A neural network model to optimize the measure of spatial proximity in geographically weighted regression approach: a case study on house price in Wuhan

The estimation of spatial heterogeneity within real estate markets holds significant importance in house price modelling. However, employing a single or straightforward distance to measure spatial proximity is probably insufficient in complex urban areas, thereby resulting in an inadequate modelling of spatial heterogeneity. To address this issue, this paper incorporates multiple distance measures within a neural network framework to achieve an optimized measure of spatial proximity (OSP). Consequently, a geographically neural network weighted regression model with optimized measure of spatial proximity (osp-GNNWR) is devised for the purpose of spatially heterogeneous modeling. Trained as a unified model, osp-GNNWR obviates the need for separate pretraining of OSP. This enables OSP to delineate the modeled spatial process through a post hoc calculated value. Through simulation experiments and a real-world case study on house prices, the proposed model reaches more accurate descriptions of diverse spatial processes and exhibits better overall performance. The interpretable results of the case study in Wuhan demonstrate the efficacy of the osp-GNNWR model in addressing spatial heterogeneity within real estate markets, suggesting its potential for modelling and predicting complex geographical phenomena.