Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Instituto de Química de Rosario (IQUIR-CONICET), Suipacha 531, Rosario S2002LRK, Argentina.
Anal Chem. 2020 Jul 7;92(13):9118-9123. doi: 10.1021/acs.analchem.0c01395. Epub 2020 Jun 11.
Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with matrix data that cannot be arranged into a trilinear three-way array, that is, mostly from chromatographic origin with spectral detection. A range of feasible solutions may be found in MCR studies, due to the phenomenon of rotational ambiguity associated with bilinear decompositions of matrices. The application of chemically driven constraints is vital to achieving an adequate solution and minimizing the degree of rotational ambiguity present in the system. However, when studying complex samples, it may not be possible to recover unique solutions, even under the application of proper constraints. In such cases, it is important to be able to assess the propagation of rotation uncertainty to the estimated analyte concentrations, which stems from the existence of a finite range of feasible solutions. In this work, we present a new analytical parameter to estimate the potential uncertainty in analyte prediction brought about by rotational ambiguity, in the form of an associated root-mean-square error, named RMSE. The proposed parameter comes in the form of a range of values, whose limits are δ/(12) and δ/(3), with δ being defined as the difference between the maximum and minimum values of the analyte concentration that would be predicted by the MCR model from its concentration profiles lying in the range of feasible solutions, and corresponding to maximum and minimum area, respectively. We support our proposal on extensive simulations for systems of varying composition, and demonstrate its application on experimental data aimed at the determination of four pollutants in environmental water samples.
多元曲线分辨-交替最小二乘法 (MCR-ALS) 是处理无法排列成三线性三方矩阵的矩阵数据的首选模型，即主要来自具有光谱检测的色谱学。由于与矩阵双线性分解相关的旋转模糊现象，在 MCR 研究中可能会找到一系列可行的解决方案。应用化学驱动的约束对于获得合适的解决方案和最小化系统中存在的旋转模糊程度至关重要。然而，在研究复杂样品时，即使应用适当的约束，也可能无法恢复唯一的解决方案。在这种情况下，能够评估旋转不确定性对估计分析物浓度的传播非常重要，这源于可行解的有限范围。在这项工作中，我们提出了一个新的分析参数，以估计由于旋转模糊性引起的分析物预测的潜在不确定性，形式为相关均方根误差 (RMSE)。所提出的参数以一系列值的形式出现，其极限值为 δ/(12) 和 δ/(3)，其中 δ 定义为在可行解范围内，MCR 模型从其浓度分布预测的分析物浓度的最大值和最小值之间的差异，分别对应于最大和最小面积。我们通过对不同组成的系统进行广泛的模拟来支持我们的建议，并将其应用于旨在确定环境水样中四种污染物的实验数据。
