Higher-Order Hierarchical Spectral Clustering for Multidimensional Data.

Understanding the community structure of countries in the international food network is of great importance for policymakers. Indeed, clusters might be the key for the understanding of the geopolitical and economic interconnectedness between countries. Their detection and analysis might lead to a bona fide evaluation of the impact of spillover effects between countries in situations of distress. In this paper, we introduce a clustering methodology that we name Higher-order Hierarchical Spectral Clustering (HHSC), which combines a higher-order tensor factorization and a hierarchical clustering algorithm. We apply this methodology to a multidimensional system of countries and products involved in the import-export trade network (FAO dataset). We find a structural proxy of countries interconnectedness that is not only valid for a specific product but for the whole trade system. We retrieve clusters that are linked to economic activity and geographical proximity.