Algorithm

Pure mathematics

Multivariate statistics

Ambiguity

Data mining

Computer science

Resolution (logic)

Tensor (intrinsic definition)

Multilinear map

Mathematics

Bilinear interpolation

Domain (mathematical analysis)

Mathematical analysis

Artificial intelligence

Heuristic

Programming language

Model selection

Machine learning

Computer vision

Analytica Chimica Acta

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.

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