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.

摘要

虽然最近的发展已经在许多方向上扩展了地理加权回归 (GWR)，但通常假设因变量和自变量之间的关系是线性的。然而，在实践中，变量通常是非线性关联的。为了解决这个问题，我们提出了一个地理加权人工神经网络（GWANN）。GWANN 将地理加权与人工神经网络相结合，人工神经网络能够以数据驱动的方式学习复杂的非线性关系，无需假设。使用具有已知空间特征的合成数据和真实案例研究，我们将 GWANN 与 GWR 进行了比较。虽然合成数据的结果表明，当数据内的关系是非线性的并且它们的空间方差很大时，GWANN 的性能优于 GWR，