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.

用于时间序列的基于相关性的层次聚类方法通常基于从成对关联度量导出的合适的相异矩阵。在这里，为了考虑到空间限制的存在，对这种差异进行了修改。这种修改利用了相关矩阵空间的几何结构，即它们的黎曼流形。具体来说，时间相关矩阵（基于 van der Waerden 系数）通过黎曼流形中的测地线聚合到空间相关矩阵（从合适的 Matérn 相关函数获得）。我们的方法使用模拟和真实数据进行介绍和讨论，强调其主要优点和计算方面。