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

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.