Historic:
The Multivariate Curve Resolution (MCR) methods are a group of techniques which intend the recovery of response profiles (spectra, pH profiles, time profiles, elution profiles,....) of the components in an unresolved mixture obtained in evolutionary processes when no prior information is available about the nature and composition of these mixtures.
MCR methods can be extended to the analysis of many types of experimental data including multiway data and non-evolutionary processes
The historical evolution of MCR methods is the following:
- Extension to more than two components
- Target Factor Analysis and Iterative Target Factor Analysis Methods
- Local Rank Detection, Window Factor Analysis and Rank Annihilation derived methods
- Selection of pure (selective) variables based methods
- Alternating Least Squares methods
- Extension to higher order data
Aim:
Under the assumption that mixtures matrices are bilinear, the aim is to recover the responses of every component (chemical species) in the different orders of
measurement: qualitative information, identification...etc
Algorithm:
The Multivariate Curve Resolultion uses Alternating Least Squares (ALS) algorithm (Optional constraints are applied at each iteration)
1- Initial estimates of C or S are obtained from OPA on a single matrix
2- From S coming from OPA, C is estimated with C = X.S.(ST.S)-1
3- C can be constrained according to selected constraints (=Cnew)
4- new S are then calculated according to Snew = XT.Cnew.(CnewT.Cnew)-1
5- Residuals are calculated: R = X - Cnew.SnewT
6- The Sum of squares of the residuals (SSR) and the change between 2 successive iterations are evaluated.
7- Go to step 1 till the maximum number of iterations is reached or till the change between 2 iterations is lower than a predefined threshold.
This method concerns here the simultaneous analysis of a set of correlated data matrices: Three-way data analysis
It works under the assumption that every data matrix included in the simultaneous analysis is still bilinear, and that is the the most common situation in chemistry
It brings the following advantages:
a- Unique decompositions are easily achieved for trilinear data
b- Resolution local rank conditions are achieved in many situations for welldesigned experiments (unique solutions)
c- Rank deficiency problems can be more easily solved
Code:
- The code of OPA is originally coming from the ChemoAC toolbox (F.C Sanchez et al.)
- The code of ALS for unfolded matrices is originally coming from the team of R.Tauler (Es). It is freely available from http://www.ub.es/gesq/mcr/mcr.htm
Applications:
Batch process data, Chromatographic data ...
Dataset reference:
VUBdatatest.mat
References:
[1] - R. Tauler, D. Barcelo, Trends in analytical chemistry, 12, 319-327 (1993)
[2] - R. Tauler, B. Kowalski, S. Fleming, Anal. Chem., 65, 2040-2047 (1993)
[3] - R.Tauler, A.Smilde, B.Kowalski, Journal of Chemometrics, 9, 31-58 (1995)
[4] - A.de Juan, S.C.Rutan, R.Tauler, D.L.Massart, Anal. Chim. Acta, 346, 307-318 (1997)
[5] - R. Tauler, Chemom. Intell. Lab. Syst., 30, 133-146 (1995)
[6] - S. Gourvénec, C. Lamotte, P. Pestiaux, D.L. Massart, Applied Spectroscopy, in press (2002)
DESCRIPTION
OF OPA3D METHOD