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

1 Introduction

European climate and resource policy has entered a phase in which decarbonization, energy security, circularity, industrial competitiveness, and technological transformation must be pursued simultaneously. European Green Deal objectives and the 2030 Agenda place energy and material efficiency at the center of economic restructuring, but Member States approach these objectives from markedly different production systems, innovation capacities, resource endowments, consumption patterns, and institutional settings (Borowiecki et al., 2023; European Commission, 2023; Stefanis et al., 2024). Recent geopolitical and energy-market shocks have reinforced this heterogeneity. National transition pathways now reflect not only environmental ambition but also exposure to energy price volatility, industrial specialization, fiscal capacity, and the speed at which cleaner technologies can be absorbed. Such conditions make cross-country comparison necessary, but they also make a single linear ranking conceptually restrictive.

Energy sustainability is often studied through relationships among energy consumption, economic growth, and emissions. Large econometric literatures examine decoupling, Environmental Kuznets Curve mechanisms, renewable-energy effects, and causal interactions between economic output and environmental pressure (Dilanchiev et al., 2024; Efayena et al., 2026; Gershon et al., 2024; Salari et al., 2021). Resource-oriented research adds material footprint, resource productivity, circular material use, and waste management to this framework (Diaz et al., 2021; Dzhengiz et al., 2023; Garg et al., 2025b). Innovation research further shows that R&D expenditure and technological capability influence green productivity, energy efficiency, and the diffusion of low-carbon technologies (Cheng et al., 2024; Dogan et al., 2025; Satrovic et al., 2025). Each stream identifies an important mechanism. None, by itself, describes how those mechanisms combine into recurrent national sustainability configurations.

Configuration matters because favorable performance in one dimension can coexist with pressure in another. High resource productivity can coexist with high material throughput. Strong R&D effort can coexist with high primary energy demand. Low emissions can reflect technological progress, structural specialization, energy composition, or weaker production scale. High municipal waste generation can coexist with sophisticated waste-management systems. Consequently, interpretations based only on the direction of individual indicators risk assigning normative meaning to multidimensional profiles that are structurally more complex. A clustering framework is useful precisely because it groups observations according to joint similarity rather than forcing every indicator into a single ordered score (Miraftabzadeh et al., 2023; Młodak, 2021; Strielkowski et al., 2024).

Application of clustering to sustainability data nevertheless creates methodological obligations. Euclidean K-Means is scale-sensitive. Variables measured in kilograms, percentages, tons, and euro per kilogram cannot be combined defensibly in raw form because large-variance variables dominate distances. Candidate cluster counts should not be selected solely because a particular partition appears substantively convenient or easy to interpret. Instead, the choice of the number of clusters should be supported by internal validation criteria, resampling-based stability assessment, examination of cluster-size structure, and sensitivity analyses with respect to data standardization and preprocessing, in order to distinguish persistent multivariate structure from specification-dependent artifacts (Hennig, 2007; Milligan and Cooper, 1988; Rousseeuw, 1987; Tibshirani et al., 2001). Panel data create an additional challenge. A country-year observation can change cluster over time, so pooled clustering cannot be narrated as a fixed country taxonomy unless the temporal aggregation rule is explicit.

Existing European clustering studies demonstrate the usefulness of configuration-based analysis but also reveal the need for stronger differentiation between substantive questions and clustering designs. (Georgescu et al. 2025c) analyzed the transition to climate neutrality using a broader set of 10 energy, environmental, social, and macroeconomic indicators for 2011–2022, K-Means clustering, ranking procedures, and subsequent policy-oriented meta-cluster consolidation. Present research addresses a different empirical object. Focus is restricted to six energy-resource indicators for 2010–2023. Unit of analysis is explicitly the Member State-year. Primary clustering is performed only after z-standardization. Candidate k values are examined from 2 to 10. Stability is assessed through repeated perturbation. Raw-scale clustering is retained only as a sensitivity comparison. Temporal mobility and convergence are then analyzed with dedicated diagnostics rather than inferred from a pooled partition. This design separates structural classification from temporal convergence and therefore avoids treating cluster membership itself as evidence of convergence or divergence.

Research gap follows from this distinction. European sustainability studies provide extensive evidence about causal drivers, national performance differences, circular-economy indicators, and cluster-based typologies. Less attention has been given to a fully validated longitudinal clustering design in which scale correction, k-selection, stability, preprocessing sensitivity, country-year membership, and convergence diagnostics are integrated in one analytical sequence. Gap is methodological and substantive at the same time. Methodologically, a robust unsupervised solution must demonstrate that the identified regimes survive plausible perturbations and are not generated by measurement units. Substantively, policy interpretation requires evidence about whether Member States remain structurally segmented, move between regimes, or become more similar while retaining stable cluster identities.

Aim of the study is to identify and explain recurrent energy-resource sustainability regimes across the EU-27 and to determine how those regimes coexist with cross-country convergence during 2010–2023. Four operational objectives structure the analysis:

• O.1 Construct a transparent and scale-corrected multivariate representation of energy consumption, innovation effort, material use, emissions, resource productivity, and municipal waste generation;
• O.2 Identify a defensible K-means partition by combining internal validation, resampling stability, cluster-size structure, parsimony, and substantive interpretability;
• O.3 Characterize cluster profiles and country-year membership, including robustness to alternative preprocessing and the exact frequency of inter-cluster mobility;
• O.4 Evaluate sigma-convergence and beta-convergence separately from clustering in order to determine whether structural persistence can coexist with declining cross-country dispersion.

Three research questions follow from these objectives.

• RQ1: Which distinct energy-resource sustainability regimes emerge across EU Member State-year observations after correcting for measurement scale and validating the cluster structure?
• RQ2: How stable and substantively interpretable is the selected partition relative to alternative values of k and alternative preprocessing specifications?
• RQ3: Does the EU-27 exhibit persistent structural regimes, inter-cluster mobility, sigma-convergence, beta-convergence, or a combination of these processes during 2010–2023?

Novelty of this study derives from the integration of structural classification and longitudinal convergence analysis within a common multidimensional framework for energy and resource sustainability. Existing clustering approaches are effective in identifying groups of countries with similar characteristics, but a static partition provides limited information about the evolution of those configurations over time. Countries can preserve a relatively stable structural profile while simultaneously reducing their distance from the broader European distribution. Conversely, apparent similarity at one point in time does not establish that national trajectories are converging. Distinguishing between structural configuration, temporal persistence, and continuous convergence is therefore essential for understanding sustainability transitions across heterogeneous economies.

Present study addresses this distinction by analyzing energy and resource sustainability as a multidimensional configuration rather than as the performance of individual indicators considered separately. Six variables capture complementary dimensions of this configuration: primary energy consumption, research and development expenditure, raw material consumption, domestic net greenhouse gas emissions, resource productivity, and municipal waste generation. Joint analysis preserves the interactions and trade-offs among these dimensions. High resource productivity, for example, does not necessarily coincide with low material consumption. Strong innovation capacity does not automatically imply low energy use or low emissions. Similarly, comparatively low environmental pressure can coexist with limited innovation intensity or weak resource productivity. Cluster analysis therefore identifies structural combinations that cannot be adequately represented by a single sustainability ranking, as low environmental pressure may coexist with structural constraints or limited technological transformation.

A second contribution concerns the relationship between structural heterogeneity and temporal change. Country-year observations are retained as the fundamental analytical unit throughout the study. This approach makes it possible to identify structural regimes without suppressing the longitudinal information contained in the panel. Annual membership sequences reveal whether countries remain within the same structural configuration or move between regimes. Continuous convergence measures complement this categorical perspective by examining whether cross-country distances decrease over time. Structural persistence and convergence consequently become distinct but related empirical processes.

Study contributes to the literature at three interconnected levels. Conceptually, it distinguishes structural regime membership from convergence in continuous multidimensional space. Methodologically, it integrates standardized clustering, multi-criterion cluster selection, resampling stability, preprocessing sensitivity, temporal mobility, and convergence analysis within a single longitudinal design. Empirically, it provides evidence on how energy and resource sustainability configurations evolved across all EU Member States during 2010–2023. Combined perspective offers a more complete representation of European sustainability dynamics than either static clustering or isolated convergence analysis.

Article proceeds from this conceptual distinction. Section 2 develops the theoretical relationships among energy use, innovation, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation and formulates the research hypotheses. Section 3 presents the panel dataset and analytical design, including standardization, K-Means estimation, cluster-number assessment, stability analysis, robustness procedures, temporal mobility, and convergence models. Section 4 reports the empirical structure of the identified regimes and their evolution during 2010–2023. Section 5 interprets these findings in relation to sustainability-transition, circular-economy, innovation, and European integration literature and develops their policy implications. Section 6 answers the research questions and synthesizes the theoretical, methodological, and empirical contributions of the study.

2 Literature review

The increasing complexity of sustainability challenges within the European Union has stimulated extensive research on the interconnections between energy consumption, resource use, environmental pressure, and technological transformation. In the context of the European Green Deal (European Commission, 2023) and the transition toward climate neutrality, sustainability is increasingly understood as a multidimensional and systemic process shaped by the interaction between energy systems, material flows, innovation dynamics, and consumption patterns (Andersen and Geels, 2023; Georgescu et al., 2025b; Stefanis et al., 2024). Consequently, analyzing energy and resource sustainability requires integrative perspectives capable of linking economic, technological, and environmental dimensions within coherent analytical frameworks.

Traditional research has primarily relied on causal econometric approaches examining the relationships between energy consumption, economic growth, and emissions (Dilanchiev et al., 2024; Gahlot and Garg, 2025; Usman et al., 2022). While these studies provide valuable insights into decoupling and environmental efficiency, they often adopt linear assumptions and predefined relationships. Parallel research streams emphasize circular economy principles, highlighting resource productivity, material efficiency, and waste management, while innovation-oriented studies stress the role of technological progress and R&D intensity in supporting green transitions (Ricciardi et al., 2026; Tabares et al., 2025). However, these perspectives frequently remain fragmented, addressing sustainability dimensions separately rather than as interconnected structural processes.

Recent literature increasingly acknowledges the structural heterogeneity of European economies, where differences in industrial structure, technological capacity, and institutional settings generate diverse sustainability outcomes (Durán-Romero et al., 2025; Pinar and Karahasan, 2026; Santos and Conte, 2025). This has encouraged the adoption of analytical approaches capable of identifying latent patterns and multidimensional configurations beyond aggregate indicators and ranking-based assessments. In this context, data-driven methods and machine learning techniques have emerged as valuable exploratory tools for uncovering hidden structural relationships within complex sustainability datasets (Bag et al., 2024; Ye et al., 2024).

Building on these developments, the present literature review is organized around four complementary thematic domains: the energy-environment nexus, resource efficiency and circular economy perspectives, innovation-driven green transitions, and data-driven analytical approaches. Together, these domains provide the theoretical foundation for a configuration-based framework aimed at capturing the multidimensional nature of sustainability performance across European Union Member States.

2.1 Energy consumption, environmental pressure, and sustainability transitions

The relationship between energy consumption and environmental pressure represents one of the most extensively debated themes within sustainability research, particularly in the context of European climate policies and decarbonization strategies (Bluszcz et al., 2025; Nagaj et al., 2024; Stefanis et al., 2024). Classical environmental economics literature has traditionally examined this nexus through the lens of growth-environment interactions, emphasizing how energy demand associated with economic expansion contributes to greenhouse gas emissions and environmental degradation (Arshad et al., 2025; Montagna et al., 2025; Raihan, 2023). Within this framework, energy intensity has been widely used as a proxy for structural efficiency, reflecting the extent to which economic systems rely on resource-intensive production models. However, recent studies increasingly acknowledge that the sustainability implications of energy consumption cannot be interpreted solely through aggregate consumption levels, but must be understood in relation to technological structure, sectoral composition, and national development trajectories (Khalili et al., 2026; Mujeeb et al., 2025; Waseem et al., 2025).

In the European Union, the transition toward climate neutrality has intensified scholarly attention on the dynamics of energy transformation, particularly the capacity of economies to reduce emissions while maintaining economic competitiveness. Research highlights that decoupling processes are often uneven across countries, reflecting differences in industrial specialization, energy mix composition, and institutional capacity (Bluszcz et al., 2025; Dhondt et al., 2025; Wigger, 2023). While some economies have successfully reduced emissions through efficiency gains and technological modernization, others continue to face structural constraints linked to legacy infrastructures and high dependence on fossil fuels (Borowiecki et al., 2023; Georgescu et al., 2025a; Shobande et al., 2025). Consequently, sustainability transitions are increasingly interpreted as path-dependent processes shaped by historical development patterns rather than uniform trajectories.

Moreover, recent contributions emphasize that energy sustainability should be analyzed as part of broader socio-economic systems in which consumption patterns, technological innovation, and policy interventions interact simultaneously (Handoyo, 2026; Lucendo-Monedero et al., 2023; Yakymchuk and Rataj, 2025). This systemic perspective challenges purely linear interpretations and suggests that environmental pressure emerges from complex interactions between energy demand, production scale, and efficiency improvements. For example, technologically advanced economies may achieve higher efficiency while simultaneously maintaining high absolute consumption levels, resulting in persistent environmental pressure despite relative improvements (Georgescu et al., 2025c; Rudolf and Schmidt, 2025; Zhen et al., 2022). Conversely, lower consumption levels may reflect structural economic limitations rather than successful sustainability outcomes.

As a result, contemporary literature increasingly calls for analytical frameworks capable of capturing multidimensional sustainability configurations rather than focusing exclusively on causal relationships between individual variables. Understanding how energy consumption interacts with emissions, innovation capacity, and resource efficiency has therefore become essential for identifying differentiated sustainability pathways within heterogeneous economic areas such as the European Union (Caglar et al., 2024; Chovancová et al., 2025; Jitmaneeroj, 2026). This perspective provides a conceptual foundation for exploring structural patterns of sustainability performance beyond traditional econometric approaches.

2.2 Resource efficiency and circular economy perspectives

Resource efficiency has emerged as a central concept in sustainability discourse, particularly through the growing influence of circular economy frameworks that seek to decouple economic growth from material consumption (Calisto Friant et al., 2024; Dzhengiz et al., 2023). Unlike linear economic models based on extraction-production-disposal processes, circular economy perspectives emphasize the optimization of material flows, waste reduction, and the reintegration of resources into production cycles (Islam et al., 2024; Pariso and Marino, 2026). Within this paradigm, resource productivity and waste generation indicators have gained increasing relevance as measures of structural sustainability performance, reflecting the capacity of economies to generate economic value while minimizing environmental impact (Bai et al., 2025; Potkány et al., 2025; Vranjanac et al., 2023).

Empirical research suggests that European countries exhibit substantial variation in resource efficiency outcomes, shaped by differences in industrial structure, technological development, and policy implementation (Chatzistamoulou and Kounetas, 2023; Fan and Wang, 2024; Sardianou et al., 2024). Advanced economies often display higher levels of resource productivity due to technological innovation and service-oriented economic models, whereas economies with stronger industrial dependence may experience higher material throughput and waste generation (Amjadi and DiMaria, 2025; Fortea et al., 2026; Li and Jiang, 2026). However, the literature also emphasizes that improvements in resource efficiency do not necessarily imply reductions in absolute material consumption, as efficiency gains may be offset by scale effects associated with economic growth and consumption expansion (Malatyinszki et al., 2025; OECD, 2022).

Another important strand of research highlights the role of waste management systems as indicators of circular economy maturity. Municipal waste generation, in particular, is frequently used to capture consumption-related environmental pressure and the effectiveness of recycling and recovery policies (Alengebawy et al., 2024; Ferronato et al., 2024; Karlilar Pata and Pata, 2025). Studies indicate that high-income economies often generate larger volumes of waste despite having more advanced recycling infrastructures, illustrating the complex relationship between economic prosperity and environmental outcomes (Blagoeva et al., 2023; Kostakis et al., 2026; Velis et al., 2023). This paradox reinforces the need to analyze sustainability performance through multidimensional frameworks capable of integrating efficiency and scale considerations simultaneously.

Furthermore, circular economy literature increasingly adopts a systemic view, arguing that material efficiency, innovation, and institutional capacity jointly determine sustainability outcomes (Castro-Lopez et al., 2023; de Oliveira Vieira and Guarnieri, 2025). Rather than evaluating countries through isolated indicators, recent studies advocate for approaches that capture structural combinations of resource use, productivity, and environmental pressure (Cerkini et al., 2025; Garg et al., 2025a). Such perspectives recognize that economies may follow distinct sustainability configurations depending on their structural characteristics and development pathways. Consequently, analyzing resource efficiency within a broader multidimensional context becomes essential for understanding the diversity of sustainability trajectories observed across European Union Member States.

2.3 Innovation capacity and technological drivers of green transition

Innovation has been widely recognized as a key enabling factor in sustainability transitions, providing the technological foundations necessary for improving energy efficiency, reducing emissions, and enhancing resource productivity (Jiang et al., 2024; Liu and Liang, 2024). Theoretical and empirical studies consistently emphasize the role of research and development (R&D) investment in fostering technological progress capable of supporting long-term decarbonization strategies (Abdelkafi, 2025; Alka et al., 2025; Di Vaio et al., 2024). In the context of the European Union, innovation policies are often positioned at the center of green transition agendas, reflecting the belief that technological advancement can reconcile economic competitiveness with environmental sustainability (Epstein, 2025; Teixeira, 2025; Vela Almeida et al., 2023).

Existing literature demonstrates that economies with higher innovation intensity tend to exhibit greater adaptive capacity in responding to environmental challenges (Alcalde-Calonge et al., 2024; Satrovic et al., 2025; Shi, 2024). Technological development contributes to the diffusion of cleaner production methods, digital resource management systems, and low-carbon energy solutions, thereby supporting structural transformation toward more sustainable economic models (Ma et al., 2024; Tan et al., 2024). However, research also indicates that the relationship between innovation and sustainability outcomes is not always straightforward (Afeltra et al., 2021; Urbinati et al., 2023). In some cases, high levels of technological development coexist with substantial energy consumption and environmental pressure, suggesting that innovation-driven productivity gains may be accompanied by increased economic scale and consumption intensity (Alam et al., 2026; Feng and Qu, 2023; OECD, 2025).

Moreover, innovation capacity itself is unevenly distributed across European economies, reflecting differences in institutional support, human capital, and investment capacity (Brodny and Tutak, 2025; Vărzaru, 2025; Xu et al., 2022). These disparities generate heterogeneous sustainability outcomes, with technologically advanced countries often positioned at the forefront of efficiency improvements, while structurally constrained economies face difficulties in adopting and implementing green technologies. As a result, innovation emerges not only as a driver of sustainability but also as a source of divergence between countries, influencing their ability to transition toward circular and low-carbon development pathways (Munir et al., 2024; Wang et al., 2025).

Recent studies increasingly highlight the need to analyze innovation within integrated sustainability frameworks rather than as an isolated variable (Ahmad et al., 2024; Miranda et al., 2023). The interaction between technological capacity, energy consumption, and resource efficiency suggests that innovation contributes to complex structural configurations that shape national sustainability profiles (Ibrahim et al., 2025; Zhang et al., 2025). Consequently, understanding the role of innovation requires analytical approaches capable of capturing multidimensional relationships and identifying latent patterns across countries, particularly within heterogeneous regional contexts such as the European Union.

2.4 Data-driven approaches and clustering methods in sustainability research

The growing availability of multidimensional sustainability data has stimulated increasing interest in analytical approaches capable of identifying hidden structures within complex datasets. Traditional econometric models, while effective for testing causal hypotheses, often rely on predefined theoretical assumptions and may not fully capture the structural heterogeneity characterizing sustainability transitions (Bistuer et al., 2026; Józwik et al., 2025; Satalkina and Steiner, 2025). As sustainability research evolves toward more systemic perspectives, data-driven methodologies have gained prominence as complementary tools capable of uncovering latent patterns without imposing rigid analytical structures (Bag et al., 2024; Quiñones-Gómez et al., 2025).

Among these approaches, machine learning techniques have been increasingly adopted in environmental and sustainability studies due to their capacity to handle multidimensional data and identify non-obvious relationships. Unsupervised learning methods, in particular, allow researchers to classify observations based on similarity structures rather than predefined dependent-independent variable relationships (Aouedi et al., 2022; Nagar et al., 2024; Valkenborg et al., 2023). This shift from explanatory modeling toward structural pattern recognition reflects a broader methodological transformation within sustainability science, where understanding diversity and configuration becomes as important as identifying causal effects (Oliveira et al., 2024; Qian et al., 2025).

Clustering algorithms, and especially the K-Means method, have proven valuable for identifying groups of countries or regions that share similar sustainability characteristics (Dai et al., 2023; Kudal et al., 2024; Miraftabzadeh et al., 2023). By minimizing within-group variance and maximizing between-group differences, K-Means enables the identification of latent sustainability regimes that may remain hidden in traditional indicator-based analyses. Such approaches are particularly relevant in the European Union context, where substantial structural heterogeneity exists across energy systems, innovation capacity, and resource efficiency. Instead of producing hierarchical rankings, clustering methods reveal structural archetypes, offering a configuration-based understanding of sustainability performance (Brunetta and Caputo, 2026; Le Dréau et al., 2023; Strielkowski et al., 2024).

Recent literature increasingly advocates for integrating machine learning techniques into sustainability research as a means of improving analytical flexibility and enhancing policy relevance (Achuthan et al., 2025; Palanichamy et al., 2025; Valencia-Arias et al., 2025). By identifying clusters of structurally similar economies, data-driven approaches can support differentiated policy design tailored to specific sustainability configurations. Consequently, clustering methods represent a promising analytical direction for exploring multidimensional sustainability dynamics and for complementing conventional econometric frameworks with exploratory, pattern-oriented perspectives.

Several recent studies provide particularly relevant methodological precedents for the present analysis. (Kudal et al. 2024) apply non-hierarchical K-Means clustering to environmental indicators across OECD countries, demonstrating the usefulness of multivariate segmentation for identifying cross-country environmental configurations. (Miraftabzadeh et al. 2023) examine K-Means together with alternative clustering approaches in modern power systems, highlighting the broader methodological relevance of clustering for complex energy-related datasets. More directly in the European sustainability context, (Georgescu et al. 2025a) employ K-Means to identify differentiated pathways toward climate neutrality across EU Member States using a broader set of energy, environmental, social, and macroeconomic indicators. These studies establish clustering as a useful configuration-based approach, but the present research extends this methodological line in several respects. The analytical unit is explicitly the Member State-year observation, all variables are scale-corrected before the primary clustering procedure, alternative values of k are evaluated rather than imposed a priori, partition stability and preprocessing sensitivity are assessed explicitly, and temporal mobility and convergence are examined separately from the pooled clustering solution. This design therefore shifts the emphasis from the identification of interpretable country groups alone toward the empirical validation and longitudinal assessment of recurrent sustainability regimes.

Beyond these applied precedents, the methodological literature emphasizes that cluster validity is multidimensional and should not be inferred from a single diagnostic criterion. Internal validation indices capture different properties of a partition, including cohesion, separation, and relative cluster geometry, and may therefore favor different numbers of clusters depending on the underlying data structure (Hassan et al., 2024; Rousseeuw, 1987; Tibshirani et al., 2001). Stability provides a complementary criterion because it evaluates whether the identified grouping is reproducible under plausible perturbations of the data rather than being specific to a particular sample realization (Hennig, 2007; Liu et al., 2022). Recent methodological reviews accordingly recommend combining internal validity assessment with stability analysis when evaluating unsupervised classifications, particularly when no external ground-truth partition is available (Hassan et al., 2024; Liu et al., 2022). For distance-based methods such as K-Means, this assessment should also consider sensitivity to standardization and preprocessing because transformations of scale and distribution can materially alter the geometry of the resulting partition (Milligan and Cooper, 1988).

2.5 Research gap

Despite the substantial body of literature addressing energy sustainability, resource efficiency, circular economy dynamics, and innovation-driven green transitions, several important limitations remain evident. First, much of the existing empirical research relies on econometric approaches focused on testing causal relationships between individual indicators, such as energy consumption, emissions, or economic growth. While these studies provide valuable insights into specific mechanisms, they often assume predefined structural relationships and therefore overlook the possibility that sustainability outcomes emerge from complex multidimensional interactions. Second, a large proportion of sustainability assessments continues to employ composite indices or ranking-based frameworks, which, although useful for benchmarking purposes, tend to reduce structural complexity to aggregated scores and mask the coexistence of heterogeneous sustainability configurations across countries.

Furthermore, although recent research increasingly recognizes the structural diversity of European economies, empirical analyses rarely adopt methodologies capable of identifying latent sustainability regimes based on multidimensional similarity. The interaction between energy intensity, innovation capacity, resource productivity, material consumption, and environmental pressure is typically examined in isolation rather than as interconnected components of broader structural systems. As a result, existing studies provide limited understanding of how distinct sustainability archetypes emerge and persist within the European Union.

From a methodological perspective, the application of unsupervised machine learning techniques remains relatively underexplored in sustainability research, particularly in studies focused on energy and resource performance at the EU level. There is therefore a clear need for exploratory analytical approaches capable of moving beyond causal inference toward structural pattern identification, allowing for the detection of latent configurations that better reflect the multidimensional nature of sustainability transitions.

Building on the theoretical perspectives discussed above, the present study positions itself at the intersection of sustainability transition research and emerging data-driven analytical approaches. By integrating insights from energy economics, circular economy theory, innovation studies, and machine learning methodologies, the research adopts a configuration-based perspective aimed at identifying structural patterns of sustainability performance across European Union Member States. Rather than testing predefined causal relationships, the study seeks to uncover latent sustainability regimes that reflect the combined interaction of energy use, environmental pressure, technological capacity, and resource efficiency. This conceptual orientation provides the foundation for employing an unsupervised clustering framework, presented in the following methodology section, as a suitable approach for capturing the multidimensional and heterogeneous nature of sustainability dynamics within the European Union.

2.6 Working hypotheses

European energy and resource sustainability develops within a common institutional framework, but Member States enter the transition from substantially different structural positions. National energy systems differ in consumption intensity, technological composition, and dependence on carbon-intensive activities. Material throughput reflects differences in productive specialization, consumption patterns, and resource dependence. Innovation capacity is also unevenly distributed, while resource productivity and environmental pressures vary considerably across national economies. These differences create multidimensional combinations that are unlikely to be represented adequately by a single homogeneous European sustainability profile. Recent empirical evidence supports this expectation of structural heterogeneity. EU Member States have been shown to follow differentiated energy-transition pathways and to form distinct groups according to their policy configurations, technological capacities, and progress toward climate neutrality (Borozan, 2022; Georgescu et al., 2025a).

Structural heterogeneity is expected to generate identifiable groups of country-year observations characterized by internally similar combinations of energy use, innovation, material consumption, emissions, resource productivity, and waste generation. Such groups represent sustainability regimes in a structural sense. They describe recurrent configurations within the multidimensional indicator space rather than positions along a predetermined hierarchy of national performance. This reasoning leads to the following hypothesis:

• H1. EU Member State-year observations exhibit a distinct and empirically validated multivariate structure, forming energy and resource sustainability regimes characterized by systematically different structural profiles.

Differences among sustainability regimes are also expected to extend beyond simple contrasts between high and low environmental performance. Energy-resource transitions involve several dimensions that can evolve at different speeds and may generate trade-offs. Strong innovation capacity can coexist with high material consumption when technological advancement develops within resource-intensive productive systems. High resource productivity can coexist with substantial absolute resource use when efficiency gains occur alongside large production and consumption volumes. Similarly, lower emissions or waste generation do not necessarily indicate stronger technological capacity or more advanced resource efficiency. Recent evidence for the EU similarly indicates that improvements in resource productivity do not necessarily imply proportional reductions in material footprint or environmental pressure, because the relationship depends on the level of material use, structural composition, technological progress, and scale effects (Guo et al., 2025; Mushafiq and Prusak, 2023).

Multidimensional sustainability regimes should therefore reflect different combinations of technological capability, resource efficiency, material throughput, energy use, and environmental pressure. Such configurations cannot be interpreted consistently as successive positions on a single sustainability scale. Their substantive meaning derives instead from the joint profile of the indicators defining each regime. Accordingly, the second hypothesis is formulated as follows:

• H2. Energy and resource sustainability regimes exhibit systematically non-uniform combinations of innovation capacity, resource productivity, material intensity, energy consumption, and environmental pressure, reflecting cross-dimensional trade-offs rather than a common sustainability ordering.

Temporal continuity represents another important characteristic of national sustainability transitions. Energy infrastructure, industrial specialization, technological capabilities, resource-use patterns, and innovation systems are shaped by cumulative investment and institutional development. These structural characteristics cannot be transformed rapidly because they depend on long-lived capital, established production networks, technological trajectories, and national policy capacities. Path dependence should consequently generate substantial continuity in the relative structural position of Member States. This expectation is consistent with recent sustainability-transition research showing that path dependence is sustained by self-reinforcing mechanisms embedded in technological systems, infrastructure, institutions, and established development trajectories, which can constrain rapid structural reconfiguration (Apajalahti and Kungl, 2022; Tomai and Papachristos, 2026).

Common European policies can stimulate adjustment without necessarily producing frequent transitions between sustainability regimes. Improvements in individual indicators may occur within an existing structural configuration before they become sufficiently large to alter a country's multidimensional position. Stable cluster membership can therefore coexist with gradual quantitative change. From this perspective, persistence represents an expected property of the structural regimes rather than an absence of sustainability progress. This reasoning supports the third hypothesis:

• H3. Energy and resource sustainability regimes exhibit substantial temporal persistence, with limited year-to-year transitions of Member States between structural regimes.

European integration simultaneously creates mechanisms capable of reducing cross-country disparities. Common climate targets, environmental regulation, energy-market integration, technology diffusion, cohesion instruments, and coordinated circular-economy policies can promote gradual approximation among Member States. Convergence should nevertheless remain heterogeneous because the six sustainability dimensions respond to different economic and institutional mechanisms. Resource productivity does not appear to converge through a single common European trajectory; instead, Member States can form distinct convergence clubs characterized by persistent disparities and different adjustment pathways (Afolabi and Islam, 2025; Thomann et al., 2026). Energy consumption and greenhouse gas emissions are directly influenced by decarbonization policies and efficiency standards. Material consumption depends strongly on productive specialization and consumption structures. Resource productivity reflects both technological efficiency and economic composition. Research and development intensity is connected to cumulative innovation capacity and can therefore display stronger persistence across countries. Recent EU evidence supports such a differentiated convergence perspective.

Consequently, convergence in multidimensional sustainability does not imply uniform convergence in every underlying indicator. Cross-country distances can decrease at the aggregate multivariate level while particular dimensions remain stable or even become more dispersed. Such a process is consistent with differentiated European transition pathways in which national economies become progressively closer without losing all structural specificity. This leads to the fourth hypothesis:

• H4. EU Member States exhibit declining multivariate dispersion in energy and resource sustainability during 2010–2023, while the direction and intensity of convergence differ across individual sustainability dimensions.

Taken together, these hypotheses describe sustainability transition as a process in which structural heterogeneity, regime persistence, and cross-country convergence can coexist. H1 concerns the existence of distinct multidimensional configurations. H2 concerns the internal composition of those configurations and the coexistence of technological strengths with environmental or resource pressures. H3 introduces the temporal stability of structural membership. H4 addresses changes in continuous cross-country distances and indicator-specific dispersion. This distinction is important because persistence and convergence describe different dimensions of structural change. Member States can remain within relatively stable sustainability regimes while simultaneously reducing their quantitative distance from the broader European distribution.

3 Methodology

3.1 Research design and analytical unit

This study adopts a quantitative, exploratory, longitudinal, and configuration-oriented research design, which aims to identify recurrent multivariate regimes and then examine their temporal persistence and convergence in European Union. Primary unit of clustering is the Member State-year observation. Every country contributes one observation for each year from 2010 through 2023. Resulting balanced panel contains 27 countries × 14 years = 378 observation The analysis allowing for a longitudinal assessment of sustainability configurations in a phase marked by the consolidation of EU climate policies, the advancement of the circular economy agenda, and the increasing focus on innovation-based decarbonization. Covering the period 2010–2023, the study encompasses the post-financial crisis recovery phase, the progressive implementation of the Europe 2020 strategy (European Commission, 2010), and the transition to the European Green Deal framework, thus ensuring political relevance and structural depth.

Pooled K-Means is used to estimate common structural profiles across the full observation space. Country-year treatment permits a country to change cluster if its multivariate position crosses a cluster boundary. Subsequent mobility analysis preserves the temporal order of those assignments. A single 2023 map is used only for cross-sectional visualization. Modal country labels are retained as descriptive summaries when useful, but they do not replace annual membership. This distinction directly separates the clustering unit from later visualization choices.

Empirical analysis is organized into five interconnected stages that progressively address data comparability, structural classification, cluster interpretation, robustness, and temporal dynamics (Figure 1).

Empirical analysis progresses from data preparation to structural classification and subsequently to the examination of temporal dynamics. Data audit and standardization establish a comparable multidimensional space for the indicators included in the analysis. Cluster estimation identifies recurrent energy-resource configurations across Member State-year observations, while complementary validation criteria assess the statistical properties and stability of alternative partitions. Cluster profiling subsequently translates the selected partition into substantively interpretable configurations by examining both standardized centroids and values expressed in the original measurement units. Robustness and sensitivity analyses evaluate the extent to which the identified structure remains consistent under alternative preprocessing specifications. Longitudinal analysis extends the structural classification by examining year-to-year membership persistence and changes in cross-country distances over time. This sequential design distinguishes structural similarity, cluster stability, temporal mobility, and convergence as related but analytically distinct dimensions of European energy-resource sustainability.

3.2 Data sources, indicators, and sample completeness

Data were obtained from Eurostat series corresponding to the SDG and circular-economy monitoring frameworks. Six indicators were selected because together they represent energy demand, innovation capacity, material throughput, environmental pressure, efficiency of material use, and consumption-related waste. Indicator selection also maintains a manageable dimensional space for clustering while preserving the major structural dimensions discussed in present research. Table 1 reports symbols, definitions, units, and dataset codes.

Table 1. Indicators included in the energy-resource sustainability framework.

All series refer to EU Member States. RMC corresponds to Eurostat SDG 12.21 material footprint/raw material consumption and is expressed in tons per inhabitant. RESPRO uses euro per kilogram in 2015-based chain-linked volumes for temporal comparability.

Sources: Eurostat datasets reported in the final column; Authors' elaboration.

No missing values were present in the analytical panel. Audit identified 378 valid observations for every indicator and zero country-year duplicates. No imputation, interpolation, or model-based replacement was performed. No country or year was removed. Complete-case sample therefore equals the full planned EU-27 panel for 2010–2023. This point is important because interpolation would have introduced artificial temporal smoothness into later mobility and convergence measures.

Distributional diagnostics indicate meaningful asymmetry in several dimensions of the EU energy-resource sustainability space. Positive skewness is particularly pronounced for primary energy consumption (1.750) and raw material consumption (1.659), indicating that a limited number of Member State-year observations are positioned substantially above the central tendency of the European distribution. IQR-based diagnostics identify 20 observations outside the conventional Tukey bounds for primary energy consumption, 16 for raw material consumption, 9 for domestic net greenhouse gas emissions, 3 for resource productivity, and 7 for municipal waste generation. Gross domestic expenditure on research and development records no observations beyond these thresholds. Such distributional patterns reflect substantial structural differences among EU Member States in energy use, material throughput, environmental pressure, resource efficiency, and innovation capacity. Values located toward the tails of these distributions are therefore informative for characterizing the multidimensional heterogeneity of European energy-resource systems rather than being interpreted automatically as anomalous observations. Preserving the observed distributions allows the empirical analysis to represent both central tendencies and structurally distinctive country-year configurations. Sensitivity analysis subsequently examines whether the identified multivariate structure remains stable under alternative treatments of distributional extremes and data transformations.

Primary energy consumption per capita captures the intensity of energy use and reflects structural characteristics of national production and consumption systems. Gross domestic expenditure on research and development (as a percentage of GDP) serves as a proxy for innovation capacity and technological advancement, given its established role in facilitating energy efficiency improvements and emissions reduction. Raw material consumption measures the material footprint of economies and is directly linked to circular economy performance and resource dependency. Domestic net greenhouse gas emissions per capita represent environmental pressure and climate impact. Resource productivity, expressed in euro per kilogram (chain-linked volumes), reflects the efficiency with which material inputs are transformed into economic output. Finally, municipal waste generation per capita captures consumption-related environmental pressure and the effectiveness of waste management systems. Data audit confirmed 27 countries, 14 years, no duplicated country-year records, and 378 complete cases. No analytical imputation, interpolation, or listwise deletion was applied. Every clustering variable contained 378 observed values in the assembled analytical dataset.

Descriptive statistics (Table 2) reveal substantial differences in both measurement units and numerical dispersion across the six dimensions of energy-resource sustainability. Municipal waste generation varies between 247 and 862 kg per capita, whereas gross domestic expenditure on research and development ranges from 0.38% to 3.71% of GDP. Comparable differences arise from the measurement scales of primary energy consumption, raw material consumption, greenhouse gas emissions, and resource productivity. Consequently, absolute numerical differences among observations do not have an equivalent meaning across indicators when expressed in their original units. This issue is particularly relevant for distance-based classification. K-Means constructs clusters by minimizing within-cluster squared Euclidean distances, and the contribution of each variable to those distances depends on its numerical dispersion. In the original measurement space, municipal waste generation accounts for approximately 99.57% of the aggregate raw variance across the six indicators. This proportion reflects differences in measurement scale rather than the substantive importance of municipal waste within the sustainability framework. Direct clustering in the original units would therefore assign markedly unequal metric influence to the dimensions included in the analysis.

Table 2. Descriptive statistics for the analytical panel, 2010–2023.

N = 378 for every variable. No imputation or interpolation was applied. SD denotes standard deviation. Skewness is reported to document distributional asymmetry before sensitivity transformations.

Source: Authors' calculation.

Standardization establishes a common metric for the six indicators while preserving the relative position of each observation within its corresponding distribution. Each variable is centered around its mean and expressed in standard-deviation units before cluster estimation. Energy consumption, innovation expenditure, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation consequently enter the multidimensional distance space on a comparable numerical basis. Cluster formation can thus reflect their joint configuration rather than differences generated by the original units of measurement.

Correlation analysis (Table 3) provides additional information on the relationships among the dimensions of energy-resource sustainability. Primary energy consumption is positively associated with raw material consumption (r = 0.619) and domestic net greenhouse gas emissions (r = 0.582). These relationships indicate that higher levels of energy use tend to coexist with greater material throughput and stronger emission pressures across Member State-year observations. At the same time, the magnitude of the coefficients remains moderate, indicating that energy consumption, material use, and emissions capture related but distinct structural characteristics of national economies.

Table 3. Pearson correlation matrix for the six raw indicators.

Pearson correlations are invariant to linear z-standardization. N = 378 for all coefficients. Matrix is descriptive and is reported to show the association structure among clustering variables, not to establish causal relationships.

Source: Authors' calculation.

Resource productivity presents a different relational pattern. Its positive correlation with municipal waste generation (r = 0.534) shows that greater economic output relative to material inputs does not necessarily coincide with lower quantities of municipal waste. Its relationship with raw material consumption is weak and negative (r = −0.197), further illustrating the distinction between resource efficiency and the absolute scale of material use. An economy can improve the value generated per unit of material input without experiencing a proportional reduction in total material consumption.

Innovation intensity is only weakly associated with several environmental dimensions. In particular, gross domestic expenditure on research and development shows a very weak positive correlation with domestic net greenhouse gas emissions (r = 0.082). Innovation capacity and environmental pressure therefore occupy different positions within the observed sustainability structure. Higher research intensity is not systematically accompanied by either proportionally higher or lower emission levels across the pooled Member State-year observations.

The correlation structure reveals interconnected dimensions without indicating strong linear redundancy among the indicators. Energy consumption, material throughput, emissions, innovation effort, resource productivity, and municipal waste generation capture different aspects of national energy-resource configurations. Their relationships also reveal combinations that are relevant for subsequent structural analysis, particularly the coexistence of efficiency gains with absolute environmental pressures and the imperfect correspondence between technological capacity and environmental outcomes.

3.3 Standardization and distance geometry

Differences in measurement units and dispersion across the six indicators require their transformation to a common metric before estimating the multivariate configurations. Standardization was performed across the complete panel of 378 Member State-year observations, using the full 2010–2023 distribution of each indicator. This transformation preserves the relative position of every observation within its respective distribution while expressing all dimensions on a comparable scale. Country and year were retained exclusively as panel identifiers and were not included among the variables used to estimate the clusters.

For each observation i and indicator j, the standardized value was calculated as Equation 1:

zij=xij-μjσj(1)

where:

z_*ij* = standardized value of indicator j for observation i;

x_*ij* = observed value of indicator j for observation i;

μ_*j* = arithmetic mean of indicator j calculated across the complete analytical sample;

σ_*j* = population standard deviation of indicator j calculated across the complete analytical sample;

i = 1, 2,…., 378 denotes the Member State-year observation;

j = 1, 2,…., 6 denotes the sustainability indicator.

Mean centering transforms each indicator around a common reference value of zero, while division by its population standard deviation expresses individual observations in standard-deviation units. Following transformation, each of the six indicators has a mean of approximately zero and a variance of one within the analytical sample. Euclidean distances used by K-Means are consequently calculated within a standardized multidimensional space in which differences among observations are expressed relative to the empirical dispersion of each sustainability dimension.

Standardization also determines the interpretation of the resulting centroids. Positive centroid values indicate that a cluster is positioned above the EU-27 panel mean for the corresponding indicator, whereas negative values indicate a position below that mean. Absolute centroid magnitude expresses the distance from the overall mean in standard-deviation units. Centroid profiles can therefore be compared across indicators despite differences in their original measurement scales.

Original observations were retained alongside their standardized counterparts and were subsequently used to characterize the empirical magnitude of each cluster profile. Standardized centroids describe the relative position of clusters within the common multivariate space, whereas cluster means expressed in original units provide their substantive interpretation in terms of energy consumption, innovation expenditure, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation. Reporting both representations connect the statistical geometry of the clustering procedure with the economic and environmental characteristics of the identified sustainability regimes.

3.4 K-Means estimation and candidate-cluster validation

K-Means clustering was employed to identify recurrent multivariate configurations of energy and resource sustainability across the EU-27 panel. Each Member State-year observation is represented by a six-dimensional standardized vector, and observations with similar positions in this multidimensional space are assigned to the same cluster. Resulting partitions characterize groups with comparable combinations of energy consumption, innovation intensity, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation.

For a predefined number of clusters k, K-Means minimizes the within-cluster sum of squared Euclidean distances between observations and their corresponding cluster centroids. The objective function is expressed as:

WCSS(k)=∑c=1k∑i∈Cc|| zi-μc||22 (2)

where:

WCSS(k) = within-cluster sum of squares for a solution containing k clusters;

k = number of clusters considered in the partition;

C_*c* = set of observations assigned to cluster c;

z_*i* = standardized six-dimensional feature vector associated with observation i;

μ_*c* = centroid vector of cluster c;

c = 1,2,…, k denotes the cluster index.

Minimization of Equation 2 produces clusters characterized by relatively small within-group distances in the standardized indicator space. Centroids represent the multivariate center of each resulting configuration and provide the basis for subsequent interpretation of the energy-resource sustainability profiles.

Cluster estimation used k-means++ initialization to distribute the initial centroids across the feature space before iterative optimization. Each candidate specification was estimated with 100 initializations, a maximum of 1,000 iterations per initialization, and a convergence tolerance of 10⁻⁴ fixed random seed of 2026 was applied throughout the main estimation procedure. Computation was performed in Python 3.14.7 using NumPy 2.5.2, pandas 3.0.5, SciPy 1.18.0, and scikit-learn 1.9.0 under Windows 11. These specifications were maintained consistently across candidate cluster solutions to ensure comparability of the estimated partitions.

Cluster structure was examined over k = 2,…,10. This range permits the empirical configuration of the panel to be evaluated at different levels of partition granularity, from broad structural differentiation to more detailed segmentation. Assessment combined complementary measures because cluster quality encompasses several properties, including within-cluster compactness, between-cluster separation, partition stability, and the empirical composition of the resulting groups. This multi-criterion strategy is consistent with methodological guidance emphasizing that no single validation index captures all relevant properties of a clustering solution and that different indices may favor different partitions depending on data geometry and structure (Hassan et al., 2024; Liu et al., 2022). Internal geometric criteria were therefore complemented by resampling-based stability assessment, since reproducibility under data perturbation captures a distinct property of the partition that cohesion and separation measures alone cannot establish (Hassan et al., 2024; Hennig, 2007). This combined approach reduces reliance on any single diagnostic criterion when selecting the primary cluster specification.

Within-cluster sum of squares was examined across candidate values of k to identify changes in the marginal reduction of within-cluster dispersion. Because WCSS necessarily decreases as additional clusters are introduced, its trajectory was considered jointly with the Silhouette coefficient, Calinski-Harabasz index, Davies-Bouldin index, and Gap Statistic.

Silhouette analysis evaluates each observation by comparing its cohesion within the assigned cluster with its separation from the nearest alternative cluster. For observation 3, the Silhouette coefficient is defined as Equation 3:

s(i)=b(i)-a(i)max{a(i),b(i)}(3)

where:

s(i) = Silhouette coefficient for observation i;

a(i) = mean Euclidean distance between observation i and all other observations assigned to the same cluster;

b(i) = minimum mean Euclidean distance between observation i and the observations belonging to any alternative cluster.

Values of s(i) range from −1 to 1. Values approaching 1 indicate that observation i is substantially closer to the observations within its assigned cluster than to those belonging to the nearest alternative cluster. Values close to zero characterize observations positioned near the boundary between two clusters, whereas negative values indicate greater similarity with an alternative cluster than with the assigned cluster. Individual Silhouette coefficients were averaged across all Member State-year observations to obtain the mean Silhouette coefficient for each candidate partition. Comparisons were performed across solutions containing between 2 and 10 clusters, with higher mean Silhouette values indicating greater within-cluster cohesion combined with stronger separation between clusters.

Calinski-Harabasz and Davies-Bouldin indices provide complementary information about cluster geometry. Calinski-Harabasz evaluates between-cluster dispersion relative to within-cluster dispersion, with larger values indicating stronger separation relative to internal compactness. Davies-Bouldin evaluates the similarity between each cluster and its most comparable neighboring cluster by relating within-cluster dispersion to between-centroid distance. Lower values indicate more clearly differentiated partitions.

Gap Statistic extends this assessment by comparing the observed within-cluster dispersion with the dispersion expected under a reference distribution without the same empirical concentration of observations. For each candidate value of k, 200 reference datasets were generated uniformly within the empirical bounding box of the standardized feature space. K-Means estimation for the reference datasets used 20 initializations. The statistic is expressed as Equation 4:

Gap(k)=𝔼 * [log(Wk*)]-log(Wk)(4)

where:

Gap(k) = Gap Statistic associated with a k-cluster solution;

W_*k* = within-cluster dispersion obtained from the observed standardized data;

Wk* = within-cluster dispersion obtained from a reference dataset for the same value of k;

𝔼 * [·] = expectation calculated across the reference datasets.

Standard errors of the Gap Statistic were calculated from the reference replications and incorporated into the evaluation of candidate solutions through the one-standard-error criterion. This provides a reference-based perspective on whether additional partitioning produces meaningful improvements in cluster structure relative to dispersion arising in data without the observed multivariate configuration.

Partition stability was examined separately from geometric validity. Resampling analysis evaluated the reproducibility of candidate partitions when the observational composition of the panel was perturbed. Repeated subsamples containing 80% of the observations were generated without replacement, and the resulting classifications were compared with the corresponding reference partitions using the Adjusted Rand Index. Five hundred replications were performed for each candidate value of k. Stability was summarized through the mean and median Adjusted Rand Index and the proportion of replications reaching high agreement with the reference classification.

Selection of the primary cluster specification integrated information from internal cluster geometry, reference-based assessment, resampling stability, cluster composition, and substantive differentiation of the resulting multivariate profiles. Candidate solutions were therefore interpreted as alternative representations of the same standardized energy-resource space at different levels of structural resolution. This approach permits the selected partition to retain sufficient differentiation among sustainability configurations while preserving clusters with meaningful empirical representation across the EU-27 panel.

3.5 Resampling stability and robustness

Stability analysis examined the reproducibility of the cluster structure under changes in the observational composition of the sample. Repeated subsampling was performed by drawing 80% of the 378 Member State-year observations without replacement. K-Means was re-estimated independently for each subsample using the same standardized feature space and the corresponding candidate number of clusters. Cluster assignments obtained from each resampled dataset were compared with the assignments of the full-sample reference partition for the observations included in that subsample.

Agreement between partitions was quantified using the Adjusted Rand Index (ARI). Unlike a direct comparison of numerical cluster labels, ARI evaluates agreement between pairs of observations and is invariant to permutations of cluster labels. Its adjustment for agreement expected by chance makes it suitable for assessing whether the grouping structure is reproduced across repeated perturbations of the analytical sample. Five hundred subsampling replications were performed for each candidate partition. Stability was summarized by the mean and median ARI and by the proportions of replications with ARI values of at least 0.80 and 0.90. These measures provide complementary information on average reproducibility, the central tendency of the stability distribution, and the frequency with which candidate partitions retain high correspondence with the full-sample structure.

Sensitivity to centroid initialization was examined separately from sensitivity to sample composition. For candidate solutions containing between two and six clusters, K-Means was repeatedly estimated from single k-means++ initializations generated under different random seeds. Five hundred replications were performed for each candidate solution, and each resulting partition was compared with the corresponding full-sample reference solution estimated using 100 initializations. This analysis characterizes the extent to which alternative starting configurations lead to different local solutions within the same standardized feature space. Subsampling and initialization analyses consequently address two distinct properties of cluster reproducibility: stability under changes in the observations entering the estimation and stability under changes in the initial centroid configuration.

Preprocessing robustness was evaluated by comparing the baseline standardized partition with alternative representations of the six-dimensional indicator space. Four specifications were considered. K-Means applied to the indicators in their original units provided a direct assessment of sensitivity to measurement scale. A Yeo-Johnson transformation followed by z-score standardization modified distributional asymmetry while maintaining a standardized metric. Winsorization at the 1st and 99th percentiles followed by z-score standardization reduced the influence of observations located at the extreme tails of the indicator distributions. Robust scaling based on the median and interquartile range provided an alternative representation in which location and dispersion were less sensitive to extreme values.

Correspondence between each alternative specification and the baseline partition was quantified using ARI. Values approaching one indicate that the same Member State-year observations remain grouped together under the alternative preprocessing procedure, whereas lower values indicate increasing changes in partition composition. Robustness is therefore evaluated at the level of cluster membership rather than solely through changes in internal validation indices.

Internal cluster-quality measures were additionally calculated for each preprocessing specification to characterize the geometry generated within the corresponding transformed feature space. Their interpretation remained specific to the metric representation from which they were calculated. Transformations such as z-score standardization, Yeo-Johnson transformation, original-unit scaling, and median/IQR scaling alter distances and dispersion directly; absolute values of distance-based internal indices across these different spaces therefore describe different geometries. Partition agreement measured through ARI provides the common basis for evaluating whether the substantive grouping of Member State-year observations is preserved across preprocessing specifications.

3.6 Cluster profiling and longitudinal membership

Cluster profiling was conducted in both standardized and original measurement spaces to provide complementary representations of the identified energy-resource sustainability regimes. Standardized centroids characterize the relative position of each cluster across the six dimensions and indicate the magnitude and direction of its deviation from the overall EU-27 panel mean. Cluster-specific means expressed in the original measurement units complement this representation by providing the substantive magnitude of energy consumption, innovation intensity, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation within each configuration.

Structural profiles were interpreted from the joint configuration of the six indicators. Cluster labels were assigned according to the characteristics that most clearly differentiate each configuration within the multidimensional space. Interpretation accounts for the distinct economic and environmental meaning of the indicators. Resource productivity reflects the efficiency with which material inputs are transformed into economic value, whereas material consumption and greenhouse gas emissions capture dimensions of environmental pressure. Research and development expenditure represents technological and innovation capacity, while energy consumption and municipal waste generation describe additional dimensions of resource use and environmental intensity. Cluster profiles therefore express characteristic combinations of these dimensions rather than positions on a unidimensional sustainability scale.

This profile-based interpretation is particularly relevant when favorable characteristics coexist with comparatively high environmental pressures. Strong innovation capacity may accompany intensive material use, while high resource productivity may coexist with elevated consumption or waste generation. Conversely, lower levels of energy use or emissions may occur in configurations characterized by more limited innovation intensity or resource productivity. Cluster identity is consequently determined by the overall configuration of characteristics rather than by the direction of any single indicator.

Longitudinal information was preserved by retaining cluster membership for each of the 378 Member State-year observations. For every Member State, the resulting sequence contains fourteen annual classifications corresponding to the period 2010–2023. Annual membership trajectories provide the basis for examining the temporal continuity of the identified structural regimes and for detecting transitions between configurations over successive years.

Two complementary graphical representations were used to describe the spatial and temporal structure of cluster membership. A country-year heatmap represents annual cluster assignments throughout 2010–2023 and makes the persistence or movement of individual Member States observable across the complete study period. A choropleth map represents cluster membership specifically for 2023 and provides a cross-sectional geographical representation of the most recent year included in the panel. Consequently, the heatmap captures longitudinal membership trajectories, whereas the choropleth describes the geographical distribution of the identified regimes at a defined point in time.

Modal cluster membership was additionally calculated for each Member State as a descriptive summary of its most frequently observed configuration during 2010–2023. Modal membership summarizes the dominant structural profile over the study period, while annual assignments remain the primary representation for longitudinal analysis. Temporal mobility is therefore derived from consecutive annual memberships rather than from the modal classification.

3.7 Temporal mobility

Temporal mobility was examined through annual changes in cluster membership for each EU Member State over the 2010–2023 period. Because the analytical unit is the Member State-year observation, the sequence of annual cluster assignments provides a longitudinal representation of each country's position within the identified energy-resource sustainability regimes. Comparing consecutive observations within the same country makes it possible to determine whether its structural configuration remains within the same regime or shifts to another configuration over time.

For each Member State, cluster membership in year t was compared with membership in year t−1. A transition was recorded when the two consecutive observations belonged to different clusters, whereas unchanged membership represented persistence within the same structural regime. With 14 annual observations for each of the 27 Member States, each country contributes 13 adjacent-year comparisons. Temporal mobility is therefore evaluated over 27 × (14 – 1) = 351 country-specific annual transitions.

For country i between years t−1 and t, the transition indicator was defined as Equation 5:

Mi,t={1, Ci,t≠ Ci,t-10, Ci,t= Ci,t-1(5)

where:

M_{*i, t*} = transition indicator for Member State i between two consecutive years;

C_{*i, t*} = cluster membership of Member State i in year t;

C_{*i, t*−1} = cluster membership of the same Member State in the preceding year;

M_{*i, t*} = 1 indicates movement from one energy-resource sustainability regime to another;

M_{*i, t*} = 0 indicates persistence within the same regime.

Overall mobility was calculated as the proportion of observed cluster changes among all valid adjacent-year comparisons (Equation 6):

MR=∑27i=1∑2023t=2011Mi,t351(6)

where:

MR = overall temporal mobility rate;

∑ M_*i,t* = total number of observed year-to-year changes in cluster membership;

351 = total number of valid adjacent-year comparisons across the EU-27 panel.

Correspondingly, the persistence rate was calculated as Equation 7:

PR=1-MR(7)

where:

PR = proportion of adjacent-year comparisons in which Member States remain within the same structural regime;

MR = temporal mobility rate.

Transition analysis was complemented by the identification of the Member States experiencing regime changes, the years in which those changes occurred, and the direction of movement between clusters. This information characterizes the temporal architecture of the estimated regimes by distinguishing highly persistent national trajectories from trajectories involving changes in structural configuration. The country-year heatmap provides the corresponding longitudinal visualization of these membership sequences over the complete 2010–2023 period.

Temporal mobility and convergence represent different dimensions of longitudinal change. Mobility is categorical and captures movement across the boundaries of the estimated energy-resource sustainability regimes. Convergence is continuous and concerns changes in the relative distances among Member States within the multidimensional indicator space. A country may therefore remain within the same structural regime throughout the observation period while progressively approaching the European distribution. Conversely, a change in cluster membership indicates a shift in structural configuration but does not, by itself, establish a general reduction in cross-country disparities. For this reason, the evolution of continuous multivariate distances is examined separately through sigma- and beta-convergence analysis.

3.8 Sigma-convergence

Sigma-convergence was examined to determine whether cross-country dispersion in energy-resource sustainability decreased across the EU-27 during 2010–2023. Analysis was conducted at two complementary levels. Indicator-specific measures describe the evolution of dispersion separately for each sustainability dimension, whereas multivariate measures capture changes in the overall distance among Member States within the six-dimensional standardized space.

For each indicator, annual cross-sectional dispersion was calculated across the 27 Member States using the globally standardized values obtained from the complete 2010–2023 panel. Because the same full-sample mean and standard deviation are used throughout the study period, annual changes in dispersion remain expressed relative to a common reference scale. A reduction in cross-sectional dispersion over time indicates increasing similarity among Member States for the corresponding sustainability dimension, whereas increasing dispersion indicates widening cross-country differences.

Temporal evolution of indicator-specific dispersion was evaluated using linear trend models in which annual cross-sectional standard deviation was related to year. The estimated slope captures the direction and average annual change in dispersion over the observation period. Negative coefficients indicate declining cross-country dispersion, while positive coefficients indicate increasing dispersion. Spearman rank correlation and Kendall rank correlation were additionally calculated between year and annual dispersion to characterize the direction and monotonicity of temporal change independently of a strictly linear specification.

Multivariate sigma-convergence was examined from the relative position of each Member State within the complete six-dimensional sustainability space. For each year, an annual EU-27 centroid was calculated from the standardized indicator vectors of the 27 Member States. Euclidean distance between each national observation and the corresponding annual centroid represents the magnitude of its multivariate deviation from the European center in that year.

Root-mean-square multivariate distance in year t was calculated as Equation 8:

Dt=1N∑i=1N|| zit-z¯t||22 (8)

where:

D_*t* = root-mean-square multivariate distance from the annual EU-27 centroid in year t;

N = number of Member States observed in each year, with N = 27;

z_*it*= six-dimensional standardized indicator vector for Member State i in year t;

z̄t= six-dimensional centroid of the 27 Member States in year t;

i = 1,2,…,27 denotes the Member State;

t = 2010,2011,…,2023 denotes the observation year.

A declining trajectory of D_*t* indicates a reduction in the overall multivariate dispersion of Member States around the annual European centroid and is interpreted as evidence of multivariate sigma-convergence. An increasing trajectory indicates widening multivariate dispersion.

Multivariate dispersion was characterized through four annual measures: mean Euclidean distance to the EU-27 centroid, median Euclidean distance to the centroid, root-mean-square distance to the centroid, and mean pairwise Euclidean distance among Member States. Mean distance describes the average national deviation from the annual European configuration, while median distance provides the central position of the cross-country distance distribution. Root-mean-square distance assigns greater influence to larger deviations and captures the overall magnitude of dispersion around the annual centroid. Mean pairwise distance measures the average separation among all pairs of Member States and therefore represents cross-country dispersion without relying on a single central reference point.

Temporal trends in these measures were examined over 2010–2023. Linear trend coefficients quantify the average direction and magnitude of change, while Spearman and Kendall coefficients characterize monotonic temporal association. Joint consideration of centroid-based and pairwise measures provides a multidimensional representation of the evolution of cross-country dispersion and permits convergence to be evaluated independently from changes in categorical cluster membership.

3.9 Beta-convergence and catch-up dynamics

Beta-convergence analysis complements the dispersion-based perspective by examining whether Member States with different initial positions subsequently experienced systematically different rates of adjustment. Whereas, sigma-convergence captures changes in the overall cross-sectional dispersion of the EU-27 distribution, beta-convergence focuses on the relationship between initial position and subsequent change. Joint consideration of these two dimensions provides information on both the evolution of aggregate disparities and the dynamics of individual national trajectories during 2010–2023.

Indicator-specific beta-convergence was examined separately for each of the six sustainability dimensions. For every Member State, the annualized change between 2010 and 2023 was related to its standardized position at the beginning of the observation period. Standardized values were used to maintain consistency with the common metric established for the multivariate analysis. For indicator j the specification can be expressed as Equation 9:

zij,2023-zij, 201013=αj+βjdj,2010+εij(9)

where:

z_{*ij*, 2010} = standardized value of indicator j for Member State i in the initial year;

z_{*ij*, 2023} = standardized value of the same indicator for Member State i in the final year;

zij,2023-zij, 201013 = average annual change in the standardized indicator over the 13 year-to-year intervals between 2010 and 2023;

α_*j* = intercept of the indicator-specific convergence model;

β_*j* = coefficient relating the initial standardized position to subsequent annualized change;

ε_*ij* = residual component for Member State i and indicator j;

i = 1,2,…,27 denotes the Member State;

j = 1,2,…,6 denotes the sustainability indicator.

A negative value of β_*j* indicates that Member States with higher initial standardized values tended to experience smaller subsequent increases or larger subsequent reductions than countries starting from lower values. Such a relationship is consistent with mean-reverting dynamics and a reduction in initial cross-country differences for the corresponding indicator. A positive coefficient indicates persistence or amplification of initial differences, depending on the direction of subsequent change.

Interpretation remains specific to the substantive meaning of each sustainability dimension. Convergence describes the evolution of cross-country differences and does not, by itself, represent improvement in sustainability performance. Declining values can be environmentally favorable for indicators representing pressures, such as greenhouse gas emissions or material consumption, whereas increasing values can be desirable for dimensions such as resource productivity or innovation intensity. Indicator-specific beta-convergence therefore characterizes the relationship between initial position and subsequent adjustment independently of the normative direction associated with the indicator.

Multivariate beta-convergence was examined using each Member State's Euclidean distance from the corresponding annual EU-27 centroid in the six-dimensional standardized space. Distance summarizes the magnitude of a country's deviation from the contemporaneous European multivariate configuration irrespective of the direction of that deviation along individual indicators. Annualized change in this distance between 2010 and 2023 was related to the country's initial distance in 2010 (Equation 10):

di,2023-di,201013=αi+βidi,2010+εi(10)

where:

d_{*i*, 2010} = Euclidean distance of Member State i from the EU-27 centroid in 2010;

d_{*i*, 2023} = Euclidean distance of Member State i from the EU-27 centroid in 2023;

di,2023-di,201013 = annualized change in multivariate distance between the initial and final years;

α_*i* = intercept of the multivariate convergence model;

β_*i*= coefficient relating initial multivariate distance to subsequent annualized change;

ε_*i* = residual component associated with Member State i.

A negative β_*i* indicates that Member States located farther from the European centroid in 2010 tended to reduce their multivariate distance more strongly over the subsequent period. This pattern characterizes catch-up toward the central EU-27 configuration. A positive coefficient indicates that initially greater distance was associated with increasing or more persistent separation from the European centroid.

Ordinary least squares estimates were accompanied by the coefficient of determination and statistical significance of the estimated slope. Spearman rank correlation between initial position and subsequent annualized change was additionally calculated for both indicator-specific and multivariate specifications. Rank-based association complements the linear specification by characterizing whether the ordering of initial positions is systematically related to the ordering of subsequent changes without requiring the relationship to be strictly linear.

Beta-convergence is interpreted together with sigma-convergence and temporal mobility. Sigma-convergence describes whether the EU-27 distribution becomes more or less dispersed over time. Beta-convergence characterizes whether subsequent adjustment is systematically related to initial position. Temporal mobility identifies movement across the boundaries of the structural regimes obtained from K-Means. Their combined analysis distinguishes changes in continuous cross-country distances from changes in categorical structural membership and provides a longitudinal representation of both catch-up dynamics and regime persistence.

3.10 Statistical interpretation, robustness, and reproducibility

Statistical interpretation follows the distinction between structural classification and longitudinal inference established by the analytical design. K-Means identifies groups by minimizing within-cluster distances across the six standardized sustainability indicators. Differences in the variables entering the clustering algorithm are therefore intrinsic to the estimated partition and are interpreted descriptively through standardized centroids, original-unit cluster means, and profile composition. Post-clustering ANOVA tests on these same variables are not employed as independent criteria of cluster validity. Statistical assessment of the partition instead relies on internal validation indices, resampling stability, and preprocessing robustness.

Inferential procedures are applied separately to the longitudinal convergence analyses. Linear trend models evaluate systematic temporal changes in annual cross-sectional dispersion, while beta-convergence specifications examine the relationship between initial position and subsequent change. Statistical significance in these models refers to the estimated temporal or catch-up relationships. Spearman and Kendall rank-based measures complement the parametric trend specifications where appropriate and provide information on monotonic temporal relationships.

Cluster labels are derived from the complete centroid configuration rather than from individual indicators considered in isolation. Standardized centroid values provide the primary basis for identifying the dimensions that differentiate each regime. Deviations of approximately +0.5 or −0.5 standard deviations from the EU-27 panel mean are treated as substantively notable characteristics, with larger absolute deviations receiving correspondingly greater interpretive emphasis. Standardized profiles are subsequently examined together with cluster means expressed in original measurement units and the composition of Member State-year observations. This procedure links statistical differentiation in standardized space with the substantive energy-resource characteristics represented by each regime.

Resampling stability is evaluated within the pooled panel structure of 378 Member State-year observations. Each 80% subsample represents a moderate perturbation of the empirical multivariate distribution from which the structural regimes are estimated. Re-estimation across 500 subsamples therefore characterizes the reproducibility of the partition when the observational composition of the dataset changes. Country-year observations retain their country and year identifiers throughout the analytical workflow, allowing the resulting classifications to be reorganized subsequently into ordered national trajectories. Temporal dependence is consequently represented in the longitudinal stage through consecutive within-country membership sequences and country-specific changes over time.

Gap Statistic calculations use reference datasets generated uniformly within the multidimensional bounding box defined by the observed minimum and maximum of each standardized indicator. The same reference-generation procedure and estimation settings are maintained across all candidate partitions containing between 2 and 10 clusters. For each candidate solution, 200 reference datasets are generated, and the resulting Gap values and associated standard errors are used to evaluate separation between the empirical clustering structure and the corresponding reference distributions. Candidate partitions are assessed through the Gap Statistic together with WCSS, Silhouette, Calinski-Harabasz, Davies-Bouldin, resampling stability, cluster size, and substantive profile differentiation. This joint assessment incorporates complementary properties of compactness, separation, reference-based structure, reproducibility, and partition composition.

Distributional sensitivity is examined while retaining all valid observations in the baseline specification. Observations located in the tails of the indicator distributions remain part of the empirical sustainability space because they represent observed national energy-resource configurations within the EU-27 panel. Their influence on cluster structure is evaluated through alternative preprocessing specifications rather than through case deletion. Winsorization at the 1st and 99th percentiles reduces the magnitude of distributional extremes while preserving the complete set of Member State-year observations. Comparison of the resulting partition with the baseline solution through ARI consequently measures the sensitivity of cluster membership to the influence of extreme indicator values.

Global standardization is applied across the complete 2010–2023 panel to establish a common coordinate system for both structural and longitudinal analyses. Each standardized observation is expressed relative to the same full-period indicator mean and standard deviation, allowing distances and centroid positions to retain a consistent metric interpretation across years. Temporal changes in national positions can therefore be observed within a fixed standardized space. This property is particularly important for the analysis of annual cluster membership, multivariate dispersion, and convergence dynamics.

Year-specific standardization would instead recenter and rescale each annual cross-section independently. Under such a transformation, standardized values would represent a Member State's relative position within the distribution of a particular year rather than its position within the common 2010–2023 distribution. Common shifts affecting the EU-27 distribution would consequently be absorbed by annual recentering and rescaling. Global standardization is therefore consistent with the analytical objective of identifying recurrent regimes across the complete panel and examining changes in Member State positions within a common multivariate metric.

Reproducibility is supported through a modular computational workflow implemented in Python. Sequential modules cover data audit and completeness assessment, descriptive analysis, standardization, candidate cluster estimation, internal validation, Gap Statistic computation, resampling stability, final cluster estimation, preprocessing robustness, cluster profiling, country-year membership, temporal mobility, sigma-convergence, beta-convergence, visualization, and consolidation of analytical outputs. Complete country-year cluster assignments are retained as analytical outputs, providing the underlying membership information used to construct longitudinal trajectories, transition counts, and the 2023 geographical representation.

4 Results

4.1 Data structure and consequences of scale correction

The empirical panel comprises all 378 Member State-year observations included in the analytical design, corresponding to 27 EU Member States observed annually over the 2010–2023 period. No missing observations are present in the six indicators, and each annual cross-section consequently contains the same 27 Member States. Similarly, each Member State contributes 14 annual observations. This balanced structure ensures temporal comparability throughout the panel and allows subsequent changes in cross-country dispersion to be examined without variation arising from changes in sample composition.

Substantial differences emerge in the numerical dispersion of the indicators when they are expressed in their original measurement units. Municipal waste generation accounts for approximately 99.57% of the aggregate raw variance across the six variables. A similar concentration is observed in the unstandardized four-cluster solution, where municipal waste generation contributes 95.72% of the variable-specific within-cluster sum of squares. Euclidean distances calculated directly from the original units are therefore predominantly shaped by the numerical scale of this indicator.

Standardization produces a markedly different multivariate configuration. Comparison between the standardized and unstandardized four-cluster partitions yields an Adjusted Rand Index of only 0.135, indicating limited correspondence between their membership structures. The magnitude of this difference shows that measurement scale has a substantial effect on the resulting partition when heterogeneous original units are used. Expressing all six indicators in standard-deviation units establishes a common metric for the subsequent cluster analysis and allows the identified configurations to reflect the joint structure of energy consumption, innovation, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation.

4.2 Candidate cluster solutions and selection of k = 4

Identification of the cluster structure requires consideration of both the statistical properties of alternative partitions and their capacity to represent meaningful differences within the EU-27 energy-resource sustainability space. Candidate solutions ranging from 2 to 10 clusters were therefore compared to determine how progressively finer partitions affect within-cluster compactness, between-cluster separation, stability, and cluster composition. Particular attention was given to whether additional clusters reveal distinct and persistent structural configurations or primarily subdivide existing national trajectories. This comparison provides the empirical basis for selecting the cluster specification used in the subsequent profiling, robustness, and longitudinal analyses (Table 4).

Table 4. Internal validation, cluster size, and subsampling stability for k = 2–10.

K, number of clusters; WCSS, within-cluster sum of squares; Silh., mean Silhouette coefficient; CH, Calinski-Harabasz index; DB, Davies-Bouldin index; Gap, Gap Statistic; Min %, percentage of observations contained in the smallest cluster; ARI, Adjusted Rand Index. Mean ARI and Median ARI summarize partition agreement across 500 subsampling replications using 80% of the observations, while ARI ≥ 0.90 % indicates the percentage of replications with an ARI of at least 0.90. Higher Silhouette and Calinski-Harabasz values and lower Davies-Bouldin values indicate stronger internal cluster separation. Gap Statistic increased throughout the evaluated range and did not identify an interior solution under the one-standard-error criterion. Selection of k = 4 integrates internal validation, resampling stability, cluster-size structure, and substantive profile differentiation.

Source: Authors' calculation.

Table 4 reports the internal validation, cluster-size, and resampling-stability results for candidate solutions ranging from k = 2 to k = 10. No single candidate dominates across all evaluation criteria. WCSS decreases continuously as the number of clusters increases, while the Gap Statistic rises from 1.026 at k = 2 to 1.711 at k = 10 without producing an interior solution under the one-standard-error criterion. Silhouette, Calinski-Harabasz, Davies-Bouldin, resampling stability, and minimum cluster size similarly reveal different aspects of the partition structure rather than a common optimum.

The two-cluster solution provides the strongest resampling stability, with a mean ARI of 0.983, a median ARI of 0.987, and 98.4% of subsampling replications reaching ARI values of at least 0.90. Its Calinski-Harabasz value of 171.3 is also comparatively high. This solution provides a parsimonious benchmark but produces a broad partition in which structurally different high-intensity configurations remain combined. Increasing the number of clusters to three does not improve the overall diagnostic profile: Silhouette decreases slightly from 0.333 to 0.332, mean ARI declines from 0.983 to 0.930, and the minimum cluster share falls from 40.7% to 7.9%.

A clearer structural differentiation emerges at k = 4. Silhouette increases to 0.364, compared with 0.332 at k = 3, while the Davies-Bouldin index decreases from 1.275 to 1.016. Resampling stability remains high, with a mean ARI of 0.938 and a median ARI of 0.976, and 74.2% of replications reach ARI values of at least 0.90. The smallest cluster contains 14 observations, representing 3.7% of the complete panel.

Country-year composition provides additional information on the structure underlying these smaller clusters. The 14 observations forming the smallest cluster correspond to Luxembourg throughout the complete 2010–2023 period, while the 28 observations of another cluster correspond to Finland and Sweden throughout the same period. These groups therefore represent temporally persistent national trajectories within the standardized multivariate space. Their identification at k = 4 separates structural configurations that remain combined under more aggregated partitions while preserving substantial resampling stability.

Candidate solutions with more than four clusters generate further improvements in several internal geometric criteria. Silhouette increases to 0.361 at k = 7, 0.366 at k = 8, 0.372 at k = 9, and 0.384 at k = 10, while the Davies-Bouldin index decreases to 0.850 at k = 10. Calinski-Harabasz similarly rises to 175.1 at k = 10, and the Gap Statistic continues increasing throughout the evaluated range. These improvements occur together with progressively finer subdivision of the country-year structure. From k = 7 onward, several clusters contain exactly 14 observations, corresponding to complete fourteen-year national trajectories, while the minimum cluster share remains 3.7%.

Resampling results also differentiate the four-cluster solution from several intermediate higher-order partitions. Mean ARI declines to 0.665 at k = 5, 0.789 at k = 6, and 0.741 at k = 7, before increasing to 0.858, 0.899, and 0.895 for k = 8, k = 9, and k = 10, respectively. None of these higher-order solutions exceeds the mean subsampling stability observed for k = 4. The additional geometric separation obtained at larger values of k is therefore accompanied by greater partition granularity and increasing representation of individual national trajectories as separate clusters.

Selection of k = 4 is consequently based on the joint configuration of internal separation, resampling stability, cluster composition, and substantive differentiation. The four-cluster solution retains high reproducibility while distinguishing four interpretable energy-resource configurations without extending the partition to the finer country-specific segmentation increasingly observed at larger values of k. It is therefore retained as the primary specification for cluster profiling, robustness analysis, temporal mobility, and subsequent convergence analysis. The two-cluster solution remains a parsimonious benchmark for assessing the broader structure of the data.

Figure 2 summarizes the evolution of the principal validation criteria across k = 2,…, 10. WCSS declines progressively as partition granularity increases and does not exhibit a uniquely defined elbow. Silhouette presents a local maximum at k = 4 among the lower-order solutions before increasing again from k = 7 onward. Davies-Bouldin shows a marked improvement at k = 4 and further decreases for the larger partitions, while Calinski-Harabasz and the Gap Statistic favor progressively finer partitions over parts of the evaluated range.

Considered together with resampling stability and cluster-size composition, these patterns characterize k = 4 as a stable and substantively differentiated intermediate partition rather than as a solution selected through maximization of a single validation statistic.

4.3 Structural interpretation of the four clusters

Selection of the four-cluster solution reveals substantial differences in the way energy use, innovation capacity, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation combine across the EU-27 panel. The resulting clusters do not follow a simple progression from lower to higher sustainability performance. Instead, each cluster is characterized by a distinct configuration of relative strengths, resource-use intensity, and environmental pressures. Standardized centroids are examined first to establish the position of each cluster relative to the complete panel distribution, while original-unit means subsequently provide the substantive magnitude of these differences (Table 5).

Table 5. Standardized centroids of the selected four-cluster solution.

N, number of Member State-year observations; %, percentage of the complete analytical sample; PENC, primary energy consumption; GDEXP, gross domestic expenditure on research and development; RMC, raw material consumption; DNGGE, domestic net greenhouse gas emissions; RESPRO, resource productivity; GENMWAS, generation of municipal waste per capita. Centroids are expressed in standard-deviation units relative to the complete 378-observation panel. Positive values indicate positions above the panel mean for the corresponding indicator, while negative values indicate positions below the panel mean. Cluster labels are descriptive and do not represent an ordinal ranking of sustainability performance.

Source: Authors' calculation.

Standardized centroids indicate substantial differentiation among the four configurations. Cluster 1 is positioned below the panel mean across all six dimensions, although the deviation for raw material consumption is comparatively limited. Cluster 2 combines above-average research and development expenditure and resource productivity with higher municipal waste generation and moderately higher greenhouse gas emissions. Cluster 3 records particularly high levels of research and development expenditure, primary energy consumption, and raw material consumption together with below-average greenhouse gas emissions. Cluster 4 occupies the highest relative position for primary energy consumption, greenhouse gas emissions, resource productivity, and municipal waste generation and also records substantially above-average raw material consumption. These contrasting combinations provide the basis for the descriptive profile labels reported in Table 6.

Table 6. Raw-scale profiles of the selected four-cluster solution.

PENC, primary energy consumption, expressed in tons of oil equivalent (toe) per capita; GDEXP, gross domestic expenditure on research and development, expressed as percentage of GDP; RMC, raw material consumption, expressed in tons per capita; DNGGE, domestic net greenhouse gas emissions, expressed in tons per capita; RESPRO, resource productivity, expressed in euro per kilogram; GENMWAS, generation of municipal waste, expressed in kilograms per capita. Values represent within-cluster means in the original Eurostat measurement units. Cluster estimation was performed using standardized indicators; original-unit means are reported for substantive interpretation.

Source: Authors' calculation.

Cluster 1 contains 224 Member State-year observations, representing 59.26% of the complete panel, and is characterized as the Lower-intensity resource and innovation profile. Its standardized centroid is below the panel mean for all six indicators, with the largest negative deviations observed for research and development expenditure (−0.595) and resource productivity (−0.571). Primary energy consumption is also below average (−0.497), as are municipal waste generation (−0.439) and domestic net greenhouse gas emissions (−0.260), while raw material consumption is comparatively closer to the panel mean (−0.229). In original units, the cluster records primary energy consumption of 2.523 toe per capita, research and development expenditure of 1.104% of GDP, raw material consumption of 16.350 tons per capita, domestic net greenhouse gas emissions of 7.035 tons per capita, resource productivity of 1.163 euro/kg, and municipal waste generation of 443.6 kg per capita. The profile is therefore distinguished by comparatively low resource and environmental intensity accompanied by lower innovation expenditure and resource productivity.

Cluster 2 comprises 112 observations, or 29.63% of the panel, and forms the Innovation and resource-productivity profile. Its most pronounced positive centroid values are recorded for resource productivity (0.942) and research and development expenditure (0.806). Municipal waste generation is also above the panel mean (0.709), while domestic net greenhouse gas emissions show a smaller positive deviation (0.423). Primary energy consumption remains relatively close to the panel mean (0.183), whereas raw material consumption is below it (−0.290). Original-unit means amount to 3.385 toe per capita for primary energy consumption, 2.352% of GDP for research and development expenditure, 15.894 tons per capita for raw material consumption, 9.532 tons per capita for domestic net greenhouse gas emissions, 2.823 euro/kg for resource productivity, and 593.4 kg per capita for municipal waste generation. The configuration combines comparatively strong innovation and resource productivity with higher waste generation and greenhouse gas emissions.

Cluster 3 contains 28 observations, representing 7.41% of the panel, and is characterized as the R&D-intensive, material-consumption profile. Research and development expenditure reaches 1.775 standard deviations above the panel mean, while raw material consumption reaches 2.187 and primary energy consumption 1.621 standard deviations above the mean. Domestic net greenhouse gas emissions, by contrast, are 0.853 standard deviations below the panel mean, while resource productivity (−0.306) and municipal waste generation (−0.163) show smaller negative deviations. Original-unit means amount to 5.207 toe per capita for primary energy consumption, 3.214% of GDP for research and development expenditure, 34.543 tons per capita for raw material consumption, 4.871 tons per capita for domestic net greenhouse gas emissions, 1.454 euro/kg for resource productivity, and 479.7 kg per capita for municipal waste generation. Finland and Sweden account for the 28 observations assigned to this configuration and remain within the cluster throughout the fourteen-year period. The resulting profile combines high innovation intensity and material consumption with comparatively low net greenhouse gas emissions.

Cluster 4 is the smallest configuration, containing 14 observations and representing 3.70% of the panel. It is characterized as the High-intensity energy, emissions and resource profile. Primary energy consumption reaches 3.251 standard deviations above the panel mean, domestic net greenhouse gas emissions 2.484, resource productivity 2.201, municipal waste generation 1.677, and raw material consumption 1.607 standard deviations above the mean. Research and development expenditure is the only dimension positioned below the panel average (−0.481). Original-unit means amount to 7.272 toe per capita for primary energy consumption, 1.205% of GDP for research and development expenditure, 30.175 tons per capita for raw material consumption, 17.057 tons per capita for domestic net greenhouse gas emissions, 4.204 euro/kg for resource productivity, and 719.6 kg per capita for municipal waste generation. All 14 observations correspond to Luxembourg, which remains assigned to this configuration throughout 2010–2023. The profile is distinguished by the simultaneous presence of high resource productivity and high levels of energy consumption, material consumption, greenhouse gas emissions, and municipal waste generation.

The results support H1, as the selected four-cluster solution identifies distinct and recurrent multivariate energy and resource sustainability regimes across the EU-27 panel. Differences among the standardized centroids show that these regimes are characterized by clearly differentiated combinations of energy consumption, innovation intensity, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation. H2 is also supported. The cluster profiles reveal non-uniform combinations of technological capacity, resource efficiency, material intensity, energy use, and environmental pressure. Higher research and development expenditure and resource productivity do not systematically coincide with lower resource use or environmental pressure. Cluster 2 combines strong innovation and resource productivity with above-average waste generation and emissions; Cluster 3 combines high research intensity with high energy and material consumption but comparatively low emissions; and Cluster 4 combines very high resource productivity with simultaneously high energy consumption, material consumption, emissions, and waste generation. These configurations demonstrate that the identified regimes differ in their multidimensional composition rather than representing successive positions along a single sustainability-performance continuum.

4.4 Robustness to scale, transformation, and outlier treatment

Robustness analysis examines whether the selected four-cluster structure is preserved when the six-dimensional indicator space is represented under alternative preprocessing specifications. The comparisons distinguish three potential sources of sensitivity: differences in the original measurement scales, the influence of observations located at the distributional tails, and changes in distributional shape introduced through non-linear transformation. Partition correspondence is evaluated relative to the baseline z-standardized solution (Table 7) using the Adjusted Rand Index (ARI).

Table 7. Robustness of the selected k = 4 partition.

ARI, Adjusted Rand Index. Each ARI value measures agreement between the partition obtained under the corresponding alternative preprocessing specification and the baseline z-standardized k = 4 partition. Values approaching 1 indicate increasingly similar membership structures, whereas values approaching 0 indicate limited agreement beyond that expected by chance. Internal validation indices calculated in differently transformed feature spaces are not interpreted as directly comparable absolute measures because each transformation modifies the underlying distance geometry.

Source: Authors' calculation.

Results reveal substantial differences in sensitivity across the alternative preprocessing specifications. The largest change occurs when K-Means is applied directly to the indicators in their original measurement units. Agreement with the baseline partition falls to ARI = 0.135. This result is consistent with the scale structure identified in Section 4.1, where municipal waste generation accounts for 99.57% of aggregate raw variance and 95.72% of the variable-specific WCSS in the unstandardized four-cluster solution. The low correspondence between the two partitions indicates that clustering in original units produces a substantially different membership structure dominated by differences in numerical scale.

Winsorization produces a markedly different result. Replacing values below the 1st percentile and above the 99th percentile with their corresponding percentile thresholds modifies eight values for each indicator while retaining all 378 observations. The resulting partition reaches ARI = 0.981 relative to the baseline solution, with only two Member State-year observations changing membership after cluster-label alignment. The 28-observation and 14-observation configurations identified in the baseline solution remain unchanged. Consequently, the principal four-cluster structure is highly stable when the influence of distributional extremes is reduced.

Robust scaling also preserves a substantial proportion of the baseline membership structure, producing ARI = 0.761. Because this transformation uses the median and interquartile range rather than the mean and standard deviation to represent location and dispersion, the observed agreement indicates that a considerable part of the four-cluster configuration persists under an alternative scaling rule that is less sensitive to extreme values. At the same time, the difference from perfect agreement shows that the relative geometry of some Member State-year observations changes when the metric is defined through median- and IQR-based scaling.

The Yeo-Johnson transformation followed by z-standardization produces the largest departure among the standardized alternative specifications, with ARI = 0.441. This transformation modifies distributional shape in addition to placing the indicators on a common scale. Its effect is particularly relevant for dimensions characterized by stronger positive asymmetry, including primary energy consumption and raw material consumption. The lower ARI therefore indicates that non-linear modification of the indicator distributions alters relative distances among observations sufficiently to produce a different partition structure.

Taken together, the sensitivity results distinguish the effects of measurement scale, distributional extremes, and distributional transformation. The very low correspondence of the unstandardized specification confirms the importance of establishing a common metric for indicators expressed in heterogeneous units. By contrast, the near-identical winsorized solution shows that the selected four-cluster structure is not generated by a small number of extreme observations. Substantial agreement under robust scaling provides additional evidence that the principal partition is preserved under an alternative treatment of location and dispersion. Greater sensitivity to the Yeo-Johnson specification indicates that cluster membership responds more strongly when the shape of the indicator distributions, and consequently their relative distance structure, is transformed. These results support retention of the z-standardized four-cluster solution as the primary specification for the subsequent longitudinal analyses.

4.5 Country-year membership and temporal mobility

Longitudinal cluster membership reveals whether the structural configurations identified in the pooled EU-27 panel persist over time or whether Member States move frequently between regimes. Annual assignments were therefore examined for each country across the complete 2010–2023 period. This representation preserves the Member State-year structure of the data and allows temporal persistence and regime changes to be observed directly rather than reducing each country to a single classification for the entire period (Figure 3).

Annual membership trajectories reveal a highly persistent cluster structure across the study period. Most Member States remain within the same structural configuration throughout 2010–2023, and changes in cluster membership are concentrated in only two countries. This persistence is quantified through the 351 adjacent-year comparisons reported in Table 8.

Table 8. Temporal mobility in cluster membership.

Temporal mobility is calculated from 351 valid adjacent-year comparisons, corresponding to 27 EU Member States observed across 13 consecutive year-to-year intervals. A cluster change occurs when a Member State is assigned to a different cluster in year t relative to year t−1. Persistence rate represents the proportion of comparisons with unchanged membership, while mobility rate represents the proportion involving a change in cluster membership.

Source: Authors' calculation.

Of the 351 adjacent-year comparisons, 348 retain the same cluster membership and only three involve movement between clusters. The resulting persistence rate is 99.145%, compared with a mobility rate of 0.855%. Twenty-five of the 27 Member States remain in the same cluster throughout all consecutive-year comparisons, while only Czechia and Italy experience changes in structural membership.

Italy moves from Cluster 1 to Cluster 2 between 2012 and 2013 and remains in Cluster 2 throughout the remainder of the observation period. Czechia moves from Cluster 1 to Cluster 2 between 2019 and 2020, remains in Cluster 2 through 2022, and returns to Cluster 1 in 2023. No transitions involve Clusters 3 or 4. Finland and Sweden remain assigned to Cluster 3 in every year from 2010 to 2023, while Luxembourg remains in Cluster 4 throughout the complete period.

The direction of the 351 transitions further confirms the predominance of within-regime persistence. Cluster 1 records 206 transitions remaining within Cluster 1 and two transitions toward Cluster 2. Cluster 2 records 103 transitions remaining within Cluster 2 and one transition toward Cluster 1. All 26 transitions originating from Cluster 3 remain within Cluster 3, while all 13 transitions originating from Cluster 4 remain within Cluster 4. Observed mobility is therefore confined entirely to exchanges between Clusters 1 and 2.

These results support H3. Energy and resource sustainability regimes exhibit very high temporal persistence, with only 0.855% of all valid adjacent-year comparisons involving a change in cluster membership. Persistence is observed not only in the two largest configurations but also in the smaller structural profiles represented by Clusters 3 and 4. The annual membership sequences therefore show that the four-cluster structure represents recurrent and temporally stable configurations within the EU-27 panel rather than groupings generated by isolated country-year observations.

Temporal persistence does not determine whether quantitative differences among Member States increase or decrease over time. Cluster membership is categorical and records movement across regime boundaries, whereas convergence concerns change in continuous cross-country distances within the standardized sustainability space. Member States may therefore remain within the same structural regime while their relative positions become progressively closer or farther apart. Sections 4.6 and 4.7 examine this second dimension through sigma- and beta-convergence.

4.6 Spatial representation for 2023

The longitudinal analysis demonstrates substantial persistence in cluster membership, but the geographical distribution of the identified regimes can be observed more clearly from a common cross-sectional reference year. The final year of the panel, 2023, was therefore used to represent the spatial configuration of the four structural regimes across the EU-27 (see Table A1). Unlike a modal classification derived from the complete 2010–2023 period, the map reports the actual cluster assignment of each Member State in 2023 and consequently preserves the correspondence between the geographical representation and the country-year analytical unit (Figure 4).

Cross-sectional map provides a transparent reference year for geographical interpretation. The 2023 spatial distribution shows that Cluster 1 is the largest configuration, comprising 16 Member States: Bulgaria, Croatia, Cyprus, Czechia, Estonia, Greece, Hungary, Latvia, Lithuania, Malta, Poland, Portugal, Romania, Slovakia, Slovenia, and Spain. Cluster 2 contains eight Member States: Austria, Belgium, Denmark, France, Germany, Ireland, Italy, and the Netherlands. Finland and Sweden constitute Cluster 3, while Luxembourg represents Cluster 4. The geographical distribution therefore reproduces the marked differences in cluster size observed in the complete panel while providing a cross-sectional representation of the structural regimes at the end of the study period.

Spatial distribution does not correspond to a simple East-West partition of the European Union. Although Cluster 1 contains several Central and Eastern European Member States, it also includes Spain, Portugal, Greece, Cyprus, and Malta. Cluster 2 is concentrated predominantly among Western and Northern Member States, whereas Finland and Sweden form the separate Cluster 3 configuration and Luxembourg occupies Cluster 4. The four-cluster solution therefore displays a geographically differentiated structure that extends beyond a binary regional division of the EU-27.

4.7 Indicator-specific sigma-convergence

Temporal persistence of cluster membership does not establish whether quantitative differences among Member States narrow or widen within the identified structural regimes. Sigma-convergence addresses this complementary dimension by examining changes in annual cross-sectional dispersion. Indicator-specific trajectories were therefore evaluated across 2010–2023 using the annual standard deviation of each indicator after standardization against its complete-panel distribution. Declining dispersion indicates convergence in the corresponding dimension, whereas increasing dispersion indicates divergence (Table 9).

Table 9. Indicator-specific sigma-convergence, 2010–2023.

SD, annual cross-sectional standard deviation; PENC, primary energy consumption; GDEXP, gross domestic expenditure on research and development; RMC, raw material consumption; DNGGE, domestic net greenhouse gas emissions; RESPRO, resource productivity; GENMWAS, generation of municipal waste per capita. Annual dispersion is calculated from indicator values standardized using the complete 2010–2023 panel distribution. Percentage change refers to the difference in annual cross-sectional SD between 2010 and 2023 relative to its 2010 value. Slope/year is the coefficient from the linear trend of annual SD on year; R², coefficient of determination; p, p-value associated with the estimated slope. A statistically significant negative slope indicates sigma-convergence, whereas a statistically significant positive slope indicates sigma-divergence.

Source: Authors' calculation.

Indicator-specific trajectories reveal substantial heterogeneity in the evolution of cross-country dispersion. The strongest reductions occur in domestic net greenhouse gas emissions and primary energy consumption. DNGGE dispersion decreases from 1.2173 in 2010 to 0.6585 in 2023, corresponding to a 45.91% reduction, with a pronounced negative annual trend (slope = −0.03887, R² = 0.918, p < 0.001). PENC dispersion declines from 1.2417 to 0.7363, representing a 40.70% reduction, and follows a similarly strong negative trend (slope = −0.03395, R² = 0.943, p < 0.001). These two dimensions therefore provide the clearest evidence of indicator-specific sigma-convergence over the study period.

Raw material consumption also exhibits decreasing cross-country dispersion, although the magnitude and temporal regularity of the change are more moderate. RMC dispersion falls from 1.0496 in 2010 to 0.8898 in 2023, corresponding to a reduction of 15.22%. The estimated annual slope is negative and statistically significant (−0.00820, R² = 0.313, p = 0.037), providing additional evidence of sigma-convergence in material consumption.

No statistically significant linear convergence trend is identified for research and development expenditure or municipal waste generation. GDEXP dispersion changes only marginally, from 1.0168 to 1.0136, equivalent to a 0.32% reduction, and its estimated slope is not statistically significant (−0.00115, R² = 0.055, p = 0.419). GENMWAS dispersion decreases from 0.9827 to 0.9088, representing a 7.52% reduction between the two endpoints, but the annual trend is likewise not statistically significant (−0.00426, R² = 0.153, p = 0.167). The endpoint reductions observed for these indicators therefore do not constitute evidence of a systematic linear convergence process across the complete period.

Resource productivity follows the opposite trajectory. RESPRO dispersion increases from 0.8763 in 2010 to 1.1933 in 2023, corresponding to a 36.18% increase. Its positive annual slope is statistically significant (+0.02042, R² = 0.895, p < 0.001), indicating sigma-divergence rather than convergence. Resource productivity is consequently the only indicator among the six dimensions to display a strong and systematic increase in cross-country dispersion over 2010–2023.

Taken together, the indicator-level results show that convergence across the EU-27 is dimension-specific rather than uniform. Statistically significant sigma-convergence is observed for primary energy consumption, raw material consumption, and domestic net greenhouse gas emissions, while research and development expenditure and municipal waste generation exhibit no significant linear trend in dispersion. Resource productivity displays significant sigma-divergence. Cross-country differences therefore narrow in several energy, material, and emissions dimensions while simultaneously widening in resource productivity. Whether these heterogeneous indicator trajectories translate into an overall reduction in multivariate distance among Member States is examined in the subsequent analysis.

4.8 Multivariate sigma-convergence

Multivariate results provide clear evidence of overall sigma-convergence (Table 10). Mean distance to annual centroid declines from 2.3338 in 2010 to 2.0690 in 2023, a reduction of 11.34%. Linear trend is negative and explains 83.1% of annual variation. RMS distance declines by 14.45%, from 2.6254 to 2.2461, with R² = 0.847 and p < 0.001. Mean pairwise Euclidean distance falls by 11.43%, with R² = 0.816 and p < 0.001.

Table 10. Multivariate sigma-convergence measures.

Distances are calculated in six-dimensional standardized space relative to the annual EU-27 centroid. Multiple measures are reported to verify that multivariate convergence is not an artifact of one dispersion statistic.

Source: Authors' calculation.

Median distance declines by only 4.36% and its linear trend is not significant. Difference between mean/RMS measures and median indicates that convergence is stronger in the outer part of the cross-country distribution than around the central observation. Countries that began farther from the annual centroid account for a substantial share of aggregate narrowing. This pattern anticipates the beta-convergence result.

Multivariate sigma-convergence coexists with 99.15% cluster persistence. Such coexistence is not contradictory. Cluster boundaries describe categorical regions of multivariate space. Sigma-convergence describes distance. Countries can move closer to the EU centroid while remaining within the same categorical region. Results therefore replace the earlier static claim of persistent divergence with a more precise finding: structural regimes persist while multivariate distances narrow.

4.9 Beta-convergence and multivariate catch-up

Beta-convergence complements the dispersion-based evidence by examining whether initial cross-country positions are systematically associated with subsequent rates of change. Indicator-specific models evaluate whether Member States with different initial standardized values experienced different adjustment trajectories between 2010 and 2023. The multivariate specification extends this assessment to each country's distance from the corresponding annual EU centroid, thereby testing whether Member States initially located farther from the common multivariate position subsequently reduced that distance more rapidly (Table 11).

Table 11. Indicator-specific and multivariate beta-convergence diagnostics.

PENC, primary energy consumption; GDEXP, gross domestic expenditure on research and development; RMC, raw material consumption; DNGGE, domestic net greenhouse gas emissions; RESPRO, resource productivity; GENMWAS, generation of municipal waste per capita; β, estimated beta-convergence coefficient; R², coefficient of determination; ρ, Spearman rank-correlation coefficient. Indicator-specific models regress the annualized standardized change between 2010 and 2023 on the corresponding standardized 2010 value. A statistically significant negative β indicates mean reversion or catch-up in the corresponding indicator, whereas a statistically significant positive β indicates divergence. The multivariate model regresses the annualized change in each Member State's distance from the annual EU centroid on its initial distance in 2010. Spearman coefficients provide a rank-based assessment of the corresponding relationship.

Source: Authors' calculation.

Indicator-specific estimates reveal significant mean-reverting dynamics in four of the six dimensions. Primary energy consumption exhibits the strongest linear relationship, with β = −0.03378, R² = 0.839, and p < 0.001. Its rank-based association is also strongly negative (ρ = −0.909, p < 0.001). Domestic net greenhouse gas emissions display a similarly pronounced pattern (β = −0.04274, R² = 0.764, p < 0.001; ρ = −0.805, p < 0.001). In both dimensions, higher standardized values in 2010 are systematically associated with more negative subsequent annualized changes.

Raw material consumption also exhibits significant beta-convergence, although the relationship is weaker than for primary energy consumption and greenhouse gas emissions. Its estimated coefficient is negative (β = −0.02744, R² = 0.294, p = 0.003), and the Spearman coefficient confirms the same direction of association (ρ = −0.580, p = 0.002). Municipal waste generation follows a comparable but more moderate pattern, with β = −0.02384 (R² = 0.202, p = 0.019) and ρ = −0.487 (p = 0.010). Initial differences in these four indicators are therefore associated with subsequent changes in the direction of mean reversion.

Research and development expenditure provides no statistically significant evidence of beta-convergence. Its coefficient is small and negative (β = −0.00647), with limited explanatory power (R² = 0.044) and a non-significant p-value of 0.295. The rank-based relationship is likewise weak and non-significant (ρ = −0.098, p = 0.628). No systematic association can therefore be established between the initial GDEXP position and its subsequent annualized change over the study period.

Resource productivity follows the opposite pattern. Its beta coefficient is positive and statistically significant (β = +0.01947, R² = 0.184, p = 0.026), while the Spearman coefficient is also positive and significant (ρ = +0.457, p = 0.017). Member States with higher standardized resource-productivity values in 2010 consequently tended to experience larger subsequent increases in this indicator. This beta-divergence is consistent with the increasing cross-country dispersion identified for RESPRO in the sigma-convergence analysis.

Evidence of catch-up is also present at the multivariate level. The coefficient estimated from initial distance to the annual EU centroid is negative and statistically significant (β = −0.03582, R² = 0.472, p < 0.001). Member States located farther from the EU centroid in 2010 therefore tended, on average, to experience larger subsequent reductions in multivariate distance. Initial distance explains approximately 47.2% of the cross-country variation in annualized distance change. The corresponding Spearman coefficient is also negative (ρ = −0.364), although it does not reach the conventional 5% significance threshold (p = 0.062). The evidence consequently supports a statistically significant linear catch-up relationship, while the rank-based association is weaker and not statistically significant at the 5% level.

Taken together, the sigma- and beta-convergence results support H4, while revealing substantial heterogeneity across the six underlying dimensions. Multivariate sigma-convergence shows a significant reduction in overall cross-country dispersion, and the negative multivariate beta coefficient indicates that Member States initially farther from the EU centroid tended to reduce their distance more rapidly. Indicator-specific evidence is not uniform: primary energy consumption, raw material consumption, and domestic net greenhouse gas emissions exhibit both declining dispersion and significant mean-reverting dynamics; research and development expenditure show neither significant sigma- nor beta-convergence; and resource productivity displays both sigma- and beta-divergence. Municipal waste generation presents significant beta-convergence without a statistically significant linear decline in annual cross-sectional dispersion. H4 is therefore supported at the multivariate level, but the convergence process is dimensionally heterogeneous rather than uniform across the constituent indicators.

4.10 Hypothesis assessment

Evidence obtained from cluster validation, structural profiling, longitudinal membership analysis, and convergence diagnostics provides differentiated support for the four hypotheses. Rather than relying on a single statistical criterion, hypothesis assessment integrates the results corresponding directly to each proposition and distinguishes structural differentiation, temporal persistence, and cross-country convergence as separate empirical properties. Table 12 summarizes the resulting assessment.

Table 12. Summary of hypothesis assessment.

ARI, Adjusted Rand Index; PENC, primary energy consumption; GDEXP, gross domestic expenditure on research and development; RMC, raw material consumption; DNGGE, domestic net greenhouse gas emissions; RESPRO, resource productivity; GENMWAS, generation of municipal waste per capita. Hypothesis assessment integrates the empirical evidence obtained from cluster validation, standardized centroid profiles, annual country-year membership, temporal mobility, and sigma- and beta-convergence analyses.

Source: Authors' elaboration.

H1 is supported by the identification of four recurrent and empirically differentiated configurations within the standardized EU-27 energy-resource sustainability space. The selected solution combines substantial resampling stability with improved separation relative to the lower-order three-cluster specification and preserves structurally distinct profiles that would otherwise remain aggregated. Standardized centroids and original-unit profiles further confirm that the four clusters represent different combinations of the six dimensions rather than arbitrary subdivisions of a homogeneous distribution.

H2 is supported by the non-uniform relationships observed among the dimensions defining the four profiles. Innovation intensity and resource productivity do not vary systematically in the same direction as energy consumption, material consumption, greenhouse gas emissions, and municipal waste generation. Cluster 2 combines comparatively high research and development expenditure and resource productivity with above-average emissions and waste generation; Cluster 3 combines high research intensity, energy consumption, and material consumption with comparatively low emissions; and Cluster 4 combines very high resource productivity with simultaneously high energy consumption, material consumption, emissions, and waste generation. Sustainability configurations are therefore multidimensional and cannot be ordered consistently along a single performance continuum.

H3 is strongly supported by the longitudinal membership analysis. Among 351 valid adjacent-year comparisons, 348 retain the same cluster assignment and only three involve a transition, corresponding to a persistence rate of 99.145% and a mobility rate of 0.855%. Twenty-five Member States experience no cluster change across the complete period, while the three observed transitions are confined to Italy and Czechia and occur exclusively between Clusters 1 and 2. Clusters 3 and 4 remain completely stable throughout 2010–2023. These results establish temporal persistence as a defining property of the identified structural regimes.

H4 is supported at the multivariate level, although the underlying convergence process is dimensionally heterogeneous. Overall multivariate dispersion decreases significantly during 2010–2023, while the beta-convergence model yields a negative and statistically significant coefficient for initial distance from the annual EU centroid (β = −0.03582, R² = 0.472, p < 0.001). Indicator-specific results qualify this general pattern. Primary energy consumption, raw material consumption, and domestic net greenhouse gas emissions exhibit significant sigma-convergence together with significant beta-convergence. Research and development expenditure shows neither a significant sigma trend nor significant beta-convergence. Resource productivity follows the opposite trajectory, displaying significant sigma- and beta-divergence, while municipal waste generation exhibits significant beta-convergence without a statistically significant linear sigma-convergence trend. Multivariate convergence therefore coexists with substantial differences in the trajectories of the constituent dimensions.

Taken together, the hypothesis tests reveal a pattern of convergence within a highly persistent structural regime system. Member States rarely cross cluster boundaries, yet their overall multivariate dispersion decreases and countries initially farther from the EU centroid tend, on average, to reduce their distance more rapidly. Structural persistence and convergence are therefore not contradictory outcomes: the former concerns stability of categorical regime membership, whereas the latter captures changes in continuous positions within the multivariate space. At the same time, divergence in resource productivity and the absence of significant convergence in research and development expenditure show that the observed catch-up process is neither uniform across sustainability dimensions nor equivalent to complete structural homogenization across the EU-27.

5 Discussion

5.1 Structural meaning of the four sustainability regimes

Standardized analysis reveals four regimes whose defining features span several dimensions. Large Cluster 1 is not simply a low-performance group. It combines lower energy and waste intensity with lower R&D and resource productivity. Cluster 2 is not simply an advanced group. It combines strong innovation and resource productivity with above-average emissions and waste. Cluster 3 illustrates the coexistence of very high R&D and material consumption with comparatively low net emissions. Cluster 4 combines exceptional energy, materials, emissions, productivity, and waste intensity. Such combinations confirm the value of a configuration-based rather than ranking-based perspective.

This pattern is consistent with circular-economy literature that distinguishes absolute resource pressure from relative efficiency. (Calisto Friant et al. 2024) argue that efficiency gains alone are insufficient to define a sustainable circular society, while (Dzhengiz et al. 2023) emphasize that circular-economy frameworks encompass multiple mechanisms and normative dimensions that cannot be reduced to a single productivity metric. Cluster 4 provides a clear empirical illustration of this distinction: exceptionally high resource productivity coexists with very high primary energy consumption, raw material consumption, greenhouse gas emissions, and municipal waste generation. This configuration indicates that strong efficiency performance does not necessarily translate into lower absolute environmental pressures, particularly when production and consumption remain intensive. Policy evaluation based exclusively on resource productivity may therefore overlook important scale effects and overstate the sustainability performance of resource-intensive economies (Rudolf and Schmidt, 2025).

Cluster 3 illustrates a different form of structural asymmetry. Finland and Sweden combine high material consumption and energy demand with strong R&D intensity and comparatively low net greenhouse gas emissions. Rather than constituting a contradiction, this configuration is consistent with differentiated European decarbonization pathways in which resource-intensive production systems can coexist with advanced technological capabilities and comparatively lower carbon pressures, depending on the composition of national energy systems and broader structural characteristics (Bluszcz et al., 2025; Chovancová et al., 2025). Material intensity and carbon intensity therefore capture different dimensions of sustainability performance. High material throughput reflects the physical scale of resource use, whereas lower net emissions may reflect progress in energy-system transformation and technological modernization. Technological strength can consequently reduce carbon intensity without necessarily eliminating material intensity.

Cluster 2 reflects a broader innovation- and resource-productivity-oriented regime, but it also reveals an efficiency–scale tension. Comparatively high R&D intensity and resource productivity coexist with higher municipal waste generation and moderately higher greenhouse gas emissions. (Cheng et al. 2024) link technological innovation to improvements in green-development efficiency, while (Dogan et al. 2025) emphasize the role of R&D, green technology, and digitalization in supporting renewable-energy innovation. However, technological and efficiency gains do not automatically generate proportional reductions in absolute environmental pressures when production and consumption scales remain high (Malatyinszki et al., 2025; Rudolf and Schmidt, 2025). The present results therefore support a conditional interpretation of innovation: technological capability expands the capacity for sustainability transition, but actual environmental outcomes depend on how that capability is translated into energy systems, material-use patterns, production structures, and consumption behavior.

5.2 Methodological implications of standardization and validation

The strong sensitivity of cluster membership to measurement scale highlights a fundamental issue in multidimensional sustainability analysis. Energy-resource frameworks commonly combine indicators expressed in physical quantities, percentages, monetary ratios, and per-capita measures. Under Euclidean distance, these differences in numerical scale become part of the geometry used to define similarity among observations. This sensitivity to measurement scale is well-established in cluster analysis, where standardization can materially affect distance-based partitions when variables differ substantially in variance and units of measurement (Milligan and Cooper, 1988; Wongoutong, 2024). The low agreement between the standardized and unstandardized partitions found in this study consequently reflects more than a technical change in preprocessing. It shows that the representation of structural heterogeneity can change substantially when indicators measured on heterogeneous scales are allowed to contribute unequally to distance calculations.

Standardization is particularly important when cluster interpretation is intended to reflect relationships among several sustainability dimensions rather than the numerical dispersion of a dominant indicator. In the present analysis, the unstandardized specification assigns most of the distance contribution to municipal waste generation, whereas z-standardization places energy consumption, innovation expenditure, material consumption, emissions, resource productivity, and waste generation on a common metric. Original measurement units remain essential for substantive interpretation, but their appropriate role differs from their role in cluster estimation. Standardized values define multivariate similarity, while original-unit profiles subsequently translate the resulting configurations into economically and environmentally interpretable quantities. This distinction is relevant to sustainability research more broadly because many composite indicator systems combine variables whose original scales are not directly comparable.

Sensitivity analysis further indicates that scale correction should be distinguished from arbitrary manipulation of the underlying distributions. The near-complete agreement between the baseline and winsorized partitions shows that the four-cluster structure is largely preserved when the influence of distributional extremes is reduced. Substantial agreement under robust scaling provides additional evidence that the principal configuration is not dependent on a single representation of location and dispersion. Greater sensitivity to the Yeo-Johnson transformation has a different interpretation because non-linear transformation changes distributional shape and, consequently, the relative distances among observations. Robustness assessment should therefore consider not only whether alternative preprocessing procedures alter cluster membership, but also which property of the multivariate space each procedure changes.

Selection of the number of clusters raises a related methodological issue. Internal validation criteria capture different properties of a partition and need not identify the same preferred solution. Recent comparative evidence confirms substantial variation in the behavior of cluster-validity indices across different data structures, supporting the use of multiple complementary criteria rather than reliance on a single statistical optimum (Hassan et al., 2024; Ikotun et al., 2025; Todeschini et al., 2024). In the present case, several geometric criteria continue to improve at higher values of k, while the Gap Statistic does not identify an interior optimum within the evaluated range. Resampling stability and cluster composition provide complementary information by showing whether increasingly fine partitions represent reproducible cross-country configurations or progressively isolate individual national trajectories. The selected four-cluster solution occupies an intermediate level of granularity: it differentiates structurally meaningful energy-resource profiles while retaining high resampling stability and avoiding the increasing country-specific segmentation observed in higher-order solutions.

This result also clarifies the role of interpretability in cluster selection. Substantive interpretation is necessary because statistical partitions are used here to characterize sustainability regimes, but interpretability cannot substitute for empirical validation. Conversely, optimization of a single internal index may favor a level of granularity that is poorly aligned with the analytical objective. A suitable cluster solution therefore emerges from the correspondence between multivariate geometry, reproducibility, cluster composition, and the substantive question being investigated. Within this framework, the two-cluster solution remains informative as a parsimonious representation of broad heterogeneity, whereas the four-cluster specification reveals configurations that are concealed by that broader partition.

The results indicate that methodological transparency is integral to the substantive interpretation of unsupervised sustainability analysis. Scaling decisions determine the metric through which similarity is defined; candidate-k assessment determines the level at which heterogeneity is represented; stability analysis evaluates whether that representation persists under perturbation; and sensitivity analysis establishes how strongly membership depends on alternative treatments of the data. Reporting these elements alongside original-unit cluster profiles makes it possible to distinguish empirical structure from patterns arising primarily from measurement scale, initialization, or preprocessing choices. Such transparency is particularly important when cluster configurations are subsequently used to interpret national sustainability pathways or formulate differentiated policy implications.

5.3 Persistence and convergence are simultaneous, not contradictory

Temporal evidence reveals that persistence of structural regimes and convergence of cross-country positions can occur simultaneously. The exceptionally limited movement between clusters indicates that the configurations identified across the EU-27 are temporally durable rather than transient classifications. This temporal durability is consistent with transition literature emphasizing path dependence, whereby technological systems, infrastructures, institutional arrangements, and accumulated capabilities can constrain rapid structural reconfiguration (Apajalahti and Kungl, 2022). At the same time, the decline in multivariate dispersion and the negative beta-convergence relationship indicates progressive narrowing of cross-country distances. These findings describe two different dimensions of structural change: cluster membership captures whether a Member State crosses the boundaries separating multivariate regimes, whereas convergence measures whether its continuous position becomes closer to those of other Member States. Stability in the former therefore does not preclude adjustment in the latter.

This distinction is important for the interpretation of longitudinal clustering studies. A persistent partition provides evidence of enduring structural heterogeneity, but it does not by itself establish divergence. Similarly, movement toward greater similarity does not require frequent changes in categorical membership. Member States can adjust their energy-resource profiles while remaining within the same broad configuration when the magnitude of change is insufficient to cross cluster boundaries. The EU-27 evidence is consistent with this pattern: structural configurations remain highly persistent while overall multivariate distances narrow over the observation period. Convergence consequently occurs predominantly within an enduring regime structure rather than through widespread redistribution of countries across regimes.

The underlying dimensions nevertheless follow different trajectories. Primary energy consumption and domestic net greenhouse gas emissions display the strongest convergence patterns, while raw material consumption also shows a significant reduction in cross-country differences. These developments are consistent with a European context characterized by increasingly shared energy-efficiency and decarbonization objectives, although the present analysis does not identify the causal contribution of individual policies or technological changes. Research and development expenditure follows a different trajectory, with no significant evidence of either sigma- or beta-convergence. Persistence in this dimension suggests that differences in national innovation capacity remain an important component of structural heterogeneity even as several environmental-pressure indicators become more similar.

Resource productivity provides the clearest counterpoint to the general convergence pattern. Both sigma- and beta-convergence analyses indicate divergence in this dimension, showing that narrowing environmental pressures do not necessarily coincide with convergence in the efficiency with which material resources are transformed into economic value. This finding is consistent with recent EU evidence showing that resource productivity does not follow a single common convergence trajectory. (Islam and Afolabi 2025) identify four distinct resource-productivity convergence clubs across the EU-27, documenting persistent cross-country disparities despite broader integration processes. Member States may therefore become more similar in energy consumption, emissions, or material pressures while differences in productive efficiency remain or increase. The resulting pattern is one of asymmetric convergence, in which environmental and resource-pressure dimensions adjust more uniformly than some of the capabilities associated with economic and technological performance.

Coexistence of multivariate convergence, persistent cluster membership, and indicator-specific divergence provides a more nuanced interpretation of European sustainability dynamics. The EU-27 cannot be characterized adequately through a binary distinction between convergence and divergence. Overall distances are narrowing, but this process takes place within persistent structural configurations and is not shared uniformly across all dimensions. Structural heterogeneity therefore remains relevant even under conditions of aggregate catch-up.

5.4 Relation to earlier European clustering and panel studies

Comparison with previous European studies places the identified energy-resource regimes within a broader literature on heterogeneous sustainability transitions. (Georgescu et al. 2025c) examined the transition toward climate neutrality through a broader set of energy, environmental, social, and macroeconomic dimensions over 2011–2022, combining K-Means classification with ranking procedures and subsequent consolidation into policy-oriented meta-clusters. The present findings address a different dimension of European heterogeneity by concentrating on the joint configuration of energy consumption, innovation expenditure, material use, greenhouse gas emissions, resource productivity, and municipal waste generation over 2010–2023. This narrower analytical focus reveals that productive efficiency, technological capacity, and environmental pressure do not necessarily occupy corresponding positions within national sustainability profiles.

Such multidimensional asymmetry is particularly visible in the regimes represented by Finland and Sweden and by Luxembourg. High research and development intensity in the former coexists with comparatively high energy and material consumption, while Luxembourg combines very high resource productivity with elevated energy, material, emissions, and waste indicators. These configurations qualify interpretations in which technological capacity or economic efficiency is treated as directly equivalent to lower absolute environmental pressure. They instead support a distinction between the efficiency with which resources generate economic value and the physical scale of energy and material demands. This distinction complements broader climate-neutrality classifications by identifying structural tensions that become more visible when energy-resource interactions constitute the primary analytical domain.

Findings also complement research examining the relationships among circularity, innovation, and environmental performance. (Georgescu et al. 2025c) investigate economic, technological, and environmental drivers of the circular economy, while (Fortea et al. 2026) examine dynamic interactions among circular-economy, innovation, and environmental variables using a panel-based econometric framework. Such approaches are designed to estimate relationships and temporal interdependencies among observed dimensions. Cluster analysis addresses a different empirical question by identifying recurrent combinations of these dimensions without imposing directional relationships among them. The subsequent mobility and convergence analyses add a temporal perspective by establishing whether those configurations persist and whether cross-country distances change over time. Econometric and unsupervised approaches are therefore complementary: one examines relationships among variables, whereas the other identifies structural configurations and the trajectories of observations within the resulting multivariate space.

Broader European clustering research similarly emphasizes that sustainability transitions follow heterogeneous national pathways. The differentiation of sustainable energy strategies reported by (Strielkowski et al. 2024) and the heterogeneous decarbonization trajectories identified by (Chovancová et al. 2025) are consistent with the persistence of distinct structural configurations found here. The present results extend this interpretation by showing that persistent heterogeneity does not necessarily imply an absence of convergence. Member States can remain within relatively stable energy-resource regimes while their continuous multivariate positions become closer. This finding links the clustering literature with convergence research and provides a longitudinal interpretation of structural heterogeneity that cannot be obtained from static country classifications alone.

Comparison with earlier research indicates that the contribution of the present study lies in the integration of structural classification with temporal adjustment rather than in clustering EU Member States as an isolated methodological exercise. The four regimes identify recurrent combinations of energy-resource characteristics, while annual membership, mobility, and convergence diagnostics establish how those configurations evolve within the panel. The resulting perspective complements broader climate-neutrality and circular-economy studies by distinguishing persistence of structural regimes from convergence of continuous country positions and by showing that both processes can coexist within the European sustainability transition.

5.5 Policy implications

Policy implications emerging from the analysis depend on the multidimensional configuration of each structural regime rather than on an ordinal interpretation of cluster membership. The four clusters do not represent successive levels of sustainability performance, and movement from one cluster to another cannot therefore be treated automatically as improvement. Their policy relevance lies instead in identifying different combinations of energy and material pressures, innovation capacity, resource productivity, emissions, and waste generation. This perspective supports differentiated intervention while preserving common EU sustainability objectives. Recent EU-wide evidence similarly indicates that Member States differ substantially in the efficiency and trajectories of their circular-economy transitions, supporting targeted innovation and policy incentives rather than uniform intervention across heterogeneous national contexts (Álvarez et al., 2026).

The Lower-intensity resource and innovation profile combines comparatively limited environmental pressures with lower research and development expenditure and resource productivity. Policy priorities for this configuration concern the strengthening of productive and technological capabilities without reproducing the higher resource intensity observed elsewhere in the EU. Investment in resource-efficient modernization, diffusion of cleaner technologies, circular production processes, and innovation capacity can contribute to productivity growth while preserving comparatively moderate levels of energy use, emissions, and waste. The relevant policy objective is therefore not convergence toward the consumption structure of higher-income regimes, but improvement in productive capability under resource and environmental constraints.

The Innovation and resource-productivity profile presents a different policy challenge. Comparatively strong research and development expenditure and resource productivity coexist with above-average emissions and municipal waste generation, indicating that technological and productive capabilities do not automatically translate into lower environmental pressure. Policy intervention in this regime should consequently place greater emphasis on the environmental outcomes associated with existing innovative capacity. Waste prevention, circular use of materials, energy decarbonization, and reductions in absolute environmental pressures are particularly relevant where efficiency gains coexist with high levels of consumption or residual generation. Innovation policy and environmental policy should therefore be evaluated jointly rather than assuming that improvements in technological capacity necessarily produce proportional reductions in physical pressures.

The R&D-intensive, material-consumption profile illustrates another form of asymmetry. Finland and Sweden combine high innovation intensity with comparatively low net greenhouse gas emissions but remain characterized by high primary energy and raw material consumption. This configuration suggests that progress in decarbonization can coexist with substantial material throughput. Policy attention in such systems should extend beyond emissions toward the material dimension of sustainability, including greater circularity, material efficiency, substitution, reuse, and reductions in resource-intensive production and consumption where feasible. Existing innovation capacity represents an important enabling condition, but the empirical profile indicates that technological strength alone does not eliminate material pressures.

The High-intensity energy, emissions and resource profile illustrates most clearly the distinction between resource productivity and absolute environmental pressure. Very high resource productivity coexists with elevated primary energy consumption, raw material consumption, greenhouse gas emissions, and municipal waste generation. Policy assessment based predominantly on efficiency indicators could therefore provide an incomplete representation of sustainability performance in this type of economy. Greater attention to absolute energy and material demand, emissions, and waste generation is required alongside productivity objectives. Because this regime is represented by Luxembourg throughout the study period, its interpretation should remain sensitive to the specific economic and demographic characteristics of a small, high-income and highly integrated economy rather than being generalized directly to other Member States.

At EU level, persistence of the four regimes supports a combination of common objectives and differentiated implementation. This interpretation is consistent with evidence showing that the effectiveness and priorities of national circular-economy policies vary across European countries, implying that common European objectives may require policy instruments adapted to country-specific resource and circularity constraints (Sanz-Torró et al., 2025). Shared targets remain appropriate for sustainability dimensions in which cross-country differences are narrowing, particularly energy consumption and greenhouse gas emissions. Persistent differences in innovation capacity and divergence in resource productivity, however, indicate that Member States do not approach these objectives from equivalent structural positions. Cohesion, innovation, circular-economy, and transition instruments can therefore play complementary roles by supporting capability development where productive constraints are more pronounced and reductions in absolute environmental pressures where high efficiency coexists with intensive resource use.

Convergence findings also have implications for the evaluation of policy progress. Cluster membership should not be interpreted as a performance score because substantial adjustment can occur without a Member State crossing a cluster boundary, while a change in membership may result from comparatively limited movement near a boundary. Continuous trajectories in the underlying indicators, changes in multivariate distance, and evolution of cross-country dispersion provide complementary information to categorical regime membership. Monitoring both structural regimes and continuous positions would therefore distinguish changes in the type of sustainability configuration from progress occurring within an otherwise persistent configuration.

In our opinion, the results support a two-level interpretation of European sustainability policy. Common EU objectives remain relevant where Member States exhibit measurable convergence, while differentiated instruments are warranted where structural configurations and productive capabilities remain persistent or divergent. Such an approach does not imply separate sustainability objectives for different groups of countries. Rather, it recognizes that comparable European objectives may require different adjustment pathways depending on the relationship among innovation capacity, resource productivity, material and energy intensity, emissions, and waste generation.

5.6 Limitations

Several limitations define the scope within which the findings should be interpreted. K-Means represents similarity through standardized Euclidean distance and therefore captures a specific geometry of the multivariate space. Alternative clustering approaches, including hierarchical clustering, Gaussian mixture models, spectral clustering, or model-based classification, may identify complementary forms of heterogeneity. Recent methodological work similarly emphasizes that conventional K-Means remains sensitive to cluster geometry, outliers, and the specification of the number of clusters, particularly when the underlying data structure departs from approximately spherical configurations (Khan et al., 2024). Nevertheless, the stability and sensitivity analyses indicate that the retained four-cluster structure is not dependent on a single initialization or on extreme observations. Accordingly, the identified regimes should be interpreted as robust configurations within the adopted K-Means framework rather than as the only possible representation of heterogeneity among EU Member States.

Indicator coverage constitutes another boundary of the analysis. The six variables capture interconnected dimensions of energy use, innovation, material consumption, greenhouse gas emissions, resource productivity, and municipal waste generation, but they do not encompass the entire sustainability domain. Renewable-energy deployment, energy poverty, circular material use, biodiversity, trade-embedded resource flows, institutional quality, and distributional outcomes remain outside the analytical framework. Cluster labels consequently describe energy-resource sustainability configurations rather than comprehensive assessments or rankings of national sustainability performance. This focused specification permits detailed examination of the relationships between resource pressures and productive efficiency, while limiting generalization beyond the dimensions represented by the selected indicators.

Standardization across the complete 2010–2023 panel provides a common metric for clustering Member State-year observations and preserves comparability across the study period. At the same time, a common full-panel transformation means that standardized positions reflect the distribution observed over the entire period rather than exclusively the distribution prevailing in each individual year. Year-specific standardization would capture a different phenomenon by expressing each country only relative to its contemporaneous cross-sectional distribution. The present specification is appropriate for examining trajectories within a common multivariate space, although alternative scaling strategies could provide additional evidence on changes in relative annual positioning.

Beta-convergence estimates should be interpreted as descriptive evidence of systematic adjustment rather than as estimates of causal relationships. Regressions linking subsequent change to initial position may be affected by regression-to-the-mean mechanisms and do not identify the economic, institutional, technological, or policy factors responsible for the observed trajectories. This distinction is particularly relevant because the multivariate linear beta coefficient indicates significant catch-up, whereas the corresponding Spearman association is weaker. The convergence results therefore establish whether initial positions are systematically associated with subsequent adjustment, while causal attribution would require a separate panel specification incorporating relevant structural covariates and appropriate identification assumptions.

Temporal dependence is not incorporated directly into the K-Means objective because country-year observations are classified according to their positions in the standardized multivariate space. Longitudinal information is instead retained after estimation through complete annual membership sequences, transition analysis, persistence measures, and sigma- and beta-convergence diagnostics. This distinction is consistent with the longitudinal-clustering literature, which emphasizes that repeated observations introduce temporal dependence that may require specialized model-based, algorithmic, or functional clustering approaches when time dependence is incorporated directly into cluster formation (Lu, 2025). This design makes it possible to distinguish persistent structural regimes from changes in continuous cross-country dispersion, but it does not estimate transition probabilities or latent temporal states within the clustering algorithm itself. Dynamic clustering, hidden-state models, or other time-dependent classification approaches could extend the analysis by integrating temporal dependence directly into the formation of sustainability regimes.

6 Conclusions

This study examines energy and resource sustainability patterns across the EU-27 through an integrated clustering and convergence framework applied to 378 Member State-year observations over 2010–2023. Six Eurostat indicators capture primary energy consumption, research and development expenditure, raw material consumption, domestic net greenhouse gas emissions, resource productivity, and municipal waste generation. The analytical design combines z-standardized K-Means clustering with extended cluster validation, resampling stability, preprocessing sensitivity analysis, annual membership tracking, and sigma- and beta-convergence diagnostics. This framework allows structural heterogeneity, temporal persistence, and changes in continuous cross-country distances to be evaluated as related but analytically distinct characteristics of the European energy-resource sustainability landscape.

RQ1 examined the structural energy-resource sustainability regimes emerging after scale correction and empirical validation. Results identify four recurrent configurations. The Lower-intensity resource and innovation profile contains the majority of Member State-year observations and combines comparatively low energy consumption, innovation expenditure, resource productivity, emissions, and municipal waste generation. The Innovation and resource-productivity profile combines comparatively high research and development expenditure and resource productivity with higher waste generation and greenhouse gas emissions. The R&D-intensive, material-consumption profile, represented persistently by Finland and Sweden, combines high innovation intensity, primary energy consumption, and raw material consumption with comparatively low net greenhouse gas emissions. The High-intensity energy, emissions and resource profile, represented by Luxembourg throughout the observation period, combines very high resource productivity with high energy consumption, material consumption, emissions, and municipal waste generation. These configurations show that the six sustainability dimensions form distinct combinations rather than successive positions along a single performance continuum.

RQ2 assessed the stability and interpretability of the selected partition relative to alternative cluster numbers and preprocessing specifications. The four-cluster solution provides a balanced representation of internal separation, resampling stability, cluster composition, and substantive differentiation. Its mean subsampling ARI of 0.938 and median ARI of 0.976 indicate high reproducibility, while the two-cluster solution remains a useful parsimonious benchmark. Higher-order partitions improve several geometric validation criteria but increasingly separate complete national trajectories into small clusters, thereby producing a finer level of segmentation than required by the study objective. Measurement scale has a substantial effect on the resulting structure. Agreement between standardized and unstandardized four-cluster partitions is only ARI = 0.135, with municipal waste generation dominating the distance structure in original units. By contrast, 1st−99th percentile winsorization produces an almost identical partition (ARI = 0.981), indicating that the baseline configuration is not driven by a small number of extreme observations. Robust scaling retains substantial agreement with the baseline, whereas the Yeo-Johnson transformation produces a larger change by modifying the distributional geometry of the indicator space.

RQ3 investigated whether the identified regimes persist over time, whether Member States move between them, and whether their multivariate positions converge. Structural persistence is exceptionally high: 348 of 351 adjacent-year comparisons retain the same cluster membership, corresponding to a persistence rate of 99.15% and a mobility rate of 0.85%. Only three transitions are observed, involving Italy and Czechia, while Clusters 3 and 4 remain unchanged throughout the complete period. Persistence of categorical membership nevertheless coexists with convergence in continuous multivariate space. RMS distance to the annual EU centroid decreases by 14.45% between 2010 and 2023, and the multivariate beta-convergence coefficient is negative and statistically significant (β = −0.03582, R² = 0.472, p < 0.001). Member States initially located farther from the EU centroid therefore tend, on average, to experience larger subsequent reductions in multivariate distance.

Convergence is not uniform across the underlying dimensions. Primary energy consumption, raw material consumption, and domestic net greenhouse gas emissions exhibit significant sigma-convergence together with significant beta-convergence. Research and development expenditure shows neither a significant linear decline in dispersion nor significant beta-convergence. Municipal waste generation exhibits significant beta-convergence without a statistically significant linear sigma-convergence trend. Resource productivity follows the opposite trajectory, with both cross-country dispersion and the beta coefficient increasing significantly. Overall convergence in the EU-27 consequently coexists with persistent or widening differences in specific structural capabilities, particularly the capacity to generate economic value from material inputs.

These findings contribute to the sustainability literature by demonstrating that structural regime persistence and cross-country convergence are not mutually exclusive processes. Cluster membership captures relatively durable configurations of energy use, innovation, material consumption, emissions, resource productivity, and waste, whereas sigma- and beta-convergence capture changes in continuous distances among Member States. The simultaneous presence of 99.15% membership persistence and significant multivariate catch-up indicates that convergence can occur predominantly within persistent structural regimes rather than through widespread movement between them. This distinction provides a more precise interpretation of European sustainability dynamics than a binary characterization of the EU as either convergent or persistently divergent.

Methodologically, the study shows that conclusions drawn from multidimensional sustainability clustering depend critically on the representation of heterogeneous indicators and on the validation of the resulting partition. Standardization materially changes cluster membership when physical and economic variables are expressed on markedly different numerical scales, while the comparison of candidate solutions demonstrates that maximizing a single internal validation criterion does not necessarily provide the most appropriate analytical granularity. Combining internal validation, Gap Statistic, resampling stability, preprocessing sensitivity, cluster composition, and longitudinal membership analysis provides a reproducible framework for distinguishing robust structural configurations from partitions generated by scale effects, extreme observations, or excessive segmentation. The explicit separation of clustering from subsequent mobility and convergence analysis further extends the usefulness of this framework to longitudinal sustainability data.

The empirical contribution is distinct from earlier EU climate-neutrality clustering because the present analysis focuses specifically on the interaction between energy and resource sustainability dimensions over 2010–2023 and retains the complete country-year structure of the panel. Its contribution lies not only in identifying four energy-resource configurations but also in determining their annual persistence and relating that persistence to continuous sigma- and beta-convergence. The resulting evidence shifts attention from static country classification toward the coexistence of structural heterogeneity and gradual cross-country adjustment.

Policy implications follow directly from this coexistence. Convergence in several environmental-pressure dimensions supports continued EU-wide coordination through common climate, energy-efficiency, and resource objectives. Persistent structural regimes and divergence in resource productivity simultaneously indicate that common targets cannot be expected to generate identical adjustment trajectories across Member States. Policy design should therefore combine shared European objectives with instruments responsive to different configurations of innovation capacity, material intensity, resource productivity, emissions, energy consumption, and waste generation. Such differentiation is particularly relevant for cohesion policy, where narrowing environmental pressures may coexist with persistent disparities in technological and productive capacity.

Future research can extend the framework in three complementary directions. Time-aware or dynamic clustering could incorporate temporal dependence directly into regime identification and examine whether longer observation horizons produce more frequent transitions between structural configurations. Causal panel and spatial models could investigate the economic, technological, institutional, and policy mechanisms underlying the sigma- and beta-convergence patterns identified here. Broader indicator frameworks and more disaggregated sectoral or regional data could determine whether the observed regimes remain stable when additional sustainability dimensions and within-country heterogeneity are incorporated.

Overall, the EU-27 exhibits neither complete structural homogenization nor persistent divergence. Member States remain overwhelmingly within stable energy-resource regimes while multivariate cross-country distances decline and countries initially farther from the common EU position tend to catch up. Convergence is strongest in several energy, material, and emissions dimensions, while innovation expenditure remains comparatively persistent and resource productivity diverges. The European sustainability transition therefore proceeds predominantly through narrowing distances within durable structural configurations rather than through repeated movement between regimes. Recognizing this distinction allows common European progress and persistent differences in national capabilities to be assessed simultaneously and provides a stronger basis for combining shared sustainability objectives with differentiated transition strategies.

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Footnotes

Edited by: Casper Boongaling Agaton, University of the Philippines Los Baños, Philippines

Reviewed by: Milena N. Rajić, University of Niš, Serbia

Divya Mishra, GL Bajaj Institute of Technology and Management (GLBITM), India