classifying complex systems.
• This approach enhances our ability to analyze and understand emergent behaviors in biological and physical systems.