With the rapid development of social networks, spatial autoregressive models with covariates are increasingly used in practice. We introduce spatial effects into the artificial neural network model and propose a new method for spatial data prediction. Our method is based on artificial neural network, combined with the idea of nonparametric spatial autoregressive model. The spatial lag term is a input of the network, considering the spatial effect of variables. The feature of strong generalization ability of the artificial neural network model is given full play. The simulation results point out that the proposed method has better prediction accuracy than the maximum likelihood method, naive least squares method and B-spline method when the random error term obey non-normal distribution; in the case of spatial effects of the data, the proposed model has significantly improved the prediction effect compared with the common artificial neural network.

随着社交网络的快速发展，具有协变量的空间自回归模型在实践中越来越多地使用。我们将空间效应引入人工神经网络模型，并提出了一种新的空间数据预测方法。我们的方法基于人工神经网络，结合非参数空间自回归模型的思想。空间滞后项是网络的输入，考虑变量的空间效应。充分发挥人工神经网络模型泛化能力强的特点。仿真结果表明，当随机误差项服从非正态分布时，该方法比最大似然法、朴素最小二乘法和B样条法具有更好的预测精度；在数据的空间效应的情况下，