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A Random Forest-Based Framework for Evaluating Regional Urban Economic Circle Characteristics and Industrial Coupling in China

Yawen Zhou1
1School of Economics and Management, Pingdingshan Polytechnic College, Pingdingshan 467000, Henan, China

Abstract

Urban economic circles in China have emerged as critical engines of regional integration and industrial transformation. However, their internal dynamics—specifically, the interplay among city hierarchy, spatial proximity, and industrial coupling—remain insufficiently quantified. This paper proposes a novel machine-learning-based framework for evaluating the characteristics of regional urban economic circles and their degree of industrial synergy. Drawing on panel data from the China Statistical Yearbook (2003–2016), we calculate city-level industrial coupling values using a Shannon-information-entropy approach that reflects the sectoral balance across seven key industries. A two-level random forest regression model is then developed to capture the nonlinear relationships between spatial features (e.g., proximity to Tier-1 through Tier-4 cities and urban hierarchy) and coupling outcomes, with residual-error learning used to enhance model accuracy. To ensure robust inference, multiple spatial sampling and cross-validation strategies are benchmarked under varying degrees of spatial autocorrelation. Furthermore, we apply K-means++ clustering to 14 nationally recognized urban economic circles using standardized features such as city-tier distribution and sectoral employment structure, revealing three dominant types: “balanced-diversified,” “specialized-core,” and “transitioning” regions. The results show that proximity to Tier-2 and Tier-3 cities strongly influences coupling entropy, whereas certain industrial compositions—such as an overconcentration in construction or manufacturing—are associated with lower synergy. Model performance is validated through predictive experiments involving urban population estimation and multivariate error analysis across CO\(_2\), NO\(_2\), and HC indicators, demonstrating strong generalizability. Spatial distribution analysis further highlights core–periphery disparities and emerging multinodal patterns in selected regions (e.g., Chengdu, Xi’an, and Haikou).

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Citation

Yawen Zhou. A Random Forest-Based Framework for Evaluating Regional Urban Economic Circle Characteristics and Industrial Coupling in China[J], Archives Des Sciences, Volume 76, Issue 2, 2026. 40-51. DOI: .