Chemometrics Group. Universitat de Barcelona. Dept. of Chemical Engineering and Analytical Chemistry, Martí I Franquès, 1, 08028, Barcelona, Spain.
IDAEA-CSIC. Environmental Chemometrics Group. Department of Environmental Chemistry, Jordi Girona 18, 08034, Barcelona, Spain.
Anal Chim Acta. 2021 Feb 8;1145:59-78. doi: 10.1016/j.aca.2020.10.051. Epub 2020 Oct 28.
Multivariate Curve Resolution (MCR) covers a wide span of algorithms designed to tackle the mixture analysis problem by expressing the original data through a bilinear model of pure component meaningful contributions. Since the seminal work by Lawton and Sylvestre in 1971, MCR methods are dynamically evolving to adapt to a wealth of diverse and demanding scientific scenarios. To do so, essential concepts, such as basic constraints, have been revisited and new modeling tasks, mathematical properties and domain-specific information have been incorporated; the initial underlying bilinear model has evolved into a flexible framework where hybrid bilinear/multilinear models can coexist, the regular data structures have undergone a turn of the screw and incomplete multisets and matrix and tensor combinations can be now analyzed. Back to the fundamentals, the theoretical core of the MCR methodology is deeply understood due to the thorough studies about the ambiguity phenomenon. The adaptation of the method to new analytical measurements and scientific domains is continuous. At this point of the story, MCR can be considered a mature yet lively methodology, where many steps forward can still be taken.
多元曲线分辨（MCR）涵盖了广泛的算法，旨在通过纯分量有意义贡献的双线性模型来表达原始数据，从而解决混合物分析问题。自 1971 年 Lawton 和 Sylvestre 的开创性工作以来，MCR 方法一直在动态发展，以适应各种多样且苛刻的科学场景。为此，基本概念（如基本约束）已经被重新审视，新的建模任务、数学性质和特定领域的信息已经被纳入；最初的基本双线性模型已经发展成为一个灵活的框架，混合双线性/多线性模型可以共存，正则数据结构发生了转变，现在可以分析不完备多集和矩阵以及张量的组合。回到基础，由于对模糊现象进行了深入研究，MCR 方法的理论核心得到了深刻的理解。该方法不断适应新的分析测量和科学领域。在故事的这一点上，MCR 可以被认为是一种成熟而充满活力的方法，它仍然可以向前迈出许多步。
