Unsupervised learning of collective patterns in self-propelled particles through persistent homology

¹ Faculty of Science and Technology, Oita University, 870-1192, Japan
² International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, 113-0033, Japan

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 12 September 2025

Abstract

We propose an approach for systematically clustering and visualizing the diverse patterns generated from a system of self-propelled particles. To extract the topological features of these patterns, we integrate topological data analysis based on persistent homology with unsupervised dimensionality reduction methods including PCA and t-SNE. We perform numerical simulations of the D’Orsogna model and analyzed the resulting data. As a result, the t-SNE embedding of persistent images obtained from a set of snapshots reveals that the collective patterns of self-propelled particles are organized according to their topological features, and that cluster structures depend on parameters as well as initial conditions of the system.