Latent variable model inversion for intervals. Application to tolerance intervals in class-modelling situations, and specification limits in process control

IF 3.7 2区化学 Q2 AUTOMATION & CONTROL SYSTEMS

Chemometrics and Intelligent Laboratory Systems Pub Date : 2024-06-18 DOI:10.1016/j.chemolab.2024.105166

M.S. Sánchez , M.C. Ortiz , S. Ruiz , O. Valencia , L.A. Sarabia

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引用次数: 0

Abstract

The paper deals with the inversion of intervals when a PLS (Partial Least Squares) model is used. However, instead of discretizing the interval, it is proved that the region resulting from the inversion of a PLS model is a convex set bounded by two parallel hyperplanes, each corresponding to the direct inversion of each endpoint of the given interval.

When the domain of the input variables is a convex set, any feasible solution with predictions within the interval set in the response can be obtained as a convex combination of a point on each of the two hyperplanes. In this way, the new solutions preserve the internal structure of the input variables.

This methodology can be of interest in several domains where the response under study is defined in terms of an interval of admissible values, such as specifications for a product in an industrial process, or tolerance intervals for computing compliant class-models.

The inversion of the corresponding fitted model defines a region in the input space (predictor variables) whose predictions fall within the specified interval. Then, estimating and exploring this region will increase the information about the problem under study.

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区间的潜变量模型反演。应用于类别建模情况下的公差区间和过程控制中的规格限制

本文涉及使用 PLS（部分最小二乘）模型时的区间反演。然而，本文并没有将区间离散化，而是证明了 PLS 模型反演所产生的区域是一个由两个平行超平面限定的凸集，每个超平面都对应于给定区间的每个端点的直接反演。这种方法适用于多个领域，在这些领域中，所研究的响应是以可接受值的区间来定义的，例如工业流程中的产品规格，或计算符合要求的类模型的公差区间。然后，对这一区域进行估算和探索将增加有关所研究问题的信息。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Chemometrics and Intelligent Laboratory Systems 工程技术-分析化学

CiteScore

7.50

自引率

7.70%

发文量

169

审稿时长

3.4 months

期刊介绍： Chemometrics and Intelligent Laboratory Systems publishes original research papers, short communications, reviews, tutorials and Original Software Publications reporting on development of novel statistical, mathematical, or computer techniques in Chemistry and related disciplines. Chemometrics is the chemical discipline that uses mathematical and statistical methods to design or select optimal procedures and experiments, and to provide maximum chemical information by analysing chemical data. The journal deals with the following topics: 1) Development of new statistical, mathematical and chemometrical methods for Chemistry and related fields (Environmental Chemistry, Biochemistry, Toxicology, System Biology, -Omics, etc.) 2) Novel applications of chemometrics to all branches of Chemistry and related fields (typical domains of interest are: process data analysis, experimental design, data mining, signal processing, supervised modelling, decision making, robust statistics, mixture analysis, multivariate calibration etc.) Routine applications of established chemometrical techniques will not be considered. 3) Development of new software that provides novel tools or truly advances the use of chemometrical methods. 4) Well characterized data sets to test performance for the new methods and software. The journal complies with International Committee of Medical Journal Editors'' Uniform requirements for manuscripts.