多维正交整体最小二乘应用研究

以往整体最小二乘的研究是在二维基础上探讨模型的适用性，但从二维延伸到多维的过程中，会引入过多的自变量与因变量误差，而在模型解算过程中，又不能完全考虑每一个误差变量，造成了误差的偏执，形成整体最小二乘最优结果的虚假现象。本文对二维延伸到多维的整体最小二乘、所产生的误差偏执、模型变异问题进行分析，引入了多维正交整体最小二乘，避开了误差变量的影响，使得二维、多维的整体最小二乘解算结果都可以达到最优。

Research on the Application of Multi-Dimensional Orthogonal Total Least Squares

The past total least squares discussed the applicability of the model in the two-dimensional. It will introduce too many errors of the independent variables and the dependent variable in the process of extending the multi-dimensional from two-dimensional. The error of each variable cannot be considered in the process of solving the model. As a result, the paranoia of the error is caused. So, the false phenomenon of the Total least squares opti-mal results form. This paper analyzes the paranoia of error and model variation in the process of extending to the multi-dimensional from two-dimensional, and then introduces the multi-dimensional orthogonal total least squares. The model avoids the impact of error variables, and makes the two-dimensional, multi-dimensional total least squares achieve optimal results.