A correlation based framework for inferring interaction geometry in collective motion

Inferring interaction geometry from trajectory data is a fundamental inverse problem in collective motion research. We introduce Interaction Geometry Inference using Correlation (IGIC), a correlation-based framework for estimating interaction radius and sensing angle directly from time-resolved trajectory data. IGIC computes lagged circular correlations between neighbor-averaged headings and subsequent individual motion across candidate interaction geometries, identifying the geometry that maximizes this correlation as the inferred interaction region. The framework is first validated using synthetic trajectory data generated from visual Vicsek model simulations with known interaction geometry, achieving an overall recovery accuracy of $$99.2\%$$ across a broad range of sensing angles and noise intensities. We further evaluate IGIC on a topological Vicsek model, where no true metric interaction radius exists, and compare its performance with transfer entropy and mutual information. Despite this deliberate model mismatch, IGIC achieves the highest overall sensing-angle recovery and accurately estimates the effective interaction scale imposed by the topological neighborhood. Application to empirical Golden Shiner trajectory data yields interaction radii and sensing angles consistent with independently reported measurements of visual range and blind zones, while remaining robust to variations in temporal lag. By leveraging lagged circular correlation, IGIC provides a transparent, interpretable, and computationally efficient framework for inferring effective interaction geometry in collective systems.