Direct classic least square method

The next example of an OTC map was treated first using a direct classic least square (DCLS) method, and then with more sophisticated multivariate analysis methods. The tablet was mapped over 800 X 800 gm with 10 gm steps. The data were baseline-corrected and normalized before being subjected to an unsupervised multivariate analysis. The first set of results was produced using univariate analysis (Figure 11.8a), when a manual exploration revealed three distinguishable and... 

The CLS method hinges on accurately modelling the calibration spectra as a weighted sum of the spectral contributions of the individual analytes. For this to work the concentrations of all the constituents in the calibration set have to be known. The implication is that constituents not of direct interest should be modelled as well and their concentrations should be under control in the calibration experiment. Unexpected constituents, physical interferents, non-linearities of the spectral responses or interaction between the various components all invalidate the simple additive, linear model underlying controlled calibration and classical least squares estimation. 

Figure 12.8 displays an organization chart of various quantitative methods, in an effort to better understand their similarities and differences. Note that the first discriminator between these methods is the direct versus inverse property. Inverse methods, such as MLR and partial least squares (PLS), have had a great deal of success in PAT over the past few decades. However, direct methods, such as classical least squares (CLS) and extensions thereof, have seen a recent resurgence [46-51]. The criterion used to distinguish between a direct and an inverse method is the general form of the model, as shown below ... 

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. ... 

In some cases, small amount of caffeine is added to soft drinks. Caffeine has a classic bitter taste that enhances other flavors. UV spectrometry, HPLC, and CE are used for the determination of caffeine in beverages. All of the above methods require sample preparation. FTIR spectroscopy with chemometrics, using partial least squares first derivative spectrum in the region between 2800 and 3000 cm have been developed to directly determine the caffeine in soft drinks. 

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