IGG权函数的地理加权回归抗差估计方法  

Robust estimation method of geographically weighted regression based on IGG weight function

作　　者：张雅格 石娟 赵阳阳[2] 陶坤旺[2] 顾杨 安俊杰 刘振涛 ZHANG Yage;SHI Juan;ZHAO Yangyang;TAO Kunwang;GU Yang;AN Junjie;LIU Zhentao(Jiangsu Ocean University,Lianyungang,Jiangsu 222023,China;Chinese Academy of Surveying and Mapping,Beijing 100036,China;Guizhou Science and Technology Information Center,Guiyang 550002,China)

机构地区：[1]江苏海洋大学,江苏连云港222023 [2]中国测绘科学研究院,北京100036 [3]贵州省科技信息中心,贵阳550002

出　　处：《测绘科学》2020年第12期168-174,共7页Science of Surveying and Mapping

基　　金：国家重点研发计划资助项目(2018YFC0807000);江苏省2018年研究生实践创新计划项目(SJCX18_0914,SJCX18_0908,SJCX18_0921);精密工程与工业测量国家测绘地理信息局重点实验室项目(PF2017-3);贵州省公共服务平台建设项目(黔科中引地[2016]4009);基于深度学习的土地利用自动分类方法研究(AR1929)。

摘　　要：针对传统的地理加权回归(GWR)方法未考虑粗差对参数估计结果的影响,导致分析模型不稳健的问题,该文对模型进行了改进,引入IGG权函数,根据残差值的大小来改变数据点的权重,以改善粗差存在环境下地理加权回归模型参数估计的精度。为验证该方法的有效性,该文采用模拟数据和真实数据分别进行试验,以MSE、RMSE、R2和R2adj作为性能评价指标,将IGG-GWR与GWR对比分析。结果表明,无论是模拟数据试验,还是真实数据试验,该文提出的方法MSE、RMSE均低于GWR,R2和R2adj均高于GWR,说明该文提出的方法可以提升地理加权回归模型的性能。The traditional geographical weighted regression(GWR)method does not consider the influence of gross error on the parameter estimation results,which leads to the problem that the analysis model is not robust.This paper improved the model and introduced the institute of geodesy and geophysics(IGG)weight function to change the data according to the size of the residual value.The weight of the points was used to improve the accuracy of the parameter estimation of the geographically weighted regression model in the presence of gross errors.In order to verify the effectiveness of the method,the simulation data and real data were used to test respectively.MSE,RMSE,R^2 and R^2adj were used as performance evaluation indicators,and IGG-GWR and GWR were compared and analyzed.The results showed that the proposed method MSE and RMSE were lower than GWR,and both R^2 and R^2adj were higher than GWR,which indicated that the proposed method could improve the performance of the geo-weighted regression model.

关 键 词：地理加权回归方法 IGG权函数 抗差估计 二手房房价分布 

分 类 号：P208[天文地球—地图制图学与地理信息工程]