潜在变量回归模型中零空间与正交空间的等价性

IF 2.1 4区化学 Q1 SOCIAL WORK

Journal of Chemometrics Pub Date : 2025-08-04 DOI:10.1002/cem.70057

Sergio García-Carrión, Francesco Sartori, Joan Borràs-Ferrís, Pierantonio Facco, Massimiliano Barolo, Alberto Ferrer

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引用次数: 0

摘要

零空间和正交空间的概念已经在独立的背景和不同的目的下发展起来：前者出现在偏最小二乘（PLS）回归模型的反演中，后者出现在正交PLS （O-PLS）建模中。在本研究中，我们通过数学证明零空间和正交空间是同一空间，架起了PLS模型反演和O-PLS建模的桥梁。我们还使用模拟和真实的案例研究，对两个空间之间的等效性进行了图形化解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On the Equivalence Between Null Space and Orthogonal Space in Latent Variable Regression Modeling

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On the Equivalence Between Null Space and Orthogonal Space in Latent Variable Regression Modeling

The concepts of null space and orthogonal space have been developed in independent contexts and with different purposes: the former arises in the inversion of partial least-squares (PLS) regression models, and the latter in orthogonal PLS (O-PLS) modeling. In this study, we bridge PLS model inversion and O-PLS modeling by mathematically proving that the null space and the orthogonal space are the same space. We also provide a graphical interpretation of the equivalence between the two spaces, using both a simulated and a real case study.

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来源期刊

Journal of Chemometrics 化学-分析化学

CiteScore

5.20

自引率

8.30%

发文量

审稿时长

2 months

期刊介绍： The Journal of Chemometrics is devoted to the rapid publication of original scientific papers, reviews and short communications on fundamental and applied aspects of chemometrics. It also provides a forum for the exchange of information on meetings and other news relevant to the growing community of scientists who are interested in chemometrics and its applications. Short, critical review papers are a particularly important feature of the journal, in view of the multidisciplinary readership at which it is aimed.