A Data-Driven Assessment of Urban–Rural Educational Equity in Northern China: Integrating Principal Component Analysis and K-Means Clustering with Digital Infrastructure Indicators

This study presents a data-driven evaluation of urban–rural educational equity in four northern Chinese provinces (Shandong, Shanxi, Henan, and Hebei) during 2009–2022, emphasizing the role of digital infrastructure in narrowing the education gap. By constructing a multidimensional index composed of fiscal input, teacher allocation, economic background, and broadband access metrics, we apply Principal Component Analysis (PCA) to extract a Comprehensive Education Equity Index (CEI). Subsequently, K-Means clustering is performed on the CEI combined with auxiliary features (urbanization rate, per-capita GDP, broadband port density, and funding gaps) to identify spatial stratification patterns. Results reveal three distinct clusters—low, medium, and high equity—characterized by divergent temporal trajectories: Shanxi Province advances directly to high equity in 2013, Shandong and Hebei achieve medium equity by 2013 and 2016 respectively, while Henan lags until 2017. These patterns underscore significant heterogeneity in policy implementation effectiveness, fiscal investment, and digital infrastructure deployment. Our findings indicate that improved broadband access (ports per 10 000 population) and balanced fiscal spending positively correlate with accelerated equity gains. The study concludes with policy recommendations for establishing dynamic monitoring systems, promoting data-driven teacher allocation strategies, and accelerating “Internet + Education” programs to target low-baseline regions. The methodological framework—combining PCA and clustering on panel data enriched with digital indicators—demonstrates the value of soft computing techniques in educational policy analysis and provides empirical guidance for stakeholders seeking to foster equitable, high-quality development in similar contexts.