DESCRIPTION OF OPA METHOD
Historic:
The Orthogonal Projection Approach (OPA) was set by F.C. Sanchez, D.L. Massart et al. in 1996
Aim:
Under the assumption that the studied mixture matrix is bilinear, the aim is to recover the responses of every component (chemical species) in the different orders of measurement: qualitative information, identification...etc (i.e. bilinear resolution of the data matrix)
Algorithm:
OPA uses the 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.
Code:
Matlab code is originally coming from the ChemoAC toolbox - Vrije Universiteit Brussel (VUB) - Belgium

Applications:
Batch process data, Chromatographic data ...
Dataset reference:
VUBdatatest.mat
References:
[1] - F.C. Sánchez, J.Toft, B. Van den Bogaert, D.L. Massart, Anal. Chem., 68, 79-85 (1996)
[2] - F.C. Sánchez, B.G.M. Vandeginste, T.M. Hancewicz, D.L. Massart, Anal. Chem., 69, 1477-1484 (1997)
[3] - K. De Braekeleer, D.L. Massart, Chemom. Intell. Lab. Sys., 39, 127-141 (1997)
[4] - F.C. Sánchez, S.C. Rutan, M.D. Gil Garcia, D.L. Massart, Chemom. Intell. Lab. Sys., 36, 153-164 (1997)
[5] - S. Gourvénec, D.L. Massart, D.N. Rutledge, Chemom. Intell. Lab. Sys., 61, Issue 1-2, 51-61 (2002)