Spatial interpolation using conditional generative adversarial neural networks

Spatial interpolation is a traditional geostatistical operation that aims at predicting the attribute values of unobserved locations given a sample of data defined on point supports. However, the continuity and heterogeneity underlying spatial data are too complex to be approximated by classic stati...

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Published in:	International journal of geographical information science : IJGIS Vol. 34; no. 4; pp. 735 - 758
Main Authors:	Zhu, Di, Cheng, Ximeng, Zhang, Fan, Yao, Xin, Gao, Yong, Liu, Yu
Format:	Journal Article
Language:	English
Published:	Abingdon Taylor & Francis 02.04.2020 Taylor & Francis LLC
Subjects:	Artificial intelligence Coders Deep learning encoder-decoder Encoders-Decoders generative adversarial networks Geostatistics Heterogeneity Interpolation Machine learning Mathematical models Neural networks Spatial data Spatial interpolation spatial prediction Statistical analysis Statistical models
ISSN:	1365-8816, 1362-3087, 1365-8824
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Abstract	Spatial interpolation is a traditional geostatistical operation that aims at predicting the attribute values of unobserved locations given a sample of data defined on point supports. However, the continuity and heterogeneity underlying spatial data are too complex to be approximated by classic statistical models. Deep learning models, especially the idea of conditional generative adversarial networks (CGANs), provide us with a perspective for formalizing spatial interpolation as a conditional generative task. In this article, we design a novel deep learning architecture named conditional encoder-decoder generative adversarial neural networks (CEDGANs) for spatial interpolation, therein combining the encoder-decoder structure with adversarial learning to capture deep representations of sampled spatial data and their interactions with local structural patterns. A case study on elevations in China demonstrates the ability of our model to achieve outstanding interpolation results compared to benchmark methods. Further experiments uncover the learned spatial knowledge in the model's hidden layers and test the potential to generalize our adversarial interpolation idea across domains. This work is an endeavor to investigate deep spatial knowledge using artificial intelligence. The proposed model can benefit practical scenarios and enlighten future research in various geographical applications related to spatial prediction.
AbstractList	Spatial interpolation is a traditional geostatistical operation that aims at predicting the attribute values of unobserved locations given a sample of data defined on point supports. However, the continuity and heterogeneity underlying spatial data are too complex to be approximated by classic statistical models. Deep learning models, especially the idea of conditional generative adversarial networks (CGANs), provide us with a perspective for formalizing spatial interpolation as a conditional generative task. In this article, we design a novel deep learning architecture named conditional encoder-decoder generative adversarial neural networks (CEDGANs) for spatial interpolation, therein combining the encoder-decoder structure with adversarial learning to capture deep representations of sampled spatial data and their interactions with local structural patterns. A case study on elevations in China demonstrates the ability of our model to achieve outstanding interpolation results compared to benchmark methods. Further experiments uncover the learned spatial knowledge in the model’s hidden layers and test the potential to generalize our adversarial interpolation idea across domains. This work is an endeavor to investigate deep spatial knowledge using artificial intelligence. The proposed model can benefit practical scenarios and enlighten future research in various geographical applications related to spatial prediction.
Author	Cheng, Ximeng Yao, Xin Gao, Yong Liu, Yu Zhu, Di Zhang, Fan
Author_xml	– sequence: 1 givenname: Di orcidid: 0000-0002-3237-6032 surname: Zhu fullname: Zhu, Di organization: SpaceTimeLab, Department of Civil, Environmental and Geomatic Engineering, University College London – sequence: 2 givenname: Ximeng orcidid: 0000-0001-9923-7240 surname: Cheng fullname: Cheng, Ximeng organization: Institute of Remote Sensing and Geographical Information Systems, School of Earth and Space Sciences, Peking University – sequence: 3 givenname: Fan orcidid: 0000-0002-3643-018X surname: Zhang fullname: Zhang, Fan organization: Senseable City Laboratory, Massachusetts Institute of Technology – sequence: 4 givenname: Xin surname: Yao fullname: Yao, Xin organization: Institute of Remote Sensing and Geographical Information Systems, School of Earth and Space Sciences, Peking University – sequence: 5 givenname: Yong surname: Gao fullname: Gao, Yong organization: Institute of Remote Sensing and Geographical Information Systems, School of Earth and Space Sciences, Peking University – sequence: 6 givenname: Yu orcidid: 0000-0002-0016-2902 surname: Liu fullname: Liu, Yu email: liuyu@urban.pku.edu.cn organization: Institute of Remote Sensing and Geographical Information Systems, School of Earth and Space Sciences, Peking University
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SubjectTerms	Artificial intelligence Coders Deep learning encoder-decoder Encoders-Decoders generative adversarial networks Geostatistics Heterogeneity Interpolation Machine learning Mathematical models Neural networks Spatial data Spatial interpolation spatial prediction Statistical analysis Statistical models
Title	Spatial interpolation using conditional generative adversarial neural networks
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