基于空间自回归神经网络模型的空间插值研究

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。

Spatial interpolation based on spatial auto-regressive neural network

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.