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Past, Present and Future of Research in Analytical Figures of Merit 功勋人物分析研究的过去、现在和未来
IF 2.3 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-11-07 DOI: 10.1002/cem.3616
Alejandro Olivieri
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引用次数: 0
Analytical Figures of Merit in Univariate, Multivariate, and Multiway Calibration: What Have We Learned? What Do We Still Need to Learn? 单变量、多变量和多途径校准中的优越性分析图:我们学到了什么?我们还需要学习什么?
IF 2.3 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-10-23 DOI: 10.1002/cem.3613
Alejandro C. Olivieri

An overview of the status of the research in analytical figures of merit is provided, including all calibration scenarios from univariate to multivariate and multiway analytical protocols. Both linear and nonlinear multivariate models are considered. Starting with the simplest multivariate model, inverse least-squares regression, the basic concepts of sensitivity, sample leverage, and limit of detection are introduced. The extension to other multivariate models is discussed, as well as to nonlinear models based on radial basis functions, kernel partial least-squares, and multilayer feed-forward artificial neural networks. Finally, multiway calibration models are discussed, including multilinear decomposition models such as parallel factor analysis (PARAFAC) and multivariate curve resolution–alternating least-squares (MCR-ALS). In the latter case, recent developments concerning the pervasive phenomenon of rotational ambiguity are discussed. Unfinished works and areas where further research efforts are needed to develop closed-form expressions and to fully understand their meaning are included.

报告概述了优越性分析数据的研究现状,包括从单变量到多变量和多途径分析协议的所有校准方案。同时考虑了线性和非线性多元模型。从最简单的多元模型--反最小二乘回归开始,介绍了灵敏度、样品杠杆和检出限的基本概念。讨论了如何扩展到其他多元模型,以及基于径向基函数、核偏最小二乘和多层前馈人工神经网络的非线性模型。最后,还讨论了多路校准模型,包括多线性分解模型,如并行因子分析(PARAFAC)和多变量曲线解析-交替最小二乘法(MCR-ALS)。在后一种情况下,讨论了有关普遍存在的旋转模糊现象的最新进展。还包括未完成的工作和需要进一步研究的领域,以开发闭式表达式并充分理解其含义。
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引用次数: 0
Paul Geladi (1951–2024) Chemometrician, spectroscopist and pioneer 保罗-格拉迪(1951-2024) 化学计量学家、光谱学家和先驱
IF 2.3 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-10-17 DOI: 10.1002/cem.3614
Beatriz Galindo-Prieto, Johan Linderholm, Hans Grahn
<p>Prof. Paul Geladi was born the 30<sup>th</sup> of June of 1951 in Schoten (Belgium) and passed away peacefully on the 18<sup>th</sup> of May of 2024 in Umeå (Sweden).</p><p>Paul Geladi was a brilliant chemometrician and professor specialized in multivariate data analysis (especially, partial least squares methods), multivariate image analysis, multiway analysis, and spectroscopy (near-infrared), as well as a kind and emphatic person with colleagues, students, friends and family. His work trajectory includes, among other, a list of more than 190 publications (with >29,000 citations) that shows the extent and vigour of Paul, both in life and work.</p><p>Paul's passion for nature and chemistry awoke in his early years in Schoten, when he was still a very young child, while playing outdoors or experimenting in the attic for hours with the “Chemistry for Beginners” kit that his parents gave him. This was likely the start of a life dedicated to science and research.</p><p>After attending Sint-Eduardus in the Londenstraat (Belgium), Paul received his B.Sc. in Chemistry (1974) and his Ph.D. (doctoral degree) in Analytical Chemistry from the University of Antwerp (1979). Afterwards, in the early 1980's, Paul worked in Norway at the non-profit foundation Norwegian Computing Centre, specializing in applied statistics, and accepted a position as Associate Professor in Chemometrics at the Department of Chemistry of Umeå University (Sweden), generating his most cited publication, the tutorial <i>Principal Component Analysis</i> (Wold, Esbensen & Geladi, 1987). Paul also worked as a visiting Professor at the Department of Chemistry, University of Washington, Seattle, where he wrote his second most cited publication, <i>Partial least-squares regression: a tutorial</i> (Geladi & Kowalski, 1986). In addition, he also held a position as Associate Professor in Chemometrics and Near Infrared Spectroscopy at the University of Vaasa (Finland) since 2003.</p><p>In 2007, Paul was appointed Professor of Chemometrics at the Swedish University of Agricultural Sciences (SLU, Umeå, Sweden), which would be his main institution until his retirement in 2016, when he would become Emeritus Professor at SLU. During the active years, Paul was awarded the title of <i>Honorary Doctor of Technology</i> by the University of Vaasa (Finland, 2011) in recognition of his esteemed scholarship on Near Infrared Spectroscopy and the international impact of his work. Paul was also External Professor at the Department of Food Science of Stellenbosch University (South Africa) between 2011 and 2014. His work and publications on NIR spectroscopy, multivariate data analysis, hyperspectral imaging, chemometric method development, and their applications in a variety of fields, had a tremendous impact in the scientific community, yielding to numerous invitations to present his work in international conferences and meetings.</p><p>His outstanding work related to chemometrics, multivariate c
保罗-格拉迪教授于 1951 年 6 月 30 日出生于比利时肖滕,于 2024 年 5 月 18 日在瑞典于默奥安详辞世。保罗-格拉迪是一位杰出的化学计量学家和教授,专长于多元数据分析(尤其是偏最小二乘法)、多元图像分析、多向分析和光谱学(近红外)。他的工作轨迹包括发表了 190 多篇论文(引用次数达 29,000 次),这显示了保罗在生活和工作中的广度和活力。保罗早年在肖腾(Schoten)还是一个非常年幼的孩子时,就对自然和化学产生了浓厚的兴趣,他经常在户外玩耍,或者在阁楼上用父母给他的 "化学入门 "工具包做几个小时的实验。在比利时朗登大街的 Sint-Eduardus 上学后,保罗获得了化学学士学位(1974 年)和安特卫普大学分析化学博士学位(1979 年)。之后,在 20 世纪 80 年代初,保罗在挪威的非营利基金会挪威计算中心工作,专门从事应用统计学研究,并在瑞典于默奥大学化学系担任化学计量学副教授,出版了他最常被引用的著作《主成分分析教程》(Wold, Esbensen &amp; Geladi, 1987)。保罗还曾在西雅图华盛顿大学化学系担任客座教授,并在那里撰写了他引用率第二高的著作《部分最小二乘回归:教程》(Geladi &amp; Kowalski, 1986)。此外,自 2003 年起,他还在瓦萨大学(芬兰)担任化学计量学和近红外光谱学副教授。2007 年,保罗被任命为瑞典农业科学大学(SLU,瑞典于默奥)的化学计量学教授,在 2016 年退休前,这一直是他的主要研究机构,届时他将成为瑞典农业科学大学的名誉教授。在活跃的岁月里,保罗被瓦萨大学(芬兰,2011 年)授予荣誉技术博士称号,以表彰他在近红外光谱学方面备受推崇的学术成就及其工作的国际影响力。2011 年至 2014 年间,保罗还担任南非斯泰伦博斯大学食品科学系外聘教授。他在近红外光谱学、多元数据分析、高光谱成像、化学计量学方法开发及其在多个领域的应用方面所做的工作和发表的论文在科学界产生了巨大影响,并多次受邀在国际会议上介绍自己的工作。他在化学计量学、多元校准、变量选择、光谱学(尤其是近红外光谱)、多向分析和多元图像分析方面的杰出工作,在国际期刊上发表了大量影响深远的论文,并获得了 2002 年东方分析研讨会化学计量学奖。他在光谱和超光谱图像方面的工作产生了重大的世界影响;保罗对图像的兴趣可能与他也是一名熟练的摄影师有关。这种兴趣促使他与他人合作撰写了几本书的章节,并出版了三本备受推崇的畅销书:保罗-格拉迪的论文范围广泛,从多元统计方法教程(如主成分分析、偏最小二乘回归、神经网络或数据预处理)到数据分析在分析化学、光谱学、环境科学、医学、高光谱成像和食品科学等领域的应用。他发表了近 200 篇经同行评审的论文,并多次参加会议。他在 1986-1987 年发表的关于主成分分析(被引用超过 14350 次)和偏最小二乘法(被引用超过 9080 次)的教程,对于想要了解 PCA 和 PLS 算法并学习如何使用它们的年轻研究人员来说,仍然是最有帮助的资源之一;其次是他在 1985 年发表的关于近红外反射光谱线性化和散射校正的文章。他在近红外光谱分析复杂样品方面的工作对工业(如食品和制药业)、医学(如皮肤癌和糖尿病相关研究)以及环境和暴露科学(如农业应用和人体急性毒性研究)产生了巨大影响。 在担任荣誉退休教授期间(2016-2024 年),保罗继续以他的知识和经验帮助多个机构的众多研究人员和学生。保罗是一位非常活跃的旅行家(我们都记得他在世界各地的旅行和国际活动,以及他娴熟的语言能力),促成了大量的全球合作,并在瑞典、挪威、芬兰、美国或南非等国建立了广泛的国际研究人员网络。他的合作范围从方法论研究(与先进算法、光谱学、成像和多元数据分析有关)到考古学、医学、化学、生物技术或人工智能方面的应用。他有时间做所有这些工作,他是一个真正的早起鸟儿,早上 5 点就能给您发送一封电子邮件,提供完美的解决方案,因为对保罗来说,合理利用时间非常重要,他经常提醒他的学生们。保罗知道,时间管理对于健康地平衡工作和生活也很重要。他的耐心、同理心以及积极倾听和建议的能力(尤其是在支持和帮助学生和初入职场者时)使他成为大学里最受尊敬和赞赏的教授之一。对于别人可能要讨论几个小时的问题,他却能寥寥数语就给出最有效的解决方案。他的思维方式条理清晰,无需事先准备幻灯片,就能在黑板上用完全易懂的方式解释最复杂的问题。与许多在数学方面极具天赋的科学家一样,保罗热爱音乐,这是他生活的重要组成部分。十几岁时,他就迷上了披头士和爵士乐;之后,在比利时安特卫普大学学习化学时,他加入了一个前卫音乐表演团体。先驱者的天性使他利用这种激情创作出创新的电子音乐,尝试各种声音,并使用突破传统的技术。退休后,他继续在于默奥学习钢琴,培养自己对音乐的热爱。他还是一名有执照的飞机驾驶员,多年来一直活跃在于默奥航空俱乐部(Umeå flygklubb, UFK),将自己和同事送往理想的目的地。保罗的开放思想和开拓思维使他将化学计量学应用于各种领域和行业,同时也对该领域提出质疑,以促进对化学计量学的发展现状和未来新挑战的建设性讨论。Intel.实验室。保罗-格拉迪教授不仅是一位杰出的科学家,也是谦逊的缩影,他个性热情,愿意帮助从学生到资深科学家的每一个人。他谦逊温和的言行举止、高质量的研究成果和大量的著作,将继续成为新一代化学计量学家和科学家的榜样和灵感源泉。
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引用次数: 0
Resampling as a Robust Measure of Model Complexity in PARAFAC Models 将重采样作为 PARAFAC 模型复杂性的稳健衡量标准
IF 2.4 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-09-05 DOI: 10.1002/cem.3601
Helene Fog Froriep Halberg, Marta Bevilacqua, Åsmund Rinnan
Fluorescence spectroscopy has been applied for analysis of complex samples, such as food and beverages. Parallel factor analysis (PARAFAC) is a well‐known decomposition method for fluorescence excitation–emission matrices (EEMs). When the complexity of the system increases, it becomes considerably more difficult to determine the optimal number of PARAFAC components, especially when the fluorophores of the system are unknown. The two commonly applied diagnostics, core consistency and split‐half analysis, appear to underestimate the model complexity due to covarying components and local minima, respectively. As a more robust alternative, we propose a resampling approach with multiple initializations and submodel comparisons for estimating the optimal number of PARAFAC components in complex data.
荧光光谱法已被用于分析食品和饮料等复杂样品。平行因子分析(PARAFAC)是一种著名的荧光激发-发射矩阵(EEM)分解方法。当系统的复杂性增加时,确定 PARAFAC 成分的最佳数量就变得相当困难,尤其是当系统中的荧光团未知时。两种常用的诊断方法--核心一致性和分割半分析--似乎分别由于共变成分和局部最小值而低估了模型的复杂性。作为一种更稳健的替代方法,我们提出了一种具有多重初始化和子模型比较的重采样方法,用于估计复杂数据中 PARAFAC 成分的最佳数量。
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引用次数: 0
A Non‐Linear Model for Multiple Alcohol Intakes and Optimal Designs Strategies 多种酒精摄入量的非线性模型和最佳设计策略
IF 2.4 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-08-27 DOI: 10.1002/cem.3599
Irene Mariñas‐Collado, Juan M. Rodríguez‐Díaz, M. Teresa Santos‐Martín
This study addresses the complex dynamics of alcohol elimination in the human body, very important in forensic and healthcare areas. Existing models often oversimplify with the assumption of linear elimination kinetics, limiting practical application. This study presents a novel non‐linear model for estimating blood alcohol concentration after multiple intakes. Initially developed for two different alcohol incorporations, it can be straightforwardly extended to the case of more intakes. Emphasising the significance of accurate parameter estimation, the research underscores the importance of precise experimental design, utilising optimal experimental design (OED) methodologies. Sensitivity analysis of model coefficients and the determination of D‐optimal designs, considering correlation structures among observations, reveal a strong linear relationship between support points. This relationship can be used to obtain nearly optimal designs that are highly efficient and much easier to compute.
这项研究探讨了酒精在人体内消除的复杂动态,这在法医和医疗保健领域非常重要。现有的模型往往过于简化,假定其为线性消除动力学,从而限制了实际应用。本研究提出了一种新的非线性模型,用于估计多次摄入后血液中的酒精浓度。该模型最初是针对两种不同的酒精摄入量而开发的,可以直接扩展到更多摄入量的情况。研究强调了精确参数估计的重要性,并强调了利用最优实验设计(OED)方法进行精确实验设计的重要性。对模型系数的敏感性分析和 D-最优设计的确定,考虑到了观测数据之间的相关结构,揭示了支持点之间强烈的线性关系。利用这种关系可以获得近乎最优的设计,这种设计效率高,而且更容易计算。
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引用次数: 0
Population Power Curves in ASCA With Permutation Testing 带有置换测试的 ASCA 人口功率曲线
IF 2.4 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-08-27 DOI: 10.1002/cem.3596
José Camacho, Michael Sorochan Armstrong
In this paper, we revisit the power curves in ANOVA simultaneous component analysis (ASCA) based on permutation testing and introduce the population curves derived from population parameters describing the relative effect among factors and interactions. The relative effect has important practical implications: The statistical power of a given factor depends on the design of other factors in the experiment and not only of the sample size. Thus, understanding the relative power in a specific experimental design can be extremely useful to maximize our capability of success when planning the experiment. In the paper, we derive relative and absolute population curves, where the former represent statistical power in terms of the normalized effect size between structure and noise, and the latter in terms of the sample size. Both types of population curves allow us to make decisions regarding the number and nature (fixed/random) of factors, their relationships (crossed/nested), and the number of levels and replicates, among others, in an multivariate experimental design (e.g., an omics study) during the planning phase of the experiment. We illustrate both types of curves through simulation.
在本文中,我们重新审视了基于置换检验的方差分析同时成分分析(ASCA)中的功率曲线,并引入了由描述因子间和交互作用间相对效应的群体参数导出的群体曲线。相对效应具有重要的实际意义:给定因素的统计能力取决于实验中其他因素的设计,而不仅仅是样本量。因此,了解特定实验设计中的相对效应对于我们在规划实验时最大限度地提高成功率非常有用。在本文中,我们推导了相对和绝对群体曲线,前者以结构和噪声之间的归一化效应大小表示统计能力,后者以样本量表示统计能力。这两类种群曲线都能让我们在实验计划阶段,就多元实验设计(如 omics 研究)中因子的数量和性质(固定/随机)、它们之间的关系(交叉/嵌套)、水平和重复的数量等做出决策。我们通过模拟来说明这两种类型的曲线。
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引用次数: 0
Chemometric Classification of Motor Oils Using 1H NMR Spectroscopy With Simultaneous Phase and Baseline Optimization 利用 1H NMR 光谱对机油进行化学计量分类,同时进行相位和基线优化
IF 2.4 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-08-26 DOI: 10.1002/cem.3598
A. Olejniczak, J. P. Łukaszewicz
Here, we demonstrate mid‐field 1H NMR spectroscopy combined with chemometrics to be powerful in the classification and authentication of motor oils (MOs). The 1H NMR data were processed with a new algorithm for simultaneous phase and baseline correction, which, for crowded spectra such as those of the refinery products, allowed for more accurate estimation of phase parameters than other literature approaches tested. A principal component analysis (PCA) model based on the unbinned CH3 fingerprint region (0.6–1.0 ppm) enabled the differentiation of hydrocracked and poly‐α‐olefin‐based MOs and was effective in resolving mixtures of these base stocks with conventional base oils. PCA analysis of the 1.0‐ to 1.14‐ppm region enabled the detection of poly (isobutylene) additive and was useful for differentiating between single‐grade and multigrade MOs. Non‐equidistantly binned 1H NMR data were used to detect the addition of esters and to establish discriminant models for classifying MOs by viscosity grade and by major categories of synthetic, semisynthetic, and mineral oils. The performances of four classifiers (linear discriminant analysis [LDA], quadratic discriminant analysis [QDA], naïve Bayes classifier [NBC], and support vector machine [SVM]) with and without PCA dimensionality reduction were compared. In both tasks, SVM showed the best efficiency, with average error rates of ~2.3% and 8.15% for predicting major MO categories and viscosity grades, respectively. The potential to merge spectra collected from different NMR instruments is discussed for models based on spectral binning. It is also shown that small errors in phase parameters are not detrimental to binning‐based PCA models.
在此,我们展示了中场 1H NMR 光谱与化学计量学相结合在机油 (MO) 分类和鉴定方面的强大功能。1H NMR 数据采用一种新算法进行处理,该算法可同时进行相位和基线校正,对于炼油厂产品等拥挤的光谱,该算法能比测试过的其他文献方法更准确地估计相位参数。基于未分馏 CH3 指纹区域(0.6-1.0 ppm)的主成分分析 (PCA) 模型能够区分加氢裂化 MO 和基于聚-α-烯烃的 MO,并能有效分辨这些基础油与传统基础油的混合物。通过对 1.0 至 1.14ppm 区域进行 PCA 分析,可以检测到聚(异丁烯)添加剂,并有助于区分单级和多级 MO。非流体分级 1H NMR 数据用于检测酯类的添加情况,并建立了按粘度等级以及合成油、半合成油和矿物油的主要类别对 MO 进行分类的判别模型。比较了四种分类器(线性判别分析器 [LDA]、二次判别分析器 [QDA]、奈夫贝叶斯分类器 [NBC] 和支持向量机 [SVM])在使用和未使用 PCA 降维的情况下的性能。在这两项任务中,SVM 的效率最高,预测主要 MO 类别和粘度等级的平均错误率分别为 ~2.3% 和 8.15%。对于基于光谱分选的模型,讨论了合并从不同 NMR 仪器收集的光谱的可能性。研究还表明,相位参数的微小误差不会对基于分选的 PCA 模型造成损害。
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引用次数: 0
Some Views on Multi-criteria Methods for Data Analysis 关于数据分析多标准方法的一些观点
IF 2.3 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-08-21 DOI: 10.1002/cem.3597
Henk A. L. Kiers, Marieke E. Timmerman

Many data analysis methods actually combine optimization of several criteria. In this paper, a framework is offered for categorizing such multi-criteria methods. In particular, it categorizes multiset and three-way analysis methods as well as penalized methods and combinations thereof. The framework aims to stimulate critical evaluation of methods and reflection on the purpose of methods and, by signaling gaps, to help the development of new data analysis methods.

许多数据分析方法实际上结合了多个标准的优化。本文为此类多标准方法的分类提供了一个框架。特别是,它对多集合和三向分析方法以及惩罚性方法及其组合进行了分类。该框架旨在激发对方法的批判性评估和对方法目的的思考,并通过指出差距,帮助开发新的数据分析方法。
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引用次数: 0
A Novel Automated System for Early Diabetic Retinopathy Detection and Severity Classification 用于早期糖尿病视网膜病变检测和严重程度分类的新型自动系统
IF 2.3 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-08-19 DOI: 10.1002/cem.3593
Santoshkumar S Ainapur, Virupakshappa Patil

Diabetes is a common and serious global disease that damages blood vessels in the eye, leading to vision loss. Early and accurate diagnosis of this issue is crucial to reduce the risk of visual impairment. The typical deep learning (DL) methods for diabetic retinopathy (DR) grading are often time-consuming, resulting in unsatisfactory detection performance due to inadequate representation of lesion features. To overcome these challenges, this research proposes a new automated mechanism for detecting and classifying DR, aiming to identify DR severities and different stages. To figure out and capture feature characteristics from DR samples, a conjugated attention mechanism and vision transformer are utilized within a collective net model, which automatically generates feature maps for diagnosing DR. These extracted feature maps are then fused through the feature fusion function in a fused attention net model, calculating attention weights to produce the most powerful feature map. Finally, the DR cases are identified and discriminated using the kernel extreme learning machine (KELM) model. For evaluating DR severity, our work utilizes four different benchmark datasets: APTOS 2019, MESSIDOR-2 dataset, DiaRetDB1 V2.1, and DIARETDB0 datasets. To illuminate data noise and unwanted variations, two preprocessing steps are carried out, which include contrast enhancement and illumination correction. The experimental results evaluated using well-known indicators demonstrate that the suggested method achieves a higher accuracy of 99.63% compared to other baseline methods. This research contributes to the development of powerful DR screening techniques that are less time-consuming and capable of automatically identifying DR severity levels at a premature level.

糖尿病是一种常见的全球性严重疾病,它会损害眼部血管,导致视力下降。对这一问题进行早期准确诊断对于降低视力损伤风险至关重要。用于糖尿病视网膜病变(DR)分级的典型深度学习(DL)方法往往耗时较长,而且由于病变特征的表征不充分,导致检测性能不尽如人意。为了克服这些挑战,本研究提出了一种新的自动检测和分级 DR 的机制,旨在识别 DR 的严重程度和不同阶段。为了找出并捕捉 DR 样本的特征,在一个集合网模型中利用了共轭注意力机制和视觉转换器,自动生成用于诊断 DR 的特征图。然后,通过融合注意力网络模型中的特征融合功能将这些提取的特征图进行融合,计算注意力权重以生成最强大的特征图。最后,使用核极端学习机(KELM)模型识别和区分 DR 病例。为了评估 DR 的严重程度,我们的工作使用了四个不同的基准数据集:APTOS 2019、MESSIDOR-2 数据集、DiaRetDB1 V2.1 和 DIARETDB0 数据集。为了消除数据噪声和不必要的变化,进行了两个预处理步骤,包括对比度增强和光照校正。使用知名指标评估的实验结果表明,与其他基线方法相比,建议的方法达到了 99.63% 的较高准确率。这项研究有助于开发功能强大的 DR 筛选技术,这种技术耗时少,能够自动识别过早出现的 DR 严重程度。
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引用次数: 0
Can Angle Measures Be Useful in MCR Analyses? 角度测量在 MCR 分析中有用吗?
IF 2.3 4区 化学 Q1 SOCIAL WORK Pub Date : 2024-08-14 DOI: 10.1002/cem.3582
Klaus Neymeyr, Martina Beese, Hamid Abdollahi, Mathias Sawall

In MCR analyses, the similarity of pairs of spectra or concentration profiles can be measured in terms of the acute angle that is enclosed by the representing vectors. Acute angles between vectors can be generalized to pairs of subspaces. So-called canonical angles, also called principal angles, measure the mutual orientation of a pair of subspaces. This work discusses how angles and canonical angles can support multivariate curve resolution analyses. A canonical angle analysis (CAA) can help to detect changes of the chemical composition during a chemical reaction in a way comparable, but different to the evolving factor analysis (EFA).

在 MCR 分析中,光谱或浓度曲线对的相似性可以用代表向量所围成的锐角来衡量。矢量之间的锐角可以推广到子空间对。所谓的典型角(也称为主角)可以测量一对子空间的相互方向。本研究将讨论角度和典型角度如何支持多元曲线解析分析。典型角分析 (CAA) 可以帮助检测化学反应过程中化学成分的变化,其方法与演化因子分析 (EFA) 类似,但又有所不同。
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引用次数: 0
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Journal of Chemometrics
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