Consistent Bayesian Spatial Domain Partitioning Using Predictive Spanning Tree Methods

2025-08-09

AI Summary

Existing Bayesian spatial clustering methods suffer from limited predictive capability, overly restrictive geometric constraints on subregions, and a lack of theoretical guarantees for posterior clustering consistency. To address these limitations, we propose the Spatial Random Partition Model (Spat-RPM), which constructs contiguous subregions via spanning-tree-based cuts, enabling automatic estimation of the unknown number of clusters and flexible modeling of spatial proximity—applicable also to spatial clustering regression. We establish, for the first time, a posterior consistency theory for spatial partitions, introducing a novel distance metric to quantify partition concentration and ensuring consistent estimation of both cluster count and parameters. Spat-RPM overcomes conventional shape restrictions and provides principled guidance for hyperparameter selection. Under the infill asymptotic framework, we derive posterior concentration rates for partitions, parameters, and predictions. Extensive simulations and application to Atlantic Ocean spatial data demonstrate its superior accuracy in regionalization and prediction.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Bayesian model-based spatial clustering methods are widely used for their flexibility in estimating latent clusters with an unknown number of clusters while accounting for spatial proximity. Many existing methods are designed for clustering finite spatial units, limiting their ability to make predictions, or may impose restrictive geometric constraints on the shapes of subregions. Furthermore, the posterior clustering consistency theory of spatial clustering models remains largely unexplored in the literature. In this study, we propose a Spatial Domain Random Partition Model (Spat-RPM) and demonstrate its application for spatially clustered regression, which extends spanning tree-based Bayesian spatial clustering by partitioning the spatial domain into disjoint blocks and using spanning tree cuts to induce contiguous domain partitions. Under an infill-domain asymptotic framework, we introduce a new distance metric to study the posterior concentration of domain partitions. We show that Spat-RPM achieves a consistent estimation of domain partitions, including the number of clusters, and derive posterior concentration rates for partition, parameter, and prediction. We also establish conditions on the hyperparameters of priors and the number of blocks, offering important practical guidance for hyperparameter selection. Finally, we examine the asymptotic properties of our model through simulation studies and apply it to Atlantic Ocean data.

Problem

• Estimating latent spatial clusters with unknown numbers
• Overcoming geometric constraints in spatial subregion shapes
• Ensuring posterior clustering consistency in spatial models

Innovation

• Bayesian spatial clustering with spanning trees
• Infill-domain asymptotic framework for consistency
• Hyperparameter guidance for practical selection