The structure inference of flocking systems based on the trajectories

Abstract

The interaction between the swarm individuals affects the dynamic behavior of the swarm, but it is difficult to obtain directly from outside observation. Therefore, the problem we focus on is inferring the structure of the interactions in the swarm from the individual behavior trajectories. Similar inference problems that existed in network science are named network reconstruction or network inference. It is a fundamental problem pervading research on complex systems. In this paper, a new method, called Motion Trajectory Similarity, is developed for inferring direct interactions from the motion state of individuals in the swarm. It constructs correlations by combining the similarity of the motion trajectories of each cross section of the time series, in which individuals with highly similar motion states are more likely to interact with each other. Experiments on the flocking systems demonstrate that our method can produce a reliable interaction inference and outperform traditional network inference methods. It can withstand a high level of noise and time delay introduced into flocking models, as well as parameter variation in the flocking system, to achieve robust reconstruction. The proposed method provides a new perspective for inferring the interaction structure of a swarm, which helps us to explore the mechanisms of collective movement in swarms and paves the way for developing the flocking models that can be quantified and predicted.

Detection of organized group movements in trajectory data

“…Our methodology with simulated data was evaluated using Entropy [7], Spectral Clustering, and a methodology similar to our references [11] in related works, utilizing measures such as entropy value, modularity, and the number of inferred edges in the evaluation, respectively, compared to ours using clustering quality via the Silhouette Coe cient as the evaluation metric.…”

“…The approach in [11] is based on the similarity of movement states. For the movement characteristics of the group formation models used, [11] considers three physical parameters of position, velocity, and angle as the movement states to examine similarity.…”

“…In the experiments of [11], they recorded the position x ti € ℝ 2 , velocity v ti € ℝ 2 , and angle ϴ ti € ℝ of each individual i (where i = 1, 2, ..., N) in the swarm at each time instant t (where t = 1,2,...,T) as time series. [11] used the existing movement state as input data and de ned the Euclidean distance d(s ti , s tj ), where s ti ℝ m (m ≥ 1) is the m-dimensional state vector of individual i at time t. s ti can be a one-dimensional angle, a two-dimensional position vector, a two-dimensional velocity vector, or a multidimensional state vector composed of the above movement states.…”

“…In the study of [11], the similarity between the movement trajectories of individuals in a swarm was measured using the Euclidean distance, where smaller distances indicate closer interactions. An adjacency matrix was generated from this measure, G t = (g tij ) N x N with t = (1, 2, ..., T), representing the connectivity between agents.…”

“…Spectral Clustering also has some limitations, such as sensitivity to tuning parameters and di culty in handling large volumes of data due to its computational complexity [10]. There are several approaches in the literature that seek to overcome these methods in identifying organized movement patterns, such as [11] and [12].…”