Spatially-encouraged spectral clustering: a technique for blending map typologies and regionalization
Clustering is a central concern in geographic data science and reflect a large, ongoing domain of research. In applied problems, it is often challenging to balance the two notions of coherence in spatial clustering problems: that of "feature" coherence, where detected clusters are internally homogeneous, and "spatial'" coherence, where detected clusters can be interpreted to represent a geographical place. While recent work has aimed to relax this tension, progress in spectral clustering methods, developed for machine learning and image segmentation, provide a useful framework to do this. This paper shows how spatial and feature coherence can be balanced using kernel combination in spectral clustering. This ensures the preservation of geographical constraints (like contiguity or compactness) while also providing the ability to relax these constraints linearly. Further, some kinds of kernel combination methods have significantly different behavior and meaning from another commonly-used method to balance objectives: convex combination. Altogether, spatially-encouraged spectral clustering is proposed as a novel spatial analysis method that bridges regionalization and spatial clustering.