Graph-based spatial segmentation of areal data

Smoothing is often used to improve the readability and interpretability of noisy areal data. However, there are many instances where the underlying quantity is discontinuous. For such cases, specific methods are needed to estimate the piecewise constant spatial process. A well-known approach in this setting is to perform segmentation of the signal using the adjacency graph, such as the graph-based fused lasso. However, this method does not scale well to large graphs. A new method is introduced for piecewise constant spatial estimation that (i) is faster to compute on large graphs and (ii) yields sparser models than the fused lasso (for the same amount of regularization), resulting in estimates that are easier to interpret. The method is illustrated on simulated data and applied to real data on overweight prevalence in the Netherlands. Healthy and unhealthy zones are identified, which cannot be explained by demographic or socio-economic characteristics alone. The method is found capable of identifying such zones and can assist policymakers with their health improving strategies.