Spatial product partition model through spanning trees

Abstract

When performing analysis of spatial data, there is often the need to aggregate geographical areas into larger regions, a process called regionalization or spatially constrained clustering. This type of aggregation can be useful to make data analysis tractable, reduce the effect of different populations for a better statistical handling of the data or even to facilitate the visualization.In this work we present a new regionalization method which incorporates the concept of spanning trees into a statistical framework, forming a new type of spatial product partition model. By conditioning the partitions to splits of spanning trees we reduce the search space and enable the construction of an effective sampling algorithm.We show how using a Bayesian statistical framework we are able to better accommodate the natural variation of the data and to diminish the effect of outliers, producing better results when compared with the traditional approaches. We also show how our model is flexible enough to accommodate distinct distributions of data. Finally, we evaluate our method through experiments with simulated data as well as with two distinct case studies.