A spatially-weighted AMH copula-based dissimilarity measure for clustering variables: An application to urban thermal efficiency

Investigating thermal energy demand is crucial for developing sustainable cities and the efficient use of renewable sources. Despite the advances made in this field, the analysis of energy data provided by smart grids is currently a demanding challenge due to their complex multivariate structure and high dimensionality. In this article, we propose a novel copula-based dissimilarity measure suitable for analyzing district heating demand and introduce a procedure to apply it to high-temporal resolution panel data. Inspired by the characteristics of the considered data, we explore the usefulness of the Ali-Mikhail-Haq copula in defining a new dissimilarity measure to cluster variables in the hierarchical framework. We show that our proposal is particularly sensitive to small dissimilarities based on tiny differences in the strength of the dependence between the involved random variables. Therefore, the measure we introduce is able to distinguish between objects with low dissimilarity better than standard rank-based dissimilarity measures. Moreover, our proposal considers a weighted version of the copula-based dissimilarity that embeds the spatial location of the involved objects. We investigate the proposed measure through Monte Carlo studies and compare it with an analogous dissimilarity measure based on Kendall's correlation. Finally, the application to real data concerning the Italian city Bozen-Bolzano makes it possible to find clusters of buildings homogeneous with respect to their main characteristics, such as energy efficiency and heating surface. In turn, our findings may support the design, expansion, and management of district heating systems.