2015/08/12 by Kelum Gajamannage, Sachit Butail, Maurizio Porfiri +1 · 1 citation
Mathematics · Computer Science · Physics and Astronomy · #math.DS #cs.MA #math-ph #math.GT #math.MP #stat.ML #msc:57M60 #msc:37E99 #msc:57N35
paper · pdf · doi:10.1140/epjst/e2015-50088-2
12 pages, 6 figures, journal article
arxiv created 2015/08/12 · arxiv updated 2017/07/21
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.