JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1077 10.6339/22-JDS1077 Statistical Data Science Supervised Spatial Regionalization using the Karhunen-Loève Expansion and Minimum Spanning Trees https://orcid.org/0000-0003-3590-909X DawRanadeepranadeepdaw@mail.missouri.edu1∗ WikleChristopher K.1 Department of Statistics, University of Missouri, Columbia, MO, USA, 65211 Corresponding author. Email: ranadeepdaw@mail.missouri.edu. 20229112022204566584 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.

19202230102022 2022 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2022 Open access article under the CC BY license.

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.

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