Spatial and Attribute Neural Network Weighted Regression for the Accurate Estimation of Spatial Non-Stationarity

Geographically neural network weighted regression is an improved model of GWR combined with a neural network. It has a stronger ability to fit nonlinear functions, and complex geographical processes can be modeled more fully. GNNWR uses the distance metric of Euclidean space to express the relationship between sample points. However, except for spatial location features, geographic entities also have many diverse attribute features. Incorporating attribute features into the modeling process can make the model more suitable for the real geographical process. Therefore, we proposed a spatial-attribute proximities deep neural network to aggregate data from the spatial feature and attribute feature, so that one unified distance metric can be used to express the spatial and attribute relationships between sample points at the same time. Based on GNNWR, we designed a spatial and attribute neural network weighted regression (SANNWR) model to adapt to this new unified distance metric. We developed one case study to examine the effectiveness of SANNWR. We used PM2.5 concentration data in China as the research object and compared the prediction accuracy between GWR, GNNWR and SANNWR. The results showed that the “spatial-attribute” unified distance metric is useful, and that the SANNWR model showed the best performance.