An information-theoretic approach to infer the underlying interaction domain among elements from finite length trajectories in a noisy environment

Abstract

Transfer entropy in information theory was recently demonstrated [Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. There, only pairs of elements whose distances are shorter than some distance variable, termed cutoff distance, are taken into account in the computation of transfer entropies. The prediction performance in capturing the underlying interaction domain is subject to noise level exerted on the elements and the sufficiency of statistics of the interaction events. In this paper, the dependence of the prediction performance is scrutinized systematically on noise level and the length of trajectories by using a modified Vicsek model. The larger the noise level and the shorter the time length of trajectories, the more the derivative of average transfer entropy fluctuates, which makes it difficult to identify the interaction domain in terms of the position of global minimum of the derivative of average transfer entropy. A measure to quantify the degree of strong convexity at coarse-grained level is proposed. It is shown that the convexity score scheme can identify the interaction distance fairly well even while the position of global minimum of the derivative of average transfer entropy does not. We also derive an analytical model to explain the relationship between the interaction domain and the change of transfer entropy that supports our cutoff distance technique to elucidate the underlying interaction domain from trajectories.