Geographically neural network weighted regression for the accurate estimation of spatial non-stationarity

Du, Zhenhong; Wang, Zhongyi; Wu, Shengjun; Zhang, Feng; Liu, Renyi

doi:10.1080/13658816.2019.1707834

Cited by 77 publications

(55 citation statements)

References 28 publications

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“…geographically weighted lasso (Wheeler 2009), ridge (Wheeler 2009), ridge (Wheeler 2007, Bárcena et al 2014, and elastic net regression (Li and Lam 2018)). Another extension is geographically neural network weighted regression (Du et al 2020), which utilizes an artificial neural network (ANN) to find appropriate geographical weights when estimating the coefficients of a GWR model. Despite these efforts, some restrictions of GWR have not yet been addressed.…”

Section: Introductionmentioning

confidence: 99%

A geographically weighted artificial neural network

Hagenauer

Helbich

2021

International Journal of Geographical Information Science

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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.

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Section: Introductionmentioning

confidence: 99%

A geographically weighted artificial neural network

Hagenauer

Helbich

2021

International Journal of Geographical Information Science

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“…The basic formulation of GNNWR is defined as Eq. (22) (Du et al, 2020), which is different from Eq. (1) (Fotheringham et al, 2003).…”

Section: Discussionmentioning

confidence: 74%

“…Based on a concept similar to GWR, a recently proposed model, called geographically neural network weighted regression (GNNWR) (Du et al, 2020), utilizes both OLS and neural networks to evaluate spatial nonstationarity. It is characterized by a designed spatially weighted neural network (SWNN) that can represent the spatial nonstationary weight matrix in spatial processes.…”

Section: Discussionmentioning

confidence: 99%

“…GTNNWR and GNNWR use the proposed ANN-based method (Eq. 23) (Du et al, 2020) to calculate the weighted matrix, which is quite different from the kernel functions used in GWR and STWR models. Although GTNNWR and GNNWR use the idea of pointwise regression, they do not consider how to "borrow points" from nearby neighbors and do not have the concept of bandwidth.…”

Section: Discussionmentioning

confidence: 99%

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A spatiotemporal weighted regression model (STWR v1.0) for analyzing local nonstationarity in space and time

Que

et al. 2020

Geosci. Model Dev.

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Abstract. Local spatiotemporal nonstationarity occurs in various natural and socioeconomic processes. Many studies have attempted to introduce time as a new dimension into a geographically weighted regression (GWR) model, but the actual results are sometimes not satisfying or even worse than the original GWR model. The core issue here is a mechanism for weighting the effects of both temporal variation and spatial variation. In many geographical and temporal weighted regression (GTWR) models, the concept of time distance has been inappropriately treated as a time interval. Consequently, the combined effect of temporal and spatial variation is often inaccurate in the resulting spatiotemporal kernel function. This limitation restricts the configuration and performance of spatiotemporal weights in many existing GTWR models. To address this issue, we propose a new spatiotemporal weighted regression (STWR) model and the calibration method for it. A highlight of STWR is a new temporal kernel function, wherein the method for temporal weighting is based on the degree of impact from each observed point to a regression point. The degree of impact, in turn, is based on the rate of value variation of the nearby observed point during the time interval. The updated spatiotemporal kernel function is based on a weighted combination of the temporal kernel with a commonly used spatial kernel (Gaussian or bi-square) by specifying a linear function of spatial bandwidth versus time. Three simulated datasets of spatiotemporal processes were used to test the performance of GWR, GTWR, and STWR. Results show that STWR significantly improves the quality of fit and accuracy. Similar results were obtained by using real-world data for precipitation hydrogen isotopes (δ2H) in the northeastern United States. The leave-one-out cross-validation (LOOCV) test demonstrates that, compared with GWR, the total prediction error of STWR is reduced by using recent observed points. Prediction surfaces of models in this case study show that STWR is more localized than GWR. Our research validates the ability of STWR to take full advantage of all the value variation of past observed points. We hope STWR can bring fresh ideas and new capabilities for analyzing and interpreting local spatiotemporal nonstationarity in many disciplines.

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“…In view of this, this study aims to estimate 750 m resolution surface PM 2.5 in the whole of China using the high-resolution VIIRS IP AOD through a newly developed spatial neural network weighted regression model. Geographically neural network weighted regression (GNNWR) that integrates OLR and a spatial weighted neural network (SWNN) can simultaneously address nonstationarity and non-linearity in PM 2.5 modeling and thus has the potential to further enhance the accuracy and rationality of PM 2.5 prediction [43][44][45]. The newly generated high-resolution PM 2.5 data provide new opportunities to precisely study the air pollution at urban city and county scales.…”

Section: Introductionmentioning

confidence: 99%

Satellite-Based Mapping of High-Resolution Ground-Level PM2.5 with VIIRS IP AOD in China through Spatially Neural Network Weighted Regression

Chen

Wang

et al. 2021

Remote Sensing

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Satellite-retrieved aerosol optical depth (AOD) data are extensively integrated with ground-level measurements to achieve spatially continuous fine particulate matters (PM2.5). Current satellite-based methods however face challenges in obtaining highly accurate and reasonable PM2.5 distributions due to the inability to handle both spatial non-stationarity and complex non-linearity in the PM2.5–AOD relationship. High-resolution (<1 km) PM2.5 products over the whole of China for fine exposure assessment and health research are also lacking. This study aimed to predict 750 m resolution ground-level PM2.5 in China with the high-resolution Visible Infrared Imaging Radiometer Suite (VIIRS) intermediate product (IP) AOD data using a newly developed geographically neural network weighted regression (GNNWR) model. The performance evaluations demonstrated that GNNWR achieved higher prediction accuracy than the widely used methods with cross-validation and predictive R2 of 0.86 and 0.85. Satellite-derived monthly 750 m resolution PM2.5 data in China were generated with robust prediction accuracy and almost complete coverage. The PM2.5 pollution was found to be greatly improved in 2018 in China with annual mean concentration of 31.07 ± 17.52 µg/m3. Nonetheless, fine-scale PM2.5 exposures at multiple administrative levels suggested that PM2.5 pollution in most urban areas needed further control, especially in southern Hebei Province. This work is the first to evaluate the potential of VIIRS IP AOD in modeling high-resolution PM2.5 over large-scale. The newly satellite-derived PM2.5 data with high spatial resolution and high prediction accuracy at the national scale are valuable to advance environmental and health researches in China.

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Geographically neural network weighted regression for the accurate estimation of spatial non-stationarity

Cited by 77 publications

References 28 publications

A geographically weighted artificial neural network

A geographically weighted artificial neural network

A spatiotemporal weighted regression model (STWR v1.0) for analyzing local nonstationarity in space and time

Satellite-Based Mapping of High-Resolution Ground-Level PM2.5 with VIIRS IP AOD in China through Spatially Neural Network Weighted Regression

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