Morphological quantification of population activity hotspots and their nonlinear relationships with urban structural and functional features

Urban structure and functional layout create complex population activity hotspot (PAH) with polycentricity, spatiotemporal dynamics, and indistinct boundaries. Current research often overlooks spatial heterogeneity and assumes linear correlations, limiting both the accurate characterization of PAH and the exploration of nonlinear relationships between PAHs and urban features. Therefore, we propose an adaptive region search method with dual-consideration of polycentricity and activity intensity gradient (DPAIG) for accurately identifying high-density population activity zones and their dynamic perimeters. Subsequently, a 2D Gaussian fitting model (2DGFM) quantifies PAH morphology with concise parameters. Using interpretable machine learning, we analyze nonlinear relationships between PAH morphology and urban features. A case study in Wuhan demonstrates that the boundaries identified by DPAIG closely align with geographic boundaries. The Gradient Volatility Index (GVI) is 0.586, a 7.57% reduction relative to the second-best method, with smoother gradient transitions. The 2DGFM offers a high-precision parametric representation of PAH morphology ( R 2 = 0.939). Further analysis identifies building-related and natural terrain features as having the highest predictive contribution to the extent and orientation of PAHs, respectively, showing “inverted U-shaped” and “W-shaped” relationships with notable threshold effects. This study presents a quantitative framework for characterizing dynamic PAHs and examining their nonlinear relationships with related urban factors, providing valuable insights for emergency management and urban sustainability.