Spatially Constrained Spectral Clustering Algorithms for Region Delineation

Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are both homogeneous and spatially contiguous. Second, it is well-recognized that landscapes are hierarchical such that fine-scale regions are nested wholly within broader-scale regions. To address these two challenges, first, we develop a spatially constrained spectral clustering framework for region delineation that incorporates the tradeoff between region homogeneity and spatial contiguity. The framework uses a flexible, truncated exponential kernel to represent the spatial contiguity constraints, which is integrated with the landscape feature similarity matrix for region delineation. To address the second challenge, we extend the framework to create fine-scale regions that are nested within broader-scaled regions using a greedy, recursive bisection approach. We present a case study of a terrestrial ecology data set in the United States that compares the proposed framework with several baseline methods for regionalization. Experimental results suggest that the proposed framework for regionalization outperforms the baseline methods, especially in terms of balancing region contiguity and homogeneity, as well as creating regions of more similar size, which is often a desired trait of regions.