Topological Data Analysis of Collective Behavior in Public Transportation

• Main Authors: Macarasig, Ralph Joshua, Soria, Guinevere, Aycardo, Joaquin Emilio, Garcia, Albert, Nable, Job A, Go, Clark C
• Format: text
• Published: Archīum Ateneo 2024
• Subjects: Applied Mathematics; Mathematics; Physical Sciences and Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/253; https://doi.org/10.1063/5.0192149
• Institution: Ateneo De Manila University

Collective behaviour is a concept in social psychology that looks at local, individual interactions and overall group behaviour, and how these affect the dynamics of each individual member. One application is in public transportation where the focus is on determining the behaviours and interactions of passengers as they embark and disembark from public transportation. We want to understand what the shape of the dynamic interactions look like in collective behaviour of this kind. In this study, we utilize techniques from topological data analysis (TDA) in observing and analyzing simulations of collective behavior in public transportation. In particular, we apply persistent homology to identify emergent features from a sample of data points and we use the Mapper algorithm to generate simplified graph representations of these data points. The results show that these TDA techniques are able to capture various features of passenger behavior such as clusters and flares and these give insight to where passenger interactions happen and are concentrated in throughout the simulations. With this, TDA is able to provide a new framework for offering insights on understanding collective behavior.