Comparative analysis of latent representation techniques for territorial entities: case study in the Community of Madrid

Abstract

This paper proposes an innovative approach to the vector representation of municipalities using graph embedding techniques, applied to the case of the Community of Madrid. The research is based on the context of territorial inequality and socio-economic reconfiguration that characterises the Madrid metropolitan area, and hypothesises that the relationships between municipalities can be learned in a latent space capable of preserving their urban, economic and temporal structure. To this end, an urban graph is constructed in which each municipality constitutes a node and the edges represent interactions of various kinds (distances, boundaries, migratory flows or connectivity). Based on a heterogeneous set of public sources, different neural networks models are developed which integrate nodal, internodal and temporal information. The validation of the embeddings combines intrinsic consistency metrics and external predictive tasks, verified by statistical tests (Friedman, Nemenyi and Wilcoxon-Holm) and parametric bootstrap. The results show significant differences between models, with E2A-SAGE-MAE standing out as the best performing and most robust, achieving the best performance in around 80 % of the configurations analysed. Furthermore, it is confirmed that the city of Madrid acts as an outlier, significantly affecting the latent structure of the graph. Overall, the results demonstrate that it is possible to generate vector representations of urban units that capture complex relationships, providing a useful tool for territorial analysis.