Clustering Methods for Asymmetric Data Using Spectral Approaches: An Application to International Student Mobility

Asymmetric data arise in many fields as directed flows or exchanges between objects and the main interest of clustering such data relies on the study of the flow imbalances. Several methods used for clustering asymmetric data are framed in the context of spectral clustering. They consist in considering objects as vertices of a directed graph to be converted into an undirected one by defining appropriate symmetrizations of the asymmetric weighted data matrix and, once the undirected graph is obtained, by applying the standard spectral clustering algorithm. In this context, the aim of this work is the comparison of different symmetrizations proposed in the literature and the analysis of the characteristics of the resulting clusters. Actually, two main types of clusters can be identified: clusters of objects that have similar behaviour in terms of directions and amounts of the flows, or that form isolated subsystems of only internal exchanges. Artificial examples and an application to international university student mobility in OECD countries are presented.