Intrinsic statistical separation of subpopulations in heterogeneous collective motion via dimensionality reduction

Abstract

Collective motion of locally interacting agents is found ubiquitously throughout nature. The inability to probe individuals has driven longstanding interest in the development of methods for inferring the underlying interactions. In the context of heterogeneous collectives, where the population consists of individuals driven by different interactions, existing approaches require some knowledge about the heterogeneities or underlying interactions. Here, we investigate the feasibility of identifying the identities in a heterogeneous collective without such prior knowledge. We numerically explore the behavior of a heterogeneous Vicsek model and find sufficiently long trajectories intrinsically cluster in a PCA-based dimensionally reduced model-agnostic description of the data. We identify how heterogeneities in each parameter in the model (interaction radius, noise, population proportions) dictate this clustering. Finally, we show the generality of this phenomenon by finding similar behavior in a heterogeneous D'Orsogna model. Altogether, our results establish and quantify the intrinsic model-agnostic statistical disentanglement of identities in heterogeneous collectives.

9 pages, 7 figures; v2: based on a great reviewer's suggestion, all numerical experiments to start after equilibration and figures updated accordingly

References in corpus (9)

• Novel type of phase transition in a system of self-driven particles
• Collective behavior of interacting self-propelled particles
• Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria
• Flocking of two unfriendly species: The two-species Vicsek model
• Heterogeneous bacterial swarms with mixed lengths
• Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
• Dimension reduction of noisy interacting systems
• Data-driven discovery of stochastic dynamical equations of collective motion
• Disentangling intrinsic motion from neighbourhood effects in heterogeneous collective motion