Surrogate Graph Partitioning for Spatial Prediction
This paper addresses the poor interpretability of black-box models in spatial prediction. We propose a graph-partitioning-based spatial segmentation method that minimizes the sum of intra-segment prediction variance. Innovatively, we formulate interpretability as a variance-constrained graph partitioning problem and introduce, for the first time, a mixed-integer quadratic programming (MIQP) formulation to capture this objective. To tackle the prohibitive computational complexity on large-scale data, we design an efficient approximation algorithm that exploits intrinsic graph structural properties, ensuring high segmentation quality while drastically improving runtime efficiency. Experiments demonstrate that our method achieves 1–2 orders of magnitude speedup over exact MIQP solvers while reducing intra-segment variance by up to 37%. The approach thus establishes a new paradigm for scalable, interpretable spatial modeling—balancing fidelity, transparency, and computational tractability.