Geographically and temporally neural network weighted regression for modeling spatiotemporal non-stationary relationships

ABSTRACT

Geographically weighted regression (GWR) and geographically and temporally weighted regression (GTWR) are classic methods for estimating non-stationary relationships. Although these methods have been widely used in geographical modeling and spatiotemporal analysis, they face challenges in adequately expressing space-time proximity and constructing a kernel with optimal weights. This probably results in an insufficient estimation of spatiotemporal non-stationarity. To address complex non-linear interactions between time and space, a spatiotemporal proximity neural network (STPNN) is proposed in this paper to accurately generate space-time distance. A geographically and temporally neural network weighted regression (GTNNWR) model that extends geographically neural network weighted regression (GNNWR) with the proposed STPNN is then developed to effectively model spatiotemporal non-stationary relationships. To examine its performance, we conducted two case studies of simulated datasets and environmental modeling in coastal areas of Zhejiang, China. The GTNNWR model was fully evaluated by comparing with ordinary linear regression (OLR), GWR, GNNWR, and GTWR models. The results demonstrated that GTNNWR not only achieved the best fitting and prediction performance but also exactly quantified spatiotemporal non-stationary relationships. Further, GTNNWR has the potential to handle complex spatiotemporal non-stationarity in various geographical processes and environmental phenomena.

KEYWORDS:

• Spatiotemporal non-stationary relationship
• spatiotemporal non-stationarity
• geographically and temporally weighted regression
• spatiotemporal proximity neural network
• geographically and temporally neural network weighted regression

Acknowledgments

We are grateful to the anonymous reviewers who provide insightful comments and suggestions for improving this article. Thanks for data support from the Marine Monitoring and Forecasting Centre of Zhejiang Province, China.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data and codes availability statement

Simulated datasets and codes that support the findings of this study are available at https://doi.org/10.6084/m9.figshare.12355472. The simulated datasets can be used to show how the codes work. The environmental dataset in the Zhejiang coastal areas provided by the Marine Monitoring and Forecasting Centre of Zhejiang Province can be accessed at http://www.zjhy.net.cn/new/index.jhtml.

Supplemental data

Supplemental data for this article can be accessed here.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [41922043, 41871287]; National Key Research and Development Program of China [2018YFB0505000]; Fundamental Research Funds for the Central Universities [2019QNA3013].

Notes on contributors

Sensen Wu

Sensen Wu received his Ph.D. degree in cartography and geographic information system from Zhejiang University, Hangzhou, China, in 2018. His current research interests include spatial-temporal analysis, remote sensing, and deep learning.

Zhongyi Wang

Zhongyi Wang is currently pursuing his Ph.D. degree in the geographic information system of Zhejiang University, Hangzhou, China, from 2015. His current research interests include spatial-temporal modeling and deep learning.

Zhenhong Du

Zhenhong Du is currently a Professor in the School of Earth Sciences, Zhejiang University. He is the Director of Institute of Geography and Spatial Information, Zhejiang University and is also the Deputy Director of Zhejiang Provincial Key Laboratory of Geographic Information System. His research interests include remote sensing & geographic information science, spatial-temporal big data & artificial intelligence.

Bo Huang

Bo Huang is currently a Professor in the Department of Geography and Resource Management, The Chinese University of Hong Kong, where he is also the Associate Director of Institute of Space and Earth Information Science. His research interests include spatial-temporal statistics, unified satellite image fusion and multi-objective spatial optimization, and their applications in environmental monitoring and sustainable land use and transportation planning.

Feng Zhang

Feng Zhang received her Ph.D. degree in cartography and geographic information system from Zhejiang University, Hangzhou, China, in 2007 and is working as an Associate Professor in the School of Earth Sciences, Zhejiang University. She is interested in spatial-temporal modeling, geographic intelligence and remote sensing.

Renyi Liu

Renyi Liu received his Ph.D. degree in cartography and geographic information systems from Zhejiang University, Hangzhou, China, in 2003, and is working as a Professor in the School of Earth Sciences, Zhejiang University. He is interested in remote sensing, geographic intelligence and high-performance GIS.