Is a Life Circle a Circle? Topological Data Analysis on Activity Space Delineation

Activity space is a foundational concept in urban and behavioral geography, yet its complex and varied morphology has long eluded conventional representations. We introduce a topological data analysis (TDA) pipeline that couples persistent homology with high-resolution raster geo-computation to model activity space as a continuous field of daily mobility intensity. Thresholding persistent clusters and loops yields concise, data-driven boundaries of life circles without imposing geometric priors. Using anonymized mobile-phone signaling data for Shenzhen, we delineate individual activity space and collective life circles at a fifteen-minute-walk scale. Persistent clusters capture frequently visited anchor points or residents’ activity clusters, whereas persistent cavities reveal activity voids encircled by high-intensity visits. The resulting maps expose systematic preferences for specific land-use mixes and built-form configurations, demonstrating that life circles adopt far richer topologies than simple discs. These empirically grounded, adaptive boundaries offer planners a robust framework for configuring pedestrian-oriented neighborhoods and tailoring fifteen-minute-city policies to actual mobility patterns.