A study of holes: Topological analysis reveals crowd dynamics regimes in a bidirectional corridor scenario

Abstract

This study harnesses topological analysis in an attempt to reveal structure in the dynamics of a crowd. Topology and in particular persistent homology characterizes relational structures in data through the number of connected components and holes, that is, a loop of pairwise connection with no connections across it. We apply this universal data analysis method to a simulated time series of individual pedestrian positions of a crowd moving through a wide corridor -- either uni- or bidirectional. We consider two pedestrians to be connected, when they are sufficiently close. This approach leads to two matrices containing the persistence signatures for the whole time series, so-called CROCKERs. Despite the high level of data abstraction, the CROCKERs' first two principal components on time-delayed positional data show a clear separation of the different parameter configurations. This holds up to symmetry. Our results support our claim that persistent homology is a useful tool to characterize crowd dynamics without introducing any prior assumptions about the detectable spatio-temporal patterns.