Probabilistic Regionalization via Evidence Accumulation with Random Spanning Trees as Weak Spatial Representations

Spatial clusters contain biases and artifacts, whether they are defined via statistical algorithms or via expert judgment. Graph-based partitioning of spatial data and associated heuristics gained popularity due to their scalability but can define suboptimal regions due to algorithmic biases such as chaining. Despite the broad literature on deterministic regionalization methods, approaches that quantify regionalization probability are sparse. In this article, we propose a local method to quantify regionalization probabilities for regions defined via graph-based cuts and expert-defined regions. We conceptualize spatial regions as consisting of two types of spatial elements: core and swing. We define three distinct types of regionalization biases that occur in graph-based methods and showcase the use of the proposed method to capture these types of biases. Additionally, we propose an efficient solution to the probabilistic graph-based regionalization problem via performing optimal tree cuts along random spanning trees within an evidence accumulation framework. We perform statistical tests on synthetic data to assess resulting probability maps for varying distinctness of underlying regions and regionalization parameters. Lastly, we showcase the application of our method to define probabilistic ecoregions using climatic and remotely sensed vegetation indicators and apply our method to assign probabilities to the expert-defined Bailey's ecoregions.