Iterative target transformation factor

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

Factor rotation by iterative target transformation factor analysis (ITTFA)... 

Iterative target transformation factor analysis (ITTFA) is an extension of TTFA and has been introduced by Hopke et al. [12] in environmetrics and by Gemperline [13,14] and Vandeginste et al. [15] in chromatography. The idea behind ITTFA is... 

B.G.M. Vandeginste, F. Leyten, M. Gerritsen, J.W. Noor, G. Kateman and J. Frank, Evaluation of curve resolution and iterative target transformation factor analysis in quantitative analysis by liquid chromatography. J. Chemom., 1 (1987) 57-71. 

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. 

This algorithm has many aspects similar to Iterative Target Transform Factor Analysis, ITTFA, as discussed in Chapter 5.2.2, and Alternating Least-Squares, ALS as introduced later in Chapter 5.4. The main difference is the inclusion of the window information as provided by the EFA plots. 

Several additional comments are due. As observed in Chapter 5.2.2, Iterative Target Transform Factor Analysis, ITTFA, iterative progress is relatively fast at the beginning and slows down continuously with the number of iterations. The third panel of Figure 5-42 demonstrates that the minimum has not been reached at all after 100 iterations. While the concentration profiles are reasonably well reproduced, there are some problems with the absorption spectra one spectrum has a substantial contribution from another. Nevertheless, considering the simplicity of the algorithm the results are astoundingly accurate. 

ALS should more correctly be called Alternating Linear Least-Squares as every step in the iterative cycle is a linear least-squares calculation followed by some correction of the results. The main advantage and strength of ALS is the ease with which any conceivable constraint can be implemented its main weakness is the inherent poor convergence. This is a property ALS shares with the very similar methods of Iterative Target Transform Factor Analysis, TTTFA and Iterative Refinement of the Concentration Profiles, discussed in Chapters 5.2.2 and 5.3.3. 

There are several different iterative algorithms that have been used for SMCR, including alternating least squares (ALS)63 and iterative target transformation factor analysis (ITTFA).64 For more detailed information, the reader is referred to these references. 

Iterative Target Transformation Factor Analysis (ITTFA)...437... 

The next subsection deals first with aspects common to all resolution methods. These include (1) issues related to the initial estimates, i.e., how to obtain the profiles used as the starting point in the iterative optimization, and (2) issues related to the use of mathematical and chemical information available about the data set in the form of so-called constraints. The last part of this section describes two of the most widely used iterative methods iterative target transformation factor analysis (ITTFA) and multivariate curve resolution-alternating least squares (MCR-ALS). 

Vandeginste, B.G.M., Derks, W., and Kateman, G., Multicomponent self-modeling curve resolution in high performance liquid chromatography by iterative target transformation factor analysis, Anal. Chim. Acta, 173, 253-264, 1985. 

ITTFA—iterative target transformation factor analysis... 

The first study on curve resolution, carried out by Kaiser [1] in 1958, proposed the varimax method, wherein factor rotation was used in factor analysis. Studies by Lawton and Sylvestre of Kodak clearly picked up on curve resolution technology as a means of reaction analysis in chemistry (1971, 1974) [2]. The idea of employing rotating matrices was first used in iterative target transformation factor analysis... 

Iterative Target Testing is another approach. The preliminary approximations of the real factors are chosen, based on the first (VARIMAX) rotation of the abstract PCA solution. With iterative target testing the factors are transformed to the best approximations. It can be considered as LSO, where PCA and VARIMAX are supplying the model. Clusters with an arbitrary number of peaks can be deconvoluted. Six component systems are tested (Vandeginste et al. 

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