Geographically neural network weighted regression accounting for accurate estimation of spatial nonstationarity

Authors: Zhongyi Wang*, Zhejiang University, Zhenhong Du, Zhejiang University, Sensen Wu, Zhejiang University
Topics: Spatial Analysis & Modeling, Geographic Information Science and Systems
Keywords: Geographically neural network weighted regression; Geographically weighted regression; Spatial nonstationarity; Neural networks; Ordinary least squares
Session Type: Paper
Day: 4/6/2019
Start / End Time: 9:55 AM / 11:35 AM
Room: 8217, Park Tower Suites, Marriott, Lobby Level
Presentation File: No File Uploaded


The estimation of spatial nonstationarity is a basic problem to the modelling of nonstationary relationships. Geographically weighted regression (GWR), the classical approach to modelling spatial nonstationarity, however, has difficulties in the adequate expression and complicated construction of weighting kernels, which accordingly results in insufficient estimation of nonstationarity for complex geographical processes. To resolve those problems, based on the powerful learning capability of neural networks, a spatial weighted neural network (SWNN) is designed to exactly construct the nonstationary weight matrix. Consequently, we propose a geographically neural network weighted regression (GNNWR) model that combines ordinary least squares (OLS) and SWNN for the accurate estimation of spatial nonstationarity. To examine its performance, we perform an experiment by conducting environmental modelling in Zhejiang coastal areas, and the GNNWR model is compared with the OLS model and three GWR models of different kernels in terms of multiple statistical indicators. The experimental results demonstrate that the GNNWR model achieves more excellent fitting accuracy and more adequate prediction capability than the OLS and GWR models. Also, the results further indicate that the SWNN is more powerful than the spatial kernels of GWR models. In addition, the GNNWR model can be used to address spatial nonstationarity in various fields and disciplines.

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