Inverse calibration, chemometrics

In chemometrics, the inverse calibration model is also denoted as the P-matrix model (the dimension of P is m x n) ... 

Partial least squares (PLS) and principal component regression (PCR) are the most widely used multivariate calibration methods in chemometrics. Both of these methods make use of the inverse calibration approach, where it i.s... 

In the field of chemometrics, PCR and PLS are the most widely used of the inverse calibration methods. Tliese methods solve the matrix inversion problem inherent to the inverse methods by using a linear combination of variables in... 

No chapter on modern chemometric methods would be complete without a mention of artificial neural networks (ANN). In a simple form these attempt to imitate the operation of neurons in the brain. Such networks have a number of linked layers of artificial neurons, including an input and an output layer (see Figure 8.13). The measured variables are presented to the input layer and are processed, by one or more intermediate ( hidden ) layers, to produce one or more outputs. For example, in inverse calibration, the inputs could be the absorbances at a number of wavelengths and the output could be the concentration of an analyte. The network is trained by an interactive procedure using a training set. Considering the example above, for each member of the training set the neural network predicts the concentration of the analyte. The discrepancy between the observed and predicted values... 

The use ofdiese classical experimental designs requires that the variables be set to prefetermined levels. Therefore, additional effon must be made to account for wiables that are not controllable. One chemometric approach is to allow these variables to vary naturally and to collect enough data to adequately modd their effect. This is the difference between the so-called natural and controllei calibration experiments (Martens and Nxs, 1989). When it is possible to mr iu e the variables, this can be done to verify that an adequate range has covered. Inverse models as discussed in Chapter 5 can then be used to implic y model their effect. (See also Appendix A.)... 

Spectrophotometric monitoring with the aid of chemometrics has also been applied to more complex mixtures. To solve the mixtures of corticosteroid de-xamethasone sodium phosphate and vitamins Bg and Bi2, the method involves multivariate calibration with the aid of partial least-squares regression. The model is evaluated by cross-validation on a number of synthetic mixtures. The compensation method and orthogonal function and difference spectrophotometry are applied to the direct determination of omeprazole, lansoprazole, and pantoprazole in grastroresistant formulations. Inverse least squares and PCA techniques are proposed for the spectrophotometric analyses of metamizol, acetaminophen, and caffeine, without prior separation. Ternary and quaternary mixtures have also been solved using iterative algorithms. 

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