Real samples statistical and hyphenated methods

The last group of methods for the exploitation of spectra of real samples involves not only factor analysis procedures and related methods but also the semi-deterministic approach. Both types of methods can be considered as statistical ones, but with a slight difference. Factors analysis and related methods are also described as black boxes, because they require no information. They function in a manner that is quite opposite to that of MLR methods, for which the response of all compounds of the sample must be known (which is obviously impossible for a real sample). Also, the semi-deterministic approach is based on a grey box type of model, where only a part of the information is needed, the other part remaining stochastic. 

In practice, for spectra exploitation, the main procedure is the principal component analysis (PCA), identifying a set of few factors (the first eigenvectors of the matrix), used for the interpretation of data. Then, any spectrum can be explained as a linear combination of these factors (as a decomposition step), the coefficients of which are the PCA scores. 

For the estimation of components concentration, a second step is required, based on a multiple linear regression (MLR, see Section 3.1.3) between the absorbance values and the PCA scores. This can be carried out automatically after the PCA step, with the principal component regression (PCR) procedure (including PCA). This methodology was first applied to analytical chemical problems by Lawton and Sylvestre [25], and has more recently been used in different models by other researchers [26-28], Finally, the PCA procedure can also be coupled with cluster analysis (CA), as described in a very recent study on the characterisation of industrial wastewater samples [29], 

Another method, very often used for NIR analysis, is the partial least squares (PLS) procedure. This method is slightly different from PCR, because the two steps of the last method (decomposition and regression) are carried out at the same time and the decomposition process also includes concentration information. The results (eigenvectors and scores) are thus different and generally more relevant, because they are more related 

A comparison between PCR and PLS is difficult because the quality of results is rather close (at least for a small set of data), but some specific advantages of the PLS can be drawn. The intermediate results (eigenvectors) are related to the initial physical data (looks like particular spectra). Moreover, the calibration step is more robust (if the data set is representative), and PLS can thus be used for the study of complex mixtures. Some known drawbacks are the computational time, the need for a large calibration set (representative) and some difficulties in understanding and explaining the resulting model. 

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