# Extending regionalization algorithms to explore spatial process heterogeneity

arXiv: https://arxiv.org/abs/2206.09429 · HTML: https://mlsanity.com/paper/2206.09429/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 84 references that are in the map.
- First posted on arXiv 19 Jun 2022.

## Builds on (most cited first, 3 of 3)

- [Spatial regionalization based on optimal information compression](https://mlsanity.com/paper/2111.01813/) (2021)
- [A two-step approach to account for unobserved spatial heterogeneity](https://mlsanity.com/paper/1602.05757/) (2016)
- [Spatially Clustered Regression](https://mlsanity.com/paper/2011.01493/) (2020)

## Built on by (most cited first, 2 of 2)

- [ProGraph: Temporally-alignable Probability Guided Graph Topological Modeling for 3D Human Reconstruction](https://mlsanity.com/paper/2411.04399/) (2024)
- [RegionGCN: Spatial-Heterogeneity-Aware Graph Convolutional Networks](https://mlsanity.com/paper/2501.17599/) (2025)

## Abstract (arXiv)

In spatial regression models, spatial heterogeneity may be considered with either continuous or discrete specifications. The latter is related to delineation of spatially connected regions with homogeneous relationships between variables (spatial regimes). Although various regionalization algorithms have been proposed and studied in the field of spatial analytics, methods to optimize spatial regimes have been largely unexplored. In this paper, we propose two new algorithms for spatial regime delineation, two-stage K-Models and Regional-K-Models. We also extend the classic Automatic Zoning Procedure to spatial regression context. The proposed algorithms are applied to a series of synthetic datasets and two real-world datasets. Results indicate that all three algorithms achieve superior or comparable performance to existing approaches, while the two-stage K-Models algorithm largely outperforms existing approaches on model fitting, region reconstruction, and coefficient estimation. Our work enriches the spatial analytics toolbox to explore spatial heterogeneous processes.