Topological analysis of group fragmentation in multiagent systems.

In social animals, the presence of conflicts of interest or multiple leaders can promote the emergence of two or more subgroups. Such subgroups are easily recognizable by human observers, yet a quantitative and objective measure of group fragmentation is currently lacking. In this paper, we explore the feasibility of detecting group fragmentation by embedding the raw data from the individuals' motions on a low-dimensional manifold and analyzing the topological features of this manifold. To perform the embedding, we employ the isomap algorithm, which is a data-driven machine learning tool extensively used in computer vision. We implement this procedure on a data set generated by a modified à la Vicsek model, where agents are partitioned into two or more subsets and an independent leader is assigned to each subset. The dimensionality of the embedding manifold is shown to be a measure of the number of emerging subgroups in the selected observation window and a cluster analysis is proposed to aid the interpretation of these findings. To explore the feasibility of using this approach to characterize group fragmentation in real time and thus reduce the computational cost in data processing and storage, we propose an interpolation method based on an inverse mapping from the embedding space to the original space. The effectiveness of the interpolation technique is illustrated on a test-bed example with potential impact on the regulation of collective behavior of animal groups using robotic stimuli.