Geographically neural network weighted regression for the accurate estimation of spatial non-stationarity |
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Authors: | Zhenhong Du Zhongyi Wang Sensen Wu Feng Zhang Renyi Liu |
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Institution: | 1. School of Earth Sciences, Zhejiang University , Hangzhou, China;2. Zhejiang Provincial Key Laboratory of Geographic Information Science , Hangzhou, China duzhenhong@zju.edu.cn https://orcid.org/0000-0001-9449-0415;4. School of Earth Sciences, Zhejiang University , Hangzhou, China https://orcid.org/0000-0002-5609-8954;5. School of Earth Sciences, Zhejiang University , Hangzhou, China https://orcid.org/0000-0001-9322-0149;6. Zhejiang Provincial Key Laboratory of Geographic Information Science , Hangzhou, China https://orcid.org/0000-0003-1475-8480;7. Zhejiang Provincial Key Laboratory of Geographic Information Science , Hangzhou, China https://orcid.org/0000-0003-4001-4266 |
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Abstract: | ABSTRACT Geographically weighted regression (GWR) is a classic and widely used approach to model spatial non-stationarity. However, the approach makes no precise expressions of its weighting kernels and is insufficient to estimate complex geographical processes. To resolve these problems, we proposed a geographically neural network weighted regression (GNNWR) model that combines ordinary least squares (OLS) and neural networks to estimate spatial non-stationarity based on a concept similar to GWR. Specifically, we designed a spatially weighted neural network (SWNN) to represent the nonstationary weight matrix in GNNWR and developed two case studies to examine the effectiveness of GNNWR. The first case used simulated datasets, and the second case, environmental observations from the coastal areas of Zhejiang. The results showed that GNNWR achieved better fitting accuracy and more adequate prediction than OLS and GWR. In addition, GNNWR is applicable to addressing spatial non-stationarity in various domains with complex geographical processes. |
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Keywords: | Geographically neural network weighted regression Geographically weighted regression Spatial non-stationarity Neural network Ordinary least squares |
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