Maximum Markovian order detection for collective behavior

Many advances have been achieved in the study of collective behavior of animal groups and human beings. Markovian order is a significant property in collective behavior, which reveals the inter-agent interaction strategy of the system. In this study, we propose a method using the time-series data of collective behavior to determine the optimal maximum Markov order of time-series motion data so as to reflect the maximum memory capacity of the interacting network. Our method combines a time-delayed causal inference algorithm and a multi-order graphical model. We apply the method to the data of pigeon flocks, dogs, and a group of midges to determine their optimal maximum order for validation and construct high-order De Bruijn graphs as a stochastic model to describe their interacting relationships. Most temporal network data of animal movements can be effectively analyzed by our method, which may provide a practical and promising solution to detection of the optimal maximum Markovian order of collective behavior.