Multivariate Curve Resolution: 50 years addressing the mixture analysis problem – A review

Highlights: • The main advances of Multivariate Curve Resolution from 1971 to 2020 are reviewed. • New constraints based on mathematical or natural profile properties are described. • New challenging data structures used in MCR are presented. • Main advances in estimating and understanding the ambiguity phenomenon are addressed. • New application domains, such as -omics, imaging or multidimensional chromatography are mentioned. 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.