A dimensionality reduction approach to model-free clustering of trajectories in heterogeneous collectives

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 naturally cluster with dimensionality reduction computed by PCA. 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'Orsogona model. Altogether, our results quantify the ability to disentangle identities in heterogeneous collectives in a model-agnostic manner.