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Journal of Data Science


Supervised Spatial Regionalization using the Karhunen-Loève Expansion and Minimum Spanning Trees
Volume 20, Issue 4 (2022): Special Issue: Large-Scale Spatial Data Science, pp. 566–584
Pub. online: 9 November 2022      Type: Statistical Data Science      Open accessOpen Access
Received
1 September 2022
Accepted
30 October 2022
Published
9 November 2022

Abstract

The article presents a methodology for supervised regionalization of data on a spatial domain. Defining a spatial process at multiple scales leads to the famous ecological fallacy problem. Here, we use the ecological fallacy as the basis for a minimization criterion to obtain the intended regions. The Karhunen-Loève Expansion of the spatial process maintains the relationship between the realizations from multiple resolutions. Specifically, we use the Karhunen-Loève Expansion to define the regionalization error so that the ecological fallacy is minimized. The contiguous regionalization is done using the minimum spanning tree formed from the spatial locations and the data. Then, regionalization becomes similar to pruning edges from the minimum spanning tree. The methodology is demonstrated using simulated and real data examples.

Supplementary material

 Supplementary Material
The supplementary material includes the following files: (1) README: a brief explanation of all the files in the supplementary material; (2) The synthetic dataset; (3) The real-world dataset; (4) Code files; (5) Images used in the paper; (6) A miscellaneous example of KLE computation directly from covariance matrices.

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Copyright
2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
connectivity graph ecological fallacy Karhunen-Loève expansion minimum spanning tree regionalization spatial data

Funding
This research was partially supported by the U.S. National Science Foundation (NSF) grant SES-1853096. The computation for this work was performed on the high performance computing infrastructure provided by the Research Computing Support Services at the University of Missouri, Columbia, MO, and is supported in part by the NSF grant CNS-1429294.

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