Two-step dimensionality reduction of human mobility data: From potential landscapes to spatiotemporal insights

Understanding the spatiotemporal patterns of human mobility is crucial for addressing societal challenges, such as epidemic control and urban transportation optimization. Despite advancements in data collection, the complexity and scale of mobility data continue to pose significant analytical challenges. Existing methods often result in losing location-specific details and fail to fully capture the intricacies of human movement. This study proposes a two-step dimensionality reduction framework to overcome existing limitations. First, we construct a potential landscape of human flow from origin-destination (OD) matrices using combinatorial Hodge theory, preserving essential spatial and structural information while enabling an intuitive visualization of flow patterns. Second, we apply principal component analysis (PCA) to the potential landscape, systematically identifying major spatiotemporal patterns. By implementing this two-step reduction method, we reveal significant shifts during a pandemic, characterized by an overall declines in mobility and stark contrasts between weekdays and holidays. These findings underscore the effectiveness of our framework in uncovering complex mobility patterns and provide valuable insights into urban planning and public health interventions.