Interpretable Graph Partitioning for Spatial Prediction

arXiv:2610.16063v1 Announce Type: new Abstract: Spatial prediction estimates unobserved values from spatially distributed observations. Although flexible predictive models are increasingly available, their practical use remains limited when interpretability is essential. In this study, we formulate a graph partitioning problem to construct a global surrogate model that approximates black-box predictions with simpler representations. Specifically, we select connected subgraphs to minimize within-cluster residuals in vertex-level predictions. Although this formulation can be viewed as a variant of spatial regionalization, it operates on model-based predictions at individual locations rather than predefined areal units. With many locations, this point-level formulation may produce artificial connections between regions, reducing interpretability. We therefore introduce a constraint that excludes such connections while retaining flexible partition boundaries. We theoretically analyze how this constraint affects the resulting partition. We also develop a computational procedure for adjusting partition boundaries. Experimental results show that the proposed method yields spatially coherent partitions with flexible boundaries.

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Source: arXiv cs.LG | 2026-10-14