Spatially constrained statistical approach for determining the optimal number of regions in regionalization

Abstract

Determining the optimal number of regions is a challenging issue in regionalization. Although cluster validity indices developed for non-spatial clustering have been used to determine the optimal number of regions, spatial contiguity constraints for regionalization are often neglected. Consequently, different regionalization results can share the same validity index value, which reduces the reliability of identifying the optimal number of regions in regionalization. To overcome this limitation, this study proposes a spatially constrained statistical approach for determining the optimal number of regions using two metrics: (i) a permutation-based variance for measuring the homogeneity within regions and (ii) a proportion index based on spatially constrained k-nearest neighbors to quantify the separation between regions. Furthermore, a distance-based method is employed to balance these two metrics to automatically determine the optimal number of regions. Experimental results on five synthetic datasets, the US presidential election and climate datasets show that the statistical approach developed in this study outperforms three widely used cluster validity indices in determining the optimal number of regions. The proposed statistical approach is straightforward to implement and can effectively reduce subjectivity in regionalization.

Keywords:

• Regionalization
• cluster validity
• spatial contiguity constraint
• REDCAP
• ARiSeL

Data and codes availability statement

The data and codes that support the findings of this study are available on ‘figshare.com,’ with the identifier at the public link: https://doi.org/10.6084/m9.figshare.24321121.v1.

Author contributions

Qiliang Liu and Yuxuan Chen conceived and designed the presented idea. Yuxuan Chen implemented the experiments and analysed the results. Qiliang Liu and Yuxuan Chen wrote the manuscript. Jie Yang and Xinghua Chen help for designing the method. Min Deng reviewed the manuscript, and provided comments.

Acknowledgements

We gratefully acknowledge the comments from the editor and the reviewers.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was funded through support from National Natural Science Foundation of China (NSFC) (No. 42271484, and 41971353) and Research Foundation of the Department of Natural Resources of Hunan Province (Grant No. HBZ20240132).

Notes on contributors

Yuxuan Chen

Yuxuan Chen is currently a Ph.D. candidate at Central South University and his research interests focus on spatio-temporal datamining.

Qiliang Liu

Qiliang Liu is currently a professor at Central South University, Hunan, China. His research interests focus on multi-scale spatio-temporal data mining and spatiotemporal statistics. He has published more than 50 peer-reviewed journal articles in these areas.

Jie Yang

Jie Yang is currently a Ph.D. candidate at Central South University and his research interests focus on spatio-temporal statistics.

Xinghua Cheng

Xinhua Cheng is currently a Ph.D. candidate at University of Connecticut and his research interests focus on spatial analysis.

Min Deng

Min Deng is currently a professor at Central South University and the associate dean of School of Geosciences and info-physics. His research interests are map generalization, spatio-temporal data analysis and mining.