Regionalization of the extremal dependence structure using spectral clustering

The influence of an extreme event depends on the geographical features of the region where the event occurs. To understand the behavior of an extreme event, we consider statistical models capable of capturing the extremes and their spatial dependence. Max-stable processes are widely used in the study of extreme events. However, assuming a fixed extremal dependence for a max-stable process may not be reasonable, depending on the topology of the region under study. In extreme environmental events, different types of extremal dependencies can appear across the spatial domain. In this study, we present an adapted spectral clustering algorithm for max-stable processes. This algorithm combines spectral clustering with extremal concurrence probability to cluster locations into k regions, each with homogeneous extremal dependence. In addition, we propose an approach to model the entire region on the basis of clustered zones. For validation, we applied the proposed methodology to two simulation cases using a nonstationary max-stable mixture model. The accuracy of the results encouraged us to apply the methodology to two datasets: rainfall data from the east coast of Australia and rainfall data from France.