The Three-Way Spectral Clustering Method for the Analysis of Territorial Fragility before and after the COVID-19 Pandemic

Territorial fragility is a dynamic phenomenon. Approaching it quantitatively requires models accounting for both structural persistence and abrupt shifts among its indicators. A Three-Way Spectral Clustering approach is applied to a longitudinal dataset of 12 indicators of territorial fragility of 7903 Italian municipalities observed over the 2018-2022 period, to optimise both the components simultaneously within a single objective function. As a result, the latent representation identifies homogeneous groups, tailoring stable profiles of municipal territories. By a comparison of the pre-pandemic baseline (2018-2019) vs. the post-emergency recovery phase (2021-2022), the results suggest that the pandemic has manifested latent patterns within the system of measurement of territorial fragility. In particular, the post-pandemic analysis shows signs of latent human capacities that had not necessarily emerged in previous analyses, where results were dependent primarily on environmental factors of territorial fragility. Thus, the frameworks of simultaneous optimisation are useful as diagnostic tools for preventive policies and to understand the role of human factors of functional resilience.