| 利用主成分分析法及地理加权回归模型分析AOD数据 |
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| 引用本文： | 李广超,李如仁,卢月明,赵阳阳,余博.利用主成分分析法及地理加权回归模型分析AOD数据[J].测绘通报,2018,0(4):50-56. |
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| 作者姓名： | 李广超 李如仁 卢月明 赵阳阳 余博 |
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| 作者单位： | 1. 沈阳建筑大学交通学院, 辽宁 沈阳 110168;
2. 中国测绘科学研究院, 北京 100830 |
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| 基金项目： | 中国测绘科学研究院基本科研业务费(7771614)，国家重点研发计划课题(2016YFC0803108) |
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| 摘 要： | 针对采用地理加权回归模型（GWR）进行预测时输入变量较多导致计算复杂度高，而输入变量较少引起预测精度降低这一问题，提出了一种基于主成分分析的地理加权回归方法（PCA-GWR）。首先，该方法检验了气溶胶光学厚度（AOD）影响因素之间的共线性；然后，通过非线性主成分分析法（NLPCA）对影响AOD值的若干相关变量进行处理，既消除了相关变量彼此之间的多重共线性，又可以起到降维的作用；最后，利用非线性主成分分析得到较少的几个综合指标，通过地理加权回归模型对AOD值进行分析预测。为验证该方法的有效性，采用京津冀地区的AOD、高程、风速、气温、湿度、气压、坡度、坡向数据，利用Pearson相关系数法选取与AOD浓度具有较高相关性的影响因素作为常规的GWR模型的输入变量，在变量个数相同的前提下，与本文方法进行对比。研究结果表明：应用非线性主成分分析法对相关变量进行预处理后，有效地解决了变量之间的共线性，保留了原始影响因素主要信息，提高了运算效率，且该方法所得的MAE、RMSE、AIC及其拟合优度R2均优于常规的GWR模型。
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| 关 键 词： | 主成分分析 GWR AOD Pearson相关系数 |
| 收稿时间： | 2017-07-04 |
Using Principal Component Analysis and Geographic Weighted Regression Methods to Analyze AOD Data |
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| LI Guangchao,LI Ruren,LU Yueming,ZHAO Yangyang,YU Bo.Using Principal Component Analysis and Geographic Weighted Regression Methods to Analyze AOD Data[J].Bulletin of Surveying and Mapping,2018,0(4):50-56. |
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| Authors: | LI Guangchao LI Ruren LU Yueming ZHAO Yangyang YU Bo |
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| Institution: | 1. School of Transportation Engineering, Shenyang Jianzhu University, Shenyang 110168, China;
2. Chinese Academy of Surveying and Mapping, Beijing 100830, China |
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| Abstract: | 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. |
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| Keywords: | principal component analysis GWR AOD Pearson correlation coefficient |
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