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浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (5): 572-581    DOI: 10.3785/j.issn.1008-9497.2020.05.009
地球科学     
基于空间自回归神经网络模型的空间插值研究
曾金迪1,2, 张丰1,2, 吴森森1,2, 杜震洪1,2, 刘仁义1,2
1.浙江大学 浙江省资源与环境信息系统重点实验室，浙江 杭州 310028
2.浙江大学 地理信息科学研究所，浙江 杭州 310027
Spatial interpolation based on spatial auto-regressive neural network
ZENG Jindi1,2, ZHANG Feng1,2, WU Sensen1,2, DU Zhenhong1,2, LIU Renyi1,2
1.Zhejiang Provincial Key Lab of GIS, Zhejiang University, Hangzhou 310028, China
2.Department of Geographic Information Science, Zhejiang University, Hangzhou 310027, China
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摘要： 基于空间距离计算的空间自相关权重系数是经典空间插值方法的核心，然而由于空间距离与自相关权重之间复杂的非线性关系，反距离权重（IDW）法和克里金（Kriging）法等传统空间插值方法，在求解权重精准解时存在一定的局限性。由此，利用神经网络超强的非线性拟合能力，通过融合神经网络与空间自回归方法，建立了空间自回归神经网络（SARNN）模型，实现了空间自相关权重的精准计算并将其应用于空间插值研究。为验证SARNN模型的有效性和可行性，采用两类模拟数据及海洋环境数据进行交叉验证，并与IDW法和Kriging法进行精度对比。实验结果表明，SARNN法显著提升了R2、RMSE、MAE、MAPE等统计指标，插值结果明显优于IDW法和Kriging法；同时，SARNN法在空间插值中对突变数据和极值数据的预测较为准确，改善了传统插值方法空间平滑过渡差，易出现“牛眼”、锯齿现象等问题，显著提高了空间插值结果的准确性与合理性。SARNN法提供了一种空间插值的新思路，具有较为广泛的应用价值。
关键词： 空间插值;  空间权重;  神经网络    
Abstract: The calculation of the spatial autocorrelation weight based on spatial distance is the core of the classical spatial interpolation method. However, due to the complex nonlinear relationship between spatial distance and the autocorrelation weight, traditional spatial interpolation methods such as inverse distance weighting (IDW) and the Kriging method have limitations on the accurate weight calculation. In this paper,based on the strong nonlinear fitting ability of neural network, we establish a spatial auto-regressive neural network (SARNN) model by combining neural network and spatial autoregressive method, and realize the accurate calculation of spatial autocorrelation weights. In order to verify the validity and feasibility of the SARNN model, we use two types of simulation data and marine environment data for cross-validation, and compare the accuracy with that of the IDW and Kriging. The results show that the performance SARNN is significantly better than IDW and Kriging, regarding all the statistical indicators such as R2, RMSE, MAE and MAPE. At the same time, SARNN predicts the mutation data and extremum more accurately and improves the problems in traditional interpolation method such as low spatial smooth transition, “bull's eye” and sawtooth phenomenon. Therefore, SARNN provides a new idea of spatial interpolation and has a wider application potential.
Key words: neural network    spatial weight    spatial interpolation
收稿日期: 2019-10-14 出版日期: 2020-09-25
CLC:  P208  
基金资助: 国家重点研发计划专项（2018YFB0505000，2016YFC0803105）；国家自然科学基金资助项目（41671391，41922043，41871287）.
通讯作者: ORCID: http: //orcid.org/0000-0003-1475-8480，E-mail：zfcarnation @zju.edu.cn.   
作者简介: 曾金迪(1996—)，ORCID: https://orcid.org/0000-0003-0616-3495，男，硕士，主要从事时空数据统计和建模研究.。
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引用本文:

曾金迪, 张丰, 吴森森, 杜震洪, 刘仁义. 基于空间自回归神经网络模型的空间插值研究[J]. 浙江大学学报（理学版）, 2020, 47(5): 572-581.

ZENG Jindi, ZHANG Feng, WU Sensen, DU Zhenhong, LIU Renyi. Spatial interpolation based on spatial auto-regressive neural network. Journal of Zhejiang University (Science Edition), 2020, 47(5): 572-581.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.05.009    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I5/572

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