A study of holes: Topological analysis reveals crowd dynamics regimes in a bidirectional corridor scenario
For researchers studying crowd dynamics, this work demonstrates a novel application of topological data analysis to identify regimes without prior assumptions, though it is limited to simulated data and does not outperform existing methods.
This study uses topological analysis (persistent homology) to characterize crowd dynamics in a simulated bidirectional corridor scenario, showing that CROCKER matrices derived from pedestrian positions can separate different parameter configurations via principal component analysis.
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.