A spatial clustering perspective on autocorrelation and regionalization

We revisit one of the classical problems in geography and cartography where multiple observations on a lattice (N) need to be grouped into many fewer regions (G), especially when this number of desired regions is unknown a priori. Since an optimization through all possible aggregations is not feasible, a hierarchical classification scheme is proposed with an objective function sensitive to spatial pattern. The objective function to be minimized during the assignment of observations to regions (classification) consists of two terms: the first characterizes accuracy and the second, model complexity. For the latter, we introduce a spatial measure that characterizes the number of homogeneous patches rather than the usual number of classes. A simulation study shows that such a classification procedure is less sensitive to random and spatially correlated error (noise) than non-spatial classification. We also show that for conditional autoregressive error (noise) fields the optimal partitioning is the one that has the highest within-units generalized Moran coefficient. The classifier is implemented in ArcView to demonstrate both a socio-economic and an environmental application to illustrate some potential applications.