Nonlinear associations between the built environment and urban vitality in Anyang using multi-source data and explainable machine learning

As China’s urban development shifts from spatial expansion toward quality-oriented renewal, scientific planning has become increasingly important for small and medium-sized cities. Taking the main urban area of Anyang, China, as a case study, this study developed an integrated framework to assess urban vitality and explore its associations with the built environment. A four-dimensional vitality index covering economic, social, cultural, and ecological dimensions was constructed. Four regression models were compared, and SHAP was employed to interpret feature importance, nonlinear relationships, thresholds, and interactions. Results showed that urban vitality was concentrated in the eastern core area, with local clusters in the west and a gradual decline toward the periphery. XGBoost achieved the best performance. SHAP analysis revealed that distance to the nearest commercial center was the most influential factor, followed by POI mix degree, health service accessibility, general POI density, and building height. Interaction analysis indicated that vitality was shaped by the combined effects of functional diversity, development intensity, facility accessibility, and transport connectivity. These findings highlight the importance of coordinated urban functions and provide insights for differentiated renewal strategies in small and medium-sized cities.