KASVA: A Variational Deep Learning Framework for Measuring Regional Sustainability and Inequality

Assessing regional sustainability is challenged by the multidimensional, non-linear, and highly correlated nature of socio-economic and environmental indicators. Conventional composite indices often rely on linear aggregation and fixed weighting schemes, which can obscure structural interdependencies and amplify scale dominance. To address these limitations, this study proposes the Knowledge-Aware Sustainability Variational Assessment (KASVA), a deep-learning-based framework that integrates variational representation learning, latent-space clustering, and robustness analysis to construct a composite sustainability index. Using a comprehensive set of demographic, economic, social, and environmental indicators for Turkish Nomenclature of Territorial Units for Statistics level 2 (NUTS2) regions, KASVA learns a compact latent representation that captures non-linear interactions among indicators exhibiting strong multicollinearity, with pairwise correlations frequently exceeding 0.8. The resulting Global Territorial Variational Sustainability Index (GTVSI) reveals substantial regional heterogeneity and pronounced spatial inequality. Latent-space clustering identifies distinct regional sustainability regimes, with silhouette scores predominantly in the range 0.4–0.5, indicating stable and well-separated clusters. Robustness analysis based on 1000 bootstrap resamples demonstrates high ranking stability, with a median Spearman rank correlation of approximately 0.69 and the majority of correlations exceeding 0.6. Compared with conventional equal-weight and principal component analysis (PCA)-based indices, the proposed framework yields more coherent and stable regional rankings. Overall, KASVA provides a data-driven, robust approach to sustainability assessment, offering improved interpretability and reliability for regional policy analysis and evidence-based decision-making.