Faculty of Chemistry, Institute for Advanced Studies in Basic Sciences , P.O. Box 45195-1159, Zanjan, Iran.
Institute of Process Engineering, Faculty of Engineering, University of Szeged , Moszkvai krt. 5-7, H-6725 Szeged, Hungary.
Anal Chem. 2017 Feb 21;89(4):2259-2266. doi: 10.1021/acs.analchem.6b03134. Epub 2017 Feb 3.
Multivariate curve resolution (MCR) is a powerful methodology for analyzing chemical data in different application fields such as pharmaceutical analysis, agriculture, food chemistry, environment, and industrial and clinical chemistry. However, MCR results are often complicated by rotational ambiguity, meaning that there is a range of feasible solutions that fulfill the constraints and explain equally well the observed experimental data. Constraints determine the properties of resolved profiles in MCR methods by enforcing different assumptions on data. The applied constraints on chemical data sets should be derived from the physical nature and prior knowledge of the system under study. Therefore, the reliability of the constraints in order to get accurate results is a critical aspect that should be considered by analytical chemists who use MCR methods. Local rank information plays a key role in the curve resolution of multicomponent chemical systems. Applying the local rank constraint can reduce the extent of rotational ambiguity considerably, and in some cases, unique solutions can be achieved. Local rank exploratory methods like Evolving Factor Analysis (EFA) method provide local rank maps in order to obtain the presence pattern of components on the main assumption that the number of components in each window is equal to its rank. It is shown in this work that the local rank is a mathematical concept that may not be in concordance with chemical information. Thus, applying the local rank constraint for restricting the rotational ambiguity in MCR methods can lead to incorrect solutions! This problem is due to "local rank deficiency", which is introduced in this contribution.
多变量曲线分辨（MCR）是一种强大的方法，可用于分析制药分析、农业、食品化学、环境以及工业和临床化学等不同应用领域的化学数据。然而，MCR 结果常常受到旋转不确定性的影响，这意味着有一系列可行的解决方案可以满足约束条件，并同样很好地解释观察到的实验数据。约束条件通过对数据施加不同的假设来确定 MCR 方法中分辨谱的性质。应用于化学数据集的约束条件应源自所研究系统的物理性质和先验知识。因此，为了获得准确的结果，分析化学家应该考虑约束条件的可靠性，这是使用 MCR 方法的关键方面。局部秩信息在多组分化学系统的曲线分辨中起着关键作用。应用局部秩约束可以大大减少旋转不确定性的程度，并且在某些情况下，可以实现唯一的解决方案。局部秩探索方法，如演化因子分析（EFA）方法，提供局部秩图，以便根据每个窗口中组分的数量等于其秩的主要假设来获得组分的存在模式。本文表明，局部秩是一个数学概念，可能与化学信息不一致。因此，在 MCR 方法中应用局部秩约束来限制旋转不确定性可能会导致错误的解决方案！这个问题是由于“局部秩不足”引起的，本文对此进行了介绍。
