The Threeway Approximate Spatiotemporal Symmetry (TASS) Algorithm: A Method for Trivariate Time Series Segmentation

Symmetry has communicative power. Psychological agents may mimic the behavior of connected others in order to communicate agreeance or affiliation. This is seen, for instance, in the gestures of conversation partners and in the signals of interrelated brain regions. Much of the research in interagent symmetry has focused on bivariate symmetry---the symmetry between two agents. The symmetry dynamics in networks of three or more psychological agents, however, may contain more than bivariate relationships. The current study presents the Threeway Approximate Spatiotemporal Symmetry (TASS) algorithm, a novel methodological approach to measuring the symmetry between three psychological agents. The TASS algorithm is an extension of the Pairwise Approximate Spatiotemporal Symmetry (PASS) algorithm to three signals. Like the PASS algorithm, the TASS algorithm determines when in time three signals exhibit symmetry and when they do not. The emphasis on symmetry as an intermittent phenomenon provides information that other symmetry algorithms, which emphasize the magnitude or lag, fail to capture. The TASS algorithm was validated using simulated time series. Then, two empirical datasets were used to demonstrate ecological validity in the TASS algorithm. Results suggest that the TASS algorithm may be used to extract meaningful segments of symmetry.