Constrained Spectral Clustering for Regionalization: Exploring the Trade-off between Spatial Contiguity and Landscape Homogeneity

A regionalization system delineates the geographical landscape into spatially contiguous, homogeneous units for landscape ecology research and applications. In this study, we investigated a quantitative approach for developing a regionalization system using constrained clustering algorithms. Unlike conventional clustering, constrained clustering uses domain constraints to help guide the clustering process towards finding a desirable solution. For region delineation, the adjacency relationship between neighboring spatial units can be provided as constraints to ensure that the resulting regions are geographically connected. However, using a large-scale terrestrial ecology data set as our case study, we showed that incorporating such constraints into existing constrained clustering algorithms is not that straightforward. First, the algorithms must carefully balance the trade-off between spatial contiguity and landscape homogeneity of the regions. Second, the effectiveness of the algorithms strongly depends on how the spatial constraints are represented and incorporated into the clustering framework. In this paper, we introduced a truncated exponential kernel to represent spatial contiguity constraints for region delineation using constrained spectral clustering. We also showed that a Hadamard product approach that combines the kernel with landscape feature similarity matrix can produce regions that are more spatially contiguous compared to other baseline algorithms.