A spatial-functional clustering algorithm for panel data with an application to Italian health tax detractions

Regional socio-economic phenomena are shaped by both geography and time: where territories are located matters, but so does how they evolve. Yet existing clustering methods treat these two dimensions in isolation, capturing either spatial proximity or dynamic similarity, but rarely both. In this paper, we introduce a spatial-functional clustering algorithm, validated through simulated and real-world data, that achieves regional segmentation by simultaneously accounting for geographical coherence and similarity in temporal trends. Applied to health tax detractions at the municipal level in Italy, the algorithm uncovers five territorially coherent clusters with distinct per-capita levels and trajectories, revealing a marked North–South gradient in which fiscal capacity, rather than healthcare need, systematically drives tax benefit utilisation.