Spectral–Entropy Network Analysis of Multidimensional Poverty: An Explainable AI Framework for Complex Socioeconomic Systems

Multidimensional poverty is a socioeconomic problem that results from nonlinear interdependencies of various socioeconomic indicators such as educational, health, and living standards indices. This paper considers an XAI-based approach for studying the structural topology and dependency structures of multidimensional poverty systems. It relies on a combination of machine learning approaches, network science, spectral graph theory, and entropy-based complexity measures for revealing the systemic interdependencies between different poverty indicators. The structure of interdependencies between socioeconomic indices associated with education is represented by the multilayer perceptron (MLP). The interpretability of the model is provided via the computation of SHAP values by means of the KernelSHAP method. Higher-order interactions between variables are revealed via the construction and analysis of SHAP-based interaction networks. The proposed methodology is then employed on the GEMPI 2025 dataset consisting of 109 countries. The results show significant consistency in the structural map (R2 = 0.9890) in combination with stable internal consistency in cross-validation (R2 = 0.9864, SD = 0.0074). The SHAP analysis shows that standards of living and health have a high influence on the structural mapping of education, while the contribution of income-related features is lower compared to other features. Entropy analysis points toward partially fragmented dependency networks with a moderate concentration of explanatory influences (H = 1.705). The proposed framework can be used to characterize structural dependencies, identify influencing system components, and map informational processes in multidimensional poverty systems by combining the methodology of explainable artificial intelligence with entropy–spectral network analysis.