Abstract
Spatial interpolation is a valuable technique that uses the data of a sample set to estimate the property values at unsampled locations. Neural networks for spatial interpolation can capture spatial trends effectively; however, they may not be optimal when a strong local correlation is present, which leads to unreliable outcomes. Neural Network Residual Kriging methods use Kriging to handle residuals, assuming strict conditions such as the stationarity of the random field and stable spatial variability. In many applications without these strict conditions, however, those Neural Network interpolation methods have limitations for obtaining highly accurate estimates. To address this problem, in this paper, we propose a new spatial interpolation method, called NNRB, based on the mechanisms of BP Neural Network with Bellman Equation. Firstly, our NNRB method employs a BP neural network for capturing nonlinear relationships and spatial trends in the data of a sample set. Secondly, NNRB uses Bellman Equation to handle residuals by accounting for interactions between multiple adjacent data and reducing the influence of distant data on the current data. Our NNRB method is utilized for a system of soil testing and formulated fertilization for intelligent agriculture. We compared NNRB with four state-of-the-art interpolation methods, and the results show that our NNRB method outperforms the three methods significantly and is highly competitive with one approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tobler, W.R.: A computer movie simulating urban growth in the Detroit region. Econ. Geogr. 46, 234–240 (1970)
Nurhadiyatna, A., Sunaryani, A., Sudriani, Y., Latifah, A.: 2D spatial interpolation for water quality parameter distribution in Maninjau Lake. In: 2016 International Conference on Computer, Control, Informatics and its Applications (IC3INA), pp. 215–220. IEEE (2016)
Dai, F., Zhou, Q., Lv, Z., Wang, X., Liu, G.: Spatial prediction of soil organic matter content integrating artificial neural network and ordinary kriging in Tibetan Plateau. Ecol. Ind. 45, 184–194 (2014)
Tziachris, P., Metaxa, E., Papadopoulos, F., Papadopoulou, M.: Spatial modelling and prediction assessment of soil iron using kriging interpolation with pH as auxiliary information. ISPRS Int. J. Geo Inf. 6, 283 (2017)
Viana, D., Barbosa, L.: Attention-based spatial interpolation for house price prediction. In: Proceedings of the 29th International Conference on Advances in Geographic Information Systems, pp. 540–549 (2021)
Tang, Y., et al.: Spatial estimation of regional PM2.5 concentrations with GWR models using PCA and RBF interpolation optimization. Remote Sens. 14, 5626 (2022)
Soto, F., Navarro, F., Díaz, G., Emery, X., Parviainen, A., Egaña, Á.: Transitive kriging for modeling tailings deposits: a case study in southwest Finland. J. Clean. Prod. 374, 133857 (2022)
Le, N.D., Zidek, J.V.: Statistical analysis of environmental space-time processes. Springer, New York (2006). https://doi.org/10.1007/0-387-35429-8
Hecht-Nielsen, R.: Kolmogorov’s mapping neural network existence theorem. In: Proceedings of the International Conference on Neural Networks, pp. 11–14. IEEE Press New York, NY, USA (1987)
Lai, Y., et al.: Reconstructing the data gap between GRACE and GRACE follow-on at the basin scale using artificial neural network. Sci. Total. Environ. 823, 153770 (2022)
Shahriari, M., Delbari, M., Afrasiab, P., Pahlavan-Rad, M.R.: Predicting regional spatial distribution of soil texture in floodplains using remote sensing data: a case of southeastern Iran. CATENA 182, 104149 (2019)
Li, J., Heap, A.D.: Spatial interpolation methods applied in the environmental sciences: a review. Environ Model Softw. 53, 173–189 (2014)
Sergeev, A., Buevich, A., Baglaeva, E., Shichkin, A.J.C.: Combining spatial autocorrelation with machine learning increases prediction accuracy of soil heavy metals. CATENA 174, 425–435 (2019)
Zhu, D., Cheng, X., Zhang, F., Yao, X., Gao, Y., Liu, Y.: Spatial interpolation using conditional generative adversarial neural networks. Res. Output Contrib. J. 34, 735–758 (2020)
Luo, P., Song, Y., Zhu, D., Cheng, J., Meng, L.: A generalized heterogeneity model for spatial interpolation. Int. J. Geograph. Inf. Sci. 37, 634–659 (2023)
Lee, M.-H., Chen, Y.J.: Markov chain random field kriging for estimating extreme precipitation at unevenly distributed sites. J. Hydrol. 616, 128591 (2023)
Park, H.I., Lee, S.R.: Evaluation of the compression index of soils using an artificial neural network. Comput. Geotech. 38, 472–481 (2011)
Xavier, A.C., Scanlon, B.R., King, C.W., Alves, A.I.: New improved Brazilian daily weather gridded data (1961–2020). Int. J. Climatol. 42, 8390–8404 (2022)
Cui, Z., Lin, L., Pu, Z., Wang, Y.: Graph Markov network for traffic forecasting with missing data. Transp. Res. Part C Emerg. Technol. 117, 102671 (2020)
Vedadi, F., Shirani, S.: A map-based image interpolation method via viterbi decoding of Markov chains of interpolation functions. IEEE Trans. Image Process. 23, 424–438 (2013)
Trombini, M., Solarna, D., Moser, G., Dellepiane, S.: A goal-driven unsupervised image segmentation method combining graph-based processing and Markov random fields. Pattern Recogn. 134, 109082 (2023)
Colonnese, S., Rinauro, S., Scarano, G.: Bayesian image interpolation using Markov random fields driven by visually relevant image features. Sig. Process. Image Commun. 28, 967–983 (2013)
Zhu, L., Hou, G., Song, X., Wei, Y., Wang, Y.: A spatial interpolation using clustering adaptive inverse distance weighting algorithm with linear regression. In: Memmi, G., Yang, B., Kong, L., Zhang, T., Qiu, M. (eds.) 15th International Conference on Knowledge Science, Engineering and Management, KSEM 2022. LNCS, Singapore, 6–8 August 2022, Proceedings, Part II, pp. 261–272. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-10986-7_21
Liu, F., et al.: Mapping high resolution National Soil Information Grids of China. Sci. Bull. 67(3), 328–340 (2022). https://doi.org/10.1016/j.scib.2021.10.013
Ishitsuka, K., Mogi, T., Sugano, K., Yamaya, Y., Uchida, T., Kajiwara, T.: Resistivity-based temperature estimation of the Kakkonda Geothermal Field, Japan, using a neural network and neural kriging. IEEE Geosci. Remote Sens. Lett. 15, 1154–1158 (2018)
Zhang, C., Luo, L., Xu, W., Ledwith, V.: Use of local Moran’s I and GIS to identify pollution hotspots of Pb in urban soils of Galway, Ireland. Sci. Total. Environ. 398, 212–221 (2008)
Peli, R., Menafoglio, A., Cervino, M., Dovera, L., Secchi, P.: Physics-based Residual Kriging for dynamically evolving functional random fields. Stoch. Env. Res. Risk Assess. 36, 3063–3080 (2022)
Agyeman, P.C., Kingsley, J., Kebonye, N.M., Khosravi, V., Borůvka, L., Vašát, R.: Prediction of the concentration of antimony in agricultural soil using data fusion, terrain attributes combined with regression kriging. Environ. Pollut. 316, 120697 (2023)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Zhu, L., Wei, H., Song, X., Wei, Y., Wang, Y. (2024). A Spatial Interpolation Method Based on BP Neural Network with Bellman Equation. In: Liu, F., Sadanandan, A.A., Pham, D.N., Mursanto, P., Lukose, D. (eds) PRICAI 2023: Trends in Artificial Intelligence. PRICAI 2023. Lecture Notes in Computer Science(), vol 14326. Springer, Singapore. https://doi.org/10.1007/978-981-99-7022-3_1
Download citation
DOI: https://doi.org/10.1007/978-981-99-7022-3_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-7021-6
Online ISBN: 978-981-99-7022-3
eBook Packages: Computer ScienceComputer Science (R0)