Potential Landscapes Reveal Spatiotemporal Structure in Urban Mobility: Hodge Decomposition and Principal Component Analysis of Tokyo Before and During COVID-19

Abstract

Understanding human mobility is vital to solving societal challenges, such as epidemic control and urban transportation optimization. Recent advancements in data collection now enable the exploration of dynamic mobility patterns in human flow. However, the vast volume and complexity of mobility data make it difficult to interpret spatiotemporal patterns directly, necessitating effective information reduction. The core challenge is to balance data simplification with information preservation: methods must retain location-specific information about human flows from origins to destinations while reducing the data to a comprehensible level. This study proposes a two-step dimensionality reduction framework: First, combinatorial Hodge theory is applied to the given origin--destination (OD) matrices with timestamps to construct a set of potential landscapes of human flow, preserving imbalanced trip information between locations. Second, principal component analysis (PCA) expresses the time series of potential landscapes as a linear combination of a few static spatial components, with their coefficients representing temporal variations. The framework systematically decouples the spatial and temporal components of the given data. By implementing this two-step reduction method, we reveal large weight variations during a pandemic, characterized by an overall decline in mobility and stark contrasts between weekdays and holidays. These findings demonstrate the effectiveness of our framework in uncovering complex mobility patterns and its potential to inform urban planning and public health interventions.