How urban amenity factors shape the geography of innovative enterprises: A geographical random forest approach in Beijing

Innovative enterprises cluster within urban environments where knowledge resources, accessibility, services, and environmental quality jointly shape locational attractiveness. Using 27,052 geocoded innovative enterprises and thirteen amenity indicators across 4708 0.5 km 2 hexagonal grids in Beijing, this study applies geographical random forest (GRF) to examine citywide importance, spatial heterogeneity, contextual variation, and nonlinear amenity-response relationships. Under five-fold spatial block cross-validation, GRF achieves the strongest geographic generalization (R 2 = 0.744), outperforming OLS, global RF, and GWR. Education and research amenities rank first citywide, followed by bus-station density and healthcare, while local importance varies substantially across the metropolitan area. Contextual comparisons show that cultural amenities become more prominent within the Fifth Ring Road, whereas greenspace and regional transportation accessibility gain importance outside it. Major innovation policy platforms display a distinct profile centered on bus accessibility, knowledge infrastructure, recreation, and culture. Nonlinear analysis further shows that several amenity relationships rise rapidly before stabilizing, whereas subway accessibility exhibits distance-decay stabilization and park and high-speed rail accessibility display turning structures. These findings indicate that amenity importance depends on both location and provision range. By integrating global and local importance, spatial validation, contextual comparisons, and nonlinear responses, the study provides a differentiated empirical basis for amenity planning in innovation-oriented urban development.