带空间结构的人工神经网络建模方法

将遍历搜索法引入带空间结构的人工神经网络模型，提出一种新的模型估计和空间数据样本外预测方法。该方法基于人工神经网络，结合空间自回归模型思想，在网络模型中引入空间滞后项来考虑变量的空间效应，提出使用遍历搜寻最优解的方式替代传统极大似然法进行空间自回归系数估计和建模。结合样本外数据和空间结构，扩展空间权重矩阵并代入所提模型进行样本外预测，充分发挥了人工神经网络模型泛化能力强的特点。仿真分析指出:在合理考虑空间效应的情况下，所提模型的预测效果较普通人工神经网络有显著提升；而且当空间变量间存在非线性关系时，所提模型的预测精度同样优于空间自回归模型。 

Artificial neural network modeling method incorporating spatial structure

In this paper, grid-search method is introduced into artificial neural network model incorporating spatial structure, which is a new method of model estimation, to do out-of-sample prediction. This method is based on the artificial neural network algorithm, is combined with the idea of spatial autoregressive model, and introduces the spatial lag term in the model to consider the spatial effect of variables. Meanwhile, instead of maximum likelihood method, it uses the method of grid-search for the optimal solution to estimate and model the spatial autoregressive coefficient. Then, combined with the out-of-sample data and spatial structure, the spatial matrix is extended and the new model is brought in to make out-of-sample prediction, which gives full play to the strong generalization ability of the neural network model. Finally, the simulation results show that, compared with ordinary artificial neural network, the prediction effect of the new model is significantly improved when the spatial effect is considered reasonably, and the prediction accuracy is better than that of the spatial autoregressive model when there is a nonlinear relationship between spatial variables.