Flow Tree: A Dynamical Classifier for Quantifying Navigation Paths and Strategies

Navigation is inherently dynamic. It involves learning the environment, as well as positions in and trajectories through it, and then executing a path to reach a target. Spatial navigation skills vary significantly among individuals. But what differentiates a good navigator from a bad one, or an easy-to-navigate path from a hard one? Studies have analyzed exploration and navigation using static quantitative measures, e.g., location tallies or distance travelled. However, static metrics are inherently limited for characterization of dynamic behaviors. To fill this gap, we introduce the Flow Tree, a novel data structure, which tracks a group of trajectories (different people or the same person over time). This is a discrete adaptation of the Reeb graph, a mathematical structure from topology, computed from multiple trajectories. Each divergence in trajectory is captured as a node, encoding variability of the collection. We apply the Flow Tree to a behavioral dataset of 100 humans exploring and then navigating a small, closed-form maze in virtual reality, where the Flow Tree encodes navigation path difficulty, based on the trials used to encode it. We (1) define the Flow Tree and the algorithm used to calculate it, (2) show that Flow Trees predict path difficulty better than static metrics, and (3) apply the Flow Tree to predict individual success. We (4) introduce a hypothesis testing framework using Flow Trees to quantitatively differentiate between strategies of the best navigators and those of the worst.