Exploring Nonlinear Built Environment Effects on Commercial Vitality in Xi’an’s Central Urban Area

In the context of urban regeneration, identifying the nonlinear and interactive effects of the built environment on commercial vitality is essential for targeted spatial improvement. Using Xi’an’s central urban area as a case study, this study integrated multi-source data, including POI, AOI, street-view imagery, and mobile phone signaling data, to delineate commercial spaces via kernel density analysis. With actual service population density as the vitality indicator, a built-environment framework was constructed using 14 indicators across four dimensions: transport accessibility, functional diversity, street quality, and environmental capacity. Random forest regression and SHAP-based interpretable machine learning were employed to examine factor importance, nonlinear thresholds, and interactions. Results show that environmental capacity and transport accessibility are the dominant dimensions, with building density, road network density, and employment density contributing most. Built-environment variables generally exhibit nonlinear threshold effects; key thresholds include road network density > 8 km/km2, building density > 40%, functional mix > 4.5, and sky view factor around 40%. Interactions involving building density are most pronounced, and its positive effect is significantly amplified under higher accessibility or employment density. These findings suggest prioritizing road network optimization and building coverage, while balancing functional mix and spatial scale in commercial space regeneration.