Identifying hidden spatial patterns that define sub-regions characterized by a similar behaviour is a central topic in statistical climatology. This task, often called regionalization, is helpful for recognizing areas in which the variables under consideration have a similar stochastic distribution and thus, potentially, for reducing the dimensionality of the data. Many examples for regionalization are available, spanning from hydrology to weather and climate science. However, the majority of regionalization techniques focuses on the spatial clustering of a single variable of interest and is often not tailored to extremes. Extreme events often have severe impacts, which can be amplified when co-occurring with extremes in other variables. Given the importance of characterizing compound extreme events at the regional scale, here we develop an algorithm that identifies homogeneous spatial sub-regions that are characterized by a common bivariate dependence structure in the tails of a bivariate distribution. In particular, we use a novel non-parametric divergence able to capture the similarities and differences in the tail behaviour of bivariate distributions as the core of our clustering procedure. We apply the approach to identify homogeneous regions that exhibit similar likelihood of compound precipitation and wind extremes in Great Britain and Ireland.