To address the issue of geographical weighted regression model (GWR) for prediction,which more input variables lead to high computational complexity and less input variables induced lower predictive accuracy,a regression method based on geographical weighted principal component analysis (PCA-GWR) was proposed in this paper.It is used to predict the accuracy of prediction,which is based on principal component analysis (PCA).Firstly,the collinearity of the aerosol optical depth (AOD) influencing factors was tested by this method.Then,some related variables of influencing AOD values were processed by nonlinear principal component analysis,which eliminates the correlation variables.Finally,the nonlinear principal component analysis was used to obtain several comprehensive indexes,and the AOD value was analyzed and predicted by the geography weighted regression model.In order to verify the effectiveness of the method,the data of AOD,elevation,wind speed,air temperature,humidity,air pressure,slope and aspect of Beijing-Tianjin-Hebei area were collected,and it selected the factors by Pearson correlation coefficient method which were in high correlation with AOD concentration as the input variables of the conventional GWR model,compared with this method under the condition of same number of variables.The results show that the nonlinear principal component analysis method can effectively solve the collinearity between variables after preprocessing the relevant variables,and can retain the main information of the original influencing factors,and improve the efficiency of the calculation.Moreover,The MAE,RMSE,AIC and R2(goodness of fit) of this method are better than that of the conventional GWR model.
