Identifying manifolds underlying group motion in Vicsek agents

Abstract

Abstract. Collective motion of animal groups often undergoes changes due to perturbations. In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents. To characterize such manifolds, first we introduce a simple mapping of agents between time-steps. Then, we construct a novel metric which is susceptible to variations in the collective motion, thus revealing distinct underlying manifolds. The method is validated through three sample scenarios simulated using a Vicsek model, namely switching of speed, coordination, and structure of a group. Combined with a dimensionality reduction technique that is used to infer the dimensionality of the embedding manifold, this approach provides an effective model-free framework for the analysis of collective behavior across animal species.

Reconstruction of Agents’ Corrupted Trajectories of Collective Motion Using Low-rank Matrix Completion

“…MOT plays an important role in collective motion studies since trajectories facilitate the learning of the dynamics of not only the entire group, but also that of either each individual agent or their clusters [5]. The trajectories constructed by the conventional MOT methods might lose some segments of the trajectories due to natural phenomenon such as occlusion, change of illumination, etc.…”

“…We are unable to compare/contrast our trajectory defragmentation technique with existing defragmentation techniques as they are not available separately out of the tracking methods. We are planning to improve the MOT method presented as a part of the study presented in [5] by prepending it onto our trajectory defragmentation technique to produce a complete MOT method. This future work allows us to compare our complete MOT method with the existing MOT methods such as the ones presented in [16,17,35,36,37,4].…”

“…With the advancements in both the video recording technology and the multi-object tracking (MOT) methods, dynamics of animal groups in wild [1], pedestrians on streets [2], vehicles on roads [3], and sport players on courts [4] are studied using agents' individual trajectories. Utilization of trajectories are favorable for such studies rather than that of raw-videos since trajectories facilitate learning of dynamics of not only the entire group, but also that of either each individual agent or their clusters [5]. MOT is an important computer vision subject that has received an increasing attention due to its broad applicability in both academic and commercial sectors [6].…”

Dynamics of animal systems

“…In a multi-agent model of collective behavior, Gajamannage et al [37] describe group motion as switching between low-dimensional embedding manifolds. They introduce a simple mapping for the agents between consecutive time-steps together with a novel metric of collective behavior, which encapsulates variations in the collective motion.…”

Detecting phase transitions in collective behavior using manifold's curvature

“…Due to an abrupt behavioral change of the group, this mapping switches from one phase space to another and indicates a phase transition of the motion. Thus, in the presence of a phase transition, the system can be represented as two distinct sub-manifolds, M (j) for j = 1 and 2, along with singularities where the phase transition physically exists [18]. Herein, the most salient scenario is that the sub-manifolds intersect and make a locus L of singularities as L = ∩M (j) .…”