术语“正交回归”的详细信息

英译术语:

orthogonal regression

汉语语境:

线性回归分析中，一般最小二乘回归的目标函数只考虑一个方向的扰动，采用基于几何距离的正交回归能克服固定单方向最优带来的拟合稳定性差的弊端。分析和比较了正交回归和一般最小二乘回归的误差，并定量地给出了两者的几何误差与原始数据的方差，相关系数之间的关系，指出正交回归的几何误差小于一般最小二乘回归，并且正交回归具有旋转不变性。

英语语境:

In linear regression analysis, the objective function of the ordinary least squares regression only takes the uncertainty of single variable into account, while the objective function in orthogonal regression or the regression based on geometric distance can overcome the ill stability incurred in the ordinary regression caused by single variable optimization. In this paper, the errors are analyzed and compared between orthogonal regression and ordinary least squares regression, which are expressed as the function.