DKNN: deep kriging neural network for interpretable geospatial interpolation

Abstract

Geospatial interpolation plays a pivotal role in spatial analysis because it provides high-quality data support for various spatiotemporal data mining (STDM) tasks. However, statistical methods, such as kriging, face challenges in dealing with complex geo-big data. Additionally, deep-learning-based methods, despite their exceptional performance, suffer from limitations, such as poor interpretability. To harness the complementary advantages of these statistical methods and deep learning approaches, this study proposes a novel geospatial artificial intelligence (GeoAI) framework called deep kriging neural network (DKNN). The primary contribution lies in the development of an asymmetric encoder-decoder structure, which includes a deep-learning-based spatial encoder and a geostatistics-based kriging decoder. The spatial encoder consists of three specialized neural networks, whereas the kriging decoder relies on the proposed unified kriging system. During forward propagation, the kriging decoder leverage messages from the spatial encoder to generate interpolation weights for prediction. Conversely, during backward propagation, the kriging decoder guides the spatial encoder in learning interpretable knowledge. Experiments were conducted using both synthetic and practical datasets. The results demonstrate an average improvement of 20.18% in MAE, 25.04% in RMSE and 24.06% in MAPE when compared to the best-performing baseline method. Furthermore, these results confirm the superior interpretability of our DKNN framework.

Keywords:

• Kriging interpolation
• GeoAI
• interpretability

Acknowledgments

This work was conducted in part using computing resources at the High Performance Computing Platform of Central South University.

Disclosure statement

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

Data and codes availability statement

The synthetic data and codes supporting the findings of this study are available at https://github.com/in1311/DKNN. Synthetic data can be used to demonstrate the working of the code.

Additional information

Funding

This project was supported by the National Natural Science Foundation of China (NSFC) under Grants 42171459 and 42071452, the Hunan Provincial Innovation Foundation for Postgraduates under Grant CX20230157 and the Central South University Innovation-Driven Research Programme under Grant 2023ZZTS0756.

Notes on contributors

Kaiqi Chen

Kaiqi Chen received a B.S. degree in 2018 from Central South University, Changsha, China. He is currently pursuing a doctorate degree with the School of Geosciences and Info-Physics, Central South University. His research interests include data mining and machine learning.

Enbo Liu

Enbo Liu received a B.S. degree in 2021 from Central South University, Changsha, China. He is currently pursuing a doctorate degree with the School of Geosciences and Info-Physics, Central South University. His research interests include data mining and machine learning.

Min Deng

Min Deng received Ph.D. degrees from Wuhan University in 2003 and the Asian Institute of Technology in 2004. He is currently a doctoral supervisor and associate dean of the School of Geosciences and Info-Physics, Central South University.

Xiaoyong Tan

Xiaoyong Tan received a B.S. degree in 2022 from Central South University, Changsha, China. He is currently a Ph.D. candidate at the School of Geosciences and Info-Physics, Central South University, Hunan, China. His research interests include data mining and modeling.

Jiaoju Wang

Jiaoju Wang received an M.S. degree in Statistics from Central South University, Changsha, China, in 2020. She is currently a doctoral candidate at the School of Mathematics and Statistics at Central South University. Her research interests include spatiotemporal data prediction and graph–neural networks.

Yan Shi

Yan Shi received a Ph.D. degree from Central South University, Changsha, China in 2015. He is currently an associate professor with the School of Geosciences and Info-Physics and a master supervisor at the School of Geosciences and Info-Physics, Central South University.

Zhizhong Wang

Zhizhong Wang received a Ph.D degree in surveying from the Central South University of Technology in 1999. He is a professor at the School of Mathematics and Statistics, Central South University, Changsha, China.