New Paper on Deep Explainable Spatial Regression published in ISPRS Journal of Photogrammetry and Remote Sensing

GeoDI Lab kicks off 2026 new year with the publication of a new research article in the ISPRS Journal of Photogrammetry and Remote Sensing (Impact Factor: 12.2), titled “Uncovering spatial process heterogeneity from graph-based deep spatial regression.” This study aims to addressing a fundamental methodological challenge in spatial regression analysis.

A long-standing issue in spatial regression is that the true statistical form of complex spatial processes is rarely known. Conventional assumptions—such as linearity, additivity, and fixed coefficients—often imply model misspecification and can lead to misleading interpretations of spatial process heterogeneity, particularly in data-rich geographic applications.

To address this challenge, the paper proposes a deep explainable spatial regression (XSR) framework based on graph convolutional neural networks (GCNs). Instead of relying on predefined parametric forms, XSR leverages graph-based deep learning to directly learn spatially varying coefficients, allowing heterogeneity to emerge from the data itself.

The proposed framework supports cross-sectional deep spatial regression modeling without restrictive statistical assumptions, enables the reconstruction of interpretable spatial heterogeneity patterns from learned neural network weights, and introduces a simple diagnostic test to explain the role of heterogeneity—thereby enhancing the explainability of GeoAI models.

Using housing prices in Greater Boston as an empirical case study, XSR demonstrates improved model performance over classical spatial regression approaches. More importantly, the learned deep local coefficients exhibit stronger explanatory power than those derived from geographically weighted regression (GWR), suggesting a more faithful representation of underlying spatial process heterogeneity.

link: https://doi.org/10.1016/j.isprsjprs.2025.12.008
Zhu, D.*, Wang, S., and Luo, P. (2026). Uncovering spatial process heterogeneity from graph-based deep spatial regression. ISPRS Journal of Photogrammetry and Remote Sensing, 232: 509-523.