Correlation-based hierarchical clustering of time series with spatial constraints

Correlation-based hierarchical clustering methods for time series typically are based on a suitable dissimilarity matrix derived from pairwise measures of association. Here, this dissimilarity is modified in order to take into account the presence of spatial constraints. This modification exploits the geometric structure of the space of correlation matrices, i.e. their Riemannian manifold. Specifically, the temporal correlation matrix (based on van der Waerden coefficient) is aggregated to the spatial correlation matrix (obtained from a suitable Matérn correlation function) via a geodesic in the Riemannian manifold. Our approach is presented and discussed using simulated and real data, highlighting its main advantages and computational aspects.