Application of equality constraints on variables during alternating least squares procedures
Application of equality constraints on variables during alternating least squares procedures
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DOI：
10.1002/cem.761
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发表时间：
2002-12-01
影响因子：
2.4
通讯作者：
Haaland, DM
中科院分区：
文献类型：
--
作者：
Van Benthem, MH;Keenan, MR;Haaland, DM
我们描述了几种应用等式约束的方法，同时执行程序，采用交替最小二乘法。其中包括应用等式约束的数学严格方法，以及化学计量学中常用的近似方法，这些方法在数学上并不严格。严格的方法是扩展的方法详细描述了劳森和汉森的里程碑文本解决最小二乘问题，表现出良好的最小二乘性能。近似方法往往易于使用和编码，但它们表现出较差的最小二乘行为，并且具有未被很好理解的属性。本文解释了严格的等式约束最小二乘法的应用，并证明了采用非严格方法的危险。我们发现，在某些情况下，在使用覆盖有噪声的合成数据的精确基向量启动多元曲线分辨率时，近似方法实际上会导致残差幅度的增加。这种现象表明近似方法的解实际上可能偏离最小二乘解。版权所有（C）2002约翰威利父子有限公司
We describe several methods of applying equality constraints while performing procedures that employ alternating least squares. Among these are mathematically rigorous methods of applying equality constraints, as well as approximate methods, commonly used in chemometrics, that are not mathematically rigorous. The rigorous methods are extensions of the methods described in detail in Lawson and Hanson's landmark text on solving least squares problems, which exhibit well-behaved least squares performance. The approximate methods tend to be easy to use and code, but they exhibit poor least squares behaviors and have properties that bare not well understood. This paper explains the application of rigorous equality-constrained least squares and demonstrates the dangers of employing non-rigorous methods. We found that in some cases, upon initiating multivariate curve resolution with the exact basis vectors underlying synthetic data overlaid with noise, the approximate method actually results in an increase in the magnitude of residuals. This phenomenon indicates that the solutions for the approximate methods May actually diverge from the least squares solution. Copyright (C) 2002 John Wiley Sons, Ltd.