北京测绘
北京測繪
북경측회
BEIJING SURVEYING AND MAPPING
2012年
6期
22-24
,共3页
直线回归问题%常规最小二乘%整体最小二乘%奇异值分解
直線迴歸問題%常規最小二乘%整體最小二乘%奇異值分解
직선회귀문제%상규최소이승%정체최소이승%기이치분해
conventional least squares%total least squares%linear regression problem%singular value decomposition
对于在实际应用中的直线回归问题,存在着因自变量和因变量选取不同拟合结果存在差异的情况,文中采用了一种线性拟合参数估计的新方法,即整体最小二乘法。文章在描述普通最小二乘和整体最小二乘原理的基础上,并对比其异同,并采用奇异值分解的方法来求解整体最小二乘问题。算例结果表明,采用整体最小二乘方法估计线性回归参数的精度明显高于常规最小二乘法,是一种值得借鉴的算法。
對于在實際應用中的直線迴歸問題,存在著因自變量和因變量選取不同擬閤結果存在差異的情況,文中採用瞭一種線性擬閤參數估計的新方法,即整體最小二乘法。文章在描述普通最小二乘和整體最小二乘原理的基礎上,併對比其異同,併採用奇異值分解的方法來求解整體最小二乘問題。算例結果錶明,採用整體最小二乘方法估計線性迴歸參數的精度明顯高于常規最小二乘法,是一種值得藉鑒的算法。
대우재실제응용중적직선회귀문제,존재착인자변량화인변량선취불동의합결과존재차이적정황,문중채용료일충선성의합삼수고계적신방법,즉정체최소이승법。문장재묘술보통최소이승화정체최소이승원리적기출상,병대비기이동,병채용기이치분해적방법래구해정체최소이승문제。산례결과표명,채용정체최소이승방법고계선성회귀삼수적정도명현고우상규최소이승법,시일충치득차감적산법。
For the linear regression problem in practical applications,there are different independent variables and the dependent variables,it selects a different fitting results using the new method of parameter estimation of a linear fit,i.e.,the overall least square method.The article based on the description of the ordinary least squares and the total least squares,compares their similarities and differences,and the singular value decomposition method to solve the total least squares problem.The example shows that,using the total least squares method to estimate the accuracy of the linear regression parameters significantly higher than that of conventional least squares method,which is a valuable algorithm.
