用神经网络增强地理加权回归，捕捉复杂空间非线性关系
Artificial Geographically Weighted Neural Network: A Novel Framework for Spatial Analysis with Geographically Weighted Layers
- 将地理加权层嵌入神经网络，动态建模空间异质性
- 在模拟与真实数据上均显著优于传统GWR和普通神经网络
- 适合需要精细空间分析的地理、城市规划等领域研究者
地理加权回归（GWR）是建模空间异质性的常用方法，但通常假设因变量与自变量间为线性关系。为此，我们提出人工地理加权神经网络（AGWNN），一种将地理加权技术与神经网络结合的新框架，以捕捉复杂的非线性空间关系。该框架的核心是地理加权层（GWL），一种专门设计用于在神经网络架构中编码空间异质性的组件。通过在模拟数据集和真实案例研究上进行系统实验，结果表明：AGWNN在模型拟合精度上显著优于传统GWR和标准人工神经网络（ANN）。尤其在建模复杂非线性关系及识别深层空间异质性模式方面表现优异，为高级空间分析提供了强大且通用的工具。
原文摘要 · Abstract (English)
Geographically Weighted Regression (GWR) is a widely recognized technique for modeling spatial heterogeneity. However, it is commonly assumed that the relationships between dependent and independent variables are linear. To overcome this limitation, we propose an Artificial Geographically Weighted Neural Network (AGWNN), a novel framework that integrates geographically weighted techniques with neural networks to capture complex nonlinear spatial relationships. Central to this framework is the Geographically Weighted Layer (GWL), a specialized component designed to encode spatial heterogeneity within the neural network architecture. To rigorously evaluate the performance of AGWNN, we conducted comprehensive experiments using both simulated datasets and real-world case studies. Our results demonstrate that AGWNN significantly outperforms traditional GWR and standard Artificial Neural Networks (ANNs) in terms of model fitting accuracy. Notably, AGWNN excels in modeling intricate nonlinear relationships and effectively identifies complex spatial heterogeneity patterns, offering a robust and versatile tool for advanced spatial analysis.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。