Census Signal Temporal Logic Inference for Multiagent Group Behavior Analysis

In this paper, we define a novel census signal temporal logic (CensusSTL) that focuses on the number of agents in different subsets of a group that complete a certain task specified by the STL. CensusSTL consists of an 'inner logic' STL formula and an 'outer logic' STL formula. We present a new inference algorithm to infer CensusSTL formulas from the trajectory data of a group of agents. We first identify the 'inner logic' STL formula and then infer the subgroups based on whether the agents' behaviors satisfy the 'inner logic' formula at each time point. We use two different approaches to infer the subgroups based on similarity and complementarity, respectively. The 'outer logic' CensusSTL formula is inferred from the census trajectories of different subgroups. We apply the algorithm in analyzing data from a soccer match by inferring the CensusSTL formula for different subgroups of a soccer team.Note to Practitioners - The method described in this paper can be used to discover subgroups of agents and their behavior patterns based on spatial-temporal data of all agents in the group. The subgroups are formed by agents that behave similarly or complementarily for a certain task. The behavior patterns of the subgroups are expressed in the form of signal temporal logic statements. These are logical statements about the number of agents in the subgroups that are in certain states during a certain time interval. For example, if there are more than two blue agents in the region, then within 2 h, there will be more than three red agents in the same region. The behavior patterns inferred using this method can be used in: 1) analysis of group behavior while performing a task, e.g., in sports tactical analysis and 2) prediction of future group behavior under similar situations.