Generalized rank annihilation factor analysis

Generalized rank annihilation factor analysis (GRAFA)... 

When several analytes have to be determined, this procedure needs to be repeated for each analyte. Because this algorithm requires that a PCA is calculated for each considered value of k, RAFA is computationally intensive. Sanchez and Kowalski [34] introduced generalized rank annihilation factor analysis (GRAFA). 

M.J.P. Gerritsen, H. Tanis, B.G.M. Vandeginste and G. Kateman, Generalized rank annihilation factor analysis, iterative target transformation factor analysis and residual bilinearization for the quantitative analysis of data from liquid-chromatography with photodiode array detection. Anal. Chem., 64 (1992) 2042-2056. 

E. Sanchez and B.R. Kowalski, Generalized rank annihilation factor analysis. Anal. Chem., 58... 

The first article of Sanchez and Kowalski [1986] on generalized rank annihilation factor analysis is purely based on equations, but later articles of the same group on spectral curve resolution contain line plots of the estimated spectra after the rank annihilation analysis [Sanchez et al. 1987, Ramos et al. 1987], Sanchez [et al. 1987] is mainly about simulated examples. See Figures 8.6 and 8.7. 

Sanchez, E. Kowalski, B.R. (1986). Generalized Rank Annihilation Factor Analysis, Analytical Chemistry, Vol.58, pp. 496-499, ISSN 0003-2700 Szabadai Z. (2005). Bazele fizico-chimice ale metodelor de control analitic al medicamentelor, Editura Mirton, Vol. II., pp. 4.38-4.96, ISBN 973-661-677-0, Timisoara, Romania... 

Rank annihilation methods employ eigenvalue-eigenvector analyses for direct determination of analyte concentration with or without intrinsic profile determination. With the exception of rank annihilation factor analysis, these methods obtain a direct, noniterative solution by solving various reconstructions of the generalized eigenvalue-eigenvector problem. 

The situation changes dramatically when two-way bilinear data are adopted to attack this kind of problem. Ho et al. [31] introduced rank annihilation factor analysis (RAFA) method to quantify the desired analytes in the presence of unknown interferents. The iterative procedure of RAFA was modified by Lorber [32], a direct approach with the generalized... 

Three-way calibrations methods, such as the generalized rank annihilation method (GRAM) and parallel factor analysis (PARAFAC), are becoming increasingly prevalent tools to solve analytical challenges. The main advantage of three-way calibration is estimation of analyte concentrations in the presence of unknown, uncalibrated... 

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