Energy and resource sustainability patterns in the European Union through clustering and convergence dynamics

Introduction Energy and resource sustainability in the European Union cannot be represented adequately by a single ranking or by isolated relationships between individual indicators. Member States combine different levels of energy use, innovation effort, material throughput, emissions, resource productivity, and waste generation. Such combinations generate structural regimes that can persist even while overall cross-country dispersion declines. This study examines those regimes and their temporal evolution across the EU-27 during 2010–2023. Methods A balanced panel of 378 Member State-year observations was assembled from Eurostat using six indicators: primary energy consumption, gross domestic expenditure on research and development, raw material consumption, domestic net greenhouse gas emissions, resource productivity, and municipal waste generation. All clustering variables were z -standardized before K-Means estimation. Candidate solutions from k = 2 to k = 10 were evaluated using within-cluster sum of squares, silhouette coefficient, Calinski-Harabasz index, Davies-Bouldin index, Gap Statistic, cluster-size structure, and resampling stability. Robustness was examined through an unstandardized specification, Yeo-Johnson transformation, 1st−99th percentile winsorization, and RobustScaler preprocessing. Country-year mobility, sigma-convergence, and beta-convergence were then analyzed separately from the clustering step. Results Joint validation supported a four-cluster primary specification rather than the previously imposed three-cluster structure. Cluster 1 represents a lower-intensity resource and innovation profile and contains 59.26% of observations. Cluster 2 combines stronger innovation and resource productivity with higher waste and emissions. Cluster 3 combines very high R&D and material consumption with comparatively low net greenhouse gas emissions. Cluster 4 captures a persistent high-intensity energy, emissions, and resource profile. Standardized and unstandardized partitions showed very low agreement (ARI = 0.135), confirming strong scale distortion in the raw metric space. Winsorization reproduced the baseline partition almost exactly (ARI = 0.981). Only 3 of 351 adjacent-year transitions changed cluster, producing 99.15% persistence. Multivariate RMS distance to the annual EU centroid declined by 14.45% and the beta-convergence coefficient was −0.0358 ( p < 0.001). Resource productivity nevertheless displayed significant divergence, while R&D dispersion showed no significant linear convergence. Discussion EU energy-resource sustainability is therefore characterized by persistent structural regimes combined with measurable convergence inside the system. Convergence does not occur mainly through widespread movement between clusters. It occurs through declining multivariate distances while most countries remain within stable structural profiles. Results support differentiated policy design, because innovation capacity, material intensity, resource productivity, energy use, and environmental pressure do not improve synchronously. Methodological findings also show that scale correction, explicit k-selection, resampling stability, and panel-aware temporal diagnostics are necessary for defensible sustainability clustering.