A geographically weighted artificial neural network

Abstract

While recent developments have extended geographically weighted regression (GWR) in many directions, it is usually assumed that the relationships between the dependent and the independent variables are linear. In practice, however, it is often the case that variables are nonlinearly associated. To address this issue, we propose a geographically weighted artificial neural network (GWANN). GWANN combines geographical weighting with artificial neural networks, which are able to learn complex nonlinear relationships in a data-driven manner without assumptions. Using synthetic data with known spatial characteristics and a real-world case study, we compared GWANN with GWR. While the results for the synthetic data show that GWANN performs better than GWR when the relationships within the data are nonlinear and their spatial variance is high, the results based on the real-world data demonstrate that the performance of GWANN can also be superior in a practical setting.