Nonlinear Modeling for the Construction of a Synthetic Index: An Approach Based on UMAP and Random Forest Applied to the Energy Performance of OECD Countries

Abstract

This article proposes a hybrid method for constructing composite indices in the context of decision-making through the integration of Uniform Manifold Approximation and Projection (UMAP) and the Random Forest algorithm. Unlike Principal Component Analysis (PCA) and the Analytic Hierarchy Process (AHP), the proposed method derives fully data-driven weights from nonlinear structure in the data, rather than relying on linear covariance or expert judgment. The method is an operations research model within the framework of multicriteria decision analysis, applied to the evaluation of energy performance in OECD countries using a multidimensional set of environmental, technological, and economic indicators. UMAP is used to detect hidden patterns in the data, while Random Forest is used to derive the importance of features and generate the weighting scheme; the final aggregation of standardized indicators into the index itself is linear. The results show that per capita CO2 emissions and investment in clean energy R&D consistently emerge as the two most influential indicators. Because the UMAP embedding and the resulting weights vary with the algorithm’s pseudo-random initialization, the reported weights and ranking are the mean of an ensemble of 20 independent runs rather than a single realization, together with a systematic robustness analysis of the framework’s hyperparameters, embedding dimensionality, and sample composition. A non-compensatory aggregation alternative produces an almost identical ranking (Spearman ρ = 0.987), indicating the linear aggregation step is not a fragile choice. Compared to traditional approaches based on linear assumptions or subjective judgments, the presented approach derives weights endogenously from the data structure, providing a transparent and empirically validated framework for constructing synthetic indices for decision-making in complex systems.