Refinement of the Concentration Profiles

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. 

A brief description of the algorithm (as usual, everything is based on Y=CA)  

Model-free methods do neither supply absolute information about the concentrations or about the spectra. Essentially they only deliver the shapes for the profiles. In this and future examples, we normalise the concentration profiles in C to a maximum of 1 and adjust the species spectra of A in such a way that the product CA is correct. This is done in the function norm max, m. 

It is worthwhile to compare this iterative refinement of concentration profiles as given on p.271 with ITTFA, the other iterative process we introduced in Chapter 5.2.2. 

The component spectra A can then be determined by the following rearrangements. Multiplication with (IFC)-1 1 from the left results in 

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The subsequent computation of the absorption spectra A from C and Y is a simple linear regression. This is followed by the normalisation of the concentration profiles to a maximum of one, as has been outlined already in the preceding chapter Iterative Refinement of the Concentration Profiles. The normalisation is done using the routine norm max. m (p.275). 

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. 

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