Spatially constrained statistical approach for determining the optimal number of regions in regionalization

Determining the optimal number of regions is a challenging issue in regionalization. Although cluster validity indices developed for non-spatial clustering have been used to determine the optimal number of regions, spatial contiguity constraints for regionalization are often neglected. Consequently, different regionalization results can share the same validity index value, which reduces the reliability of identifying the optimal number of regions in regionalization. To overcome this limitation, this study proposes a spatially constrained statistical approach for determining the optimal number of regions using two metrics: (i) a permutation-based variance for measuring the homogeneity within regions and (ii) a proportion index based on spatially constrained k-nearest neighbors to quantify the separation between regions. Furthermore, a distance-based method is employed to balance these two metrics to automatically determine the optimal number of regions. Experimental results on five synthetic datasets, the US presidential election and climate datasets show that the statistical approach developed in this study outperforms three widely used cluster validity indices in determining the optimal number of regions. The proposed statistical approach is straightforward to implement and can effectively reduce subjectivity in regionalization.