An innovative approach to co-clustering of directional data: a methodological framework with an application on interregional mobility in the Italian national health care system

The aim of this work is to propose an innovative methodology for the co-clustering of transition tables expressed as directional data. The clustering method used is the Depth-Based Medoids Clustering Algorithm (DBMCA), and the evaluation of the quality of the cluster is carried out using the k-elbow method, duly adapted taking into account that the data represent values of angular depth. Transition tables are square asymmetric matrices of frequencies in which the rows and columns represent the same objects. The motivating example concerns particular frequency tables within the Italian national health care system, in which the objects in rows and columns are the Italian regions of residence and hospitalization, respectively. The distances between the clusters of the regions of hospitalization and residence highlight differences and similarities in healthcare mobility patterns, allowing for the identification of relationships between flows and regional behaviors. This approach provides a useful overview for understanding hospitalization dynamics and the connections between the analyzed territories.