Beyond geographical proximity: a graph-enhanced spatial weight matrix integrating attributes and spatial interactions

Spatial weight matrices represent spatial relationships among spatial observations and govern the influence of neighboring observations in spatial regression models such as geographically weighted regression (GWR). Traditionally, spatial weights are specified using geographical proximity, which may fail to capture contextual or relational dependencies arising from attribute similarity or spatial interactions. To address this limitation, this research proposes a graph-enhanced spatial weight matrix (GSWM) that extends conventional geographical weighting by jointly integrating geographical distance, attribute similarity, and spatial interactions in a data-driven manner. Specifically, a graph convolutional network (GCN) encodes attribute and interaction information into learned contextual and relational proximity representations, which are then combined with geographical distance through a multi-layer perceptron (MLP) to construct the GSWM. The proposed GSWM is incorporated into the GWR framework and evaluated through a simulation experiment and an empirical analysis of urban vibrancy in Guangzhou, China. The results demonstrate that GWR incorporating GSWM not only outperforms existing spatial weighting formulations, but also enables interpretation of how contextual similarity and spatial interactions shape local estimation. By extending spatial weight formulation beyond geographical proximity, this research provides a spatially grounded and data-driven approach for modeling spatial relationships.