Chemometrics-based approach

In Chapter 69, we worked out the relationship between the calculus-based approach to least squares calculations and the matrix algebra approach to least-squares calculations, using a chemometrics-based approach [1], Now we need to discuss a topic squarely based in the science of Statistics. 

Kell DB, Winson MK, Goodacre R, Woodward AM, Alsberg BK, Jones A, Timmins EM, Rowland JJ (1998) DRASTIC (Diffuse Reflectance Absorbance Spectroscopy Taking In Chemometrics). A novel, rapid, hyperspectral, FT-IR-based approach to screening for biocatalytic activity and metabolite overproduction. In Kieslich K (ed) New Frontiers in Screening for Microbial Biocatalysts. Elsevier Science B. V., The Netherlands, p 61... 

DRASTIC (Diffuse Reflectance Absorbance Spectroscopy Taking In Chemometrics). a novel, rapid, hyperspectral, FT-IR-based approach to screening for biocatalytic activity and metabolite overproduction... 

Winson, M. K., Goodacre, R., Timmins, E. et al (1997a) Diffuse reflectance absorbance spectroscopy taking in chemometrics (DRASTIC). A hyperspectral FT-IR-based approach to rapid screening for metabolite overproduction. Analytica Chimica Acta, in press. 

Although the above statement defines the concept of /-chemometric methods, many important aspects remain to be clarified in order to better understand what an interval-based approach consists of and what its implications are. 

We have previously underlined that the absence of a common linear intensity axis (spectra not properly normalized) would lead to erroneous predictions in quantitative spectral analyses and in meaningless interpretations for exploratory data analyses. Another prerequisite for multivariate data analysis is that the data conform to the selected model. An assumption that applies to most of the multivariate methods is that the data are low rank bilinear. For most multivariate methods, this implies that the spectral axis must remain constant, that is, the signal(s) for a given chemical compound must appear at the same position in all the spectra. We will see how a different interval-based approach, not aimed at building chemometric models, but rather at spectral data preprocessing can effectively contribute to achieve an efficient and comprehensive horizontal signal alignment. 

Mathews and Rawlings (1998) successfully applied model-based control using solids hold-up and liquid density measurements to control the filtrability of a photochemical product. Togkalidou etal. (2001) report results of a factorial design approach to investigate relative effects of operating conditions on the filtration resistance of slurry produced in a semi-continuous batch crystallizer using various empirical chemometric methods. This method is proposed as an alternative approach to the development of first principle mathematical models of crystallization for application to non-ideal crystals shapes such as needles found in many pharmaceutical crystals. 

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. ... 

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

There are some chemometric (chemometrics is a statistical area which combines statistics and chemistry) tools which use the chemical descriptors and/or fragments of the chemicals used to build up the model, and compare if the chemical descriptors and/or fragments of the target chemical are similar. An example of this approach is given by the freely available software AMBIT. A major disadvantage of this approach is that it is based only on the chemical information. 

Another recent tool has been developed within the ORCHESTRA project. The tool keeps into account both the chemometric information and the toxicity predictions done by the model, and in particular what kind of errors have been done by the model. It applies to the CAESAR QSAR models. Furthermore, this tool is based not only on the a priori data and information, as the other approaches, but also on the a posteriori result of the model. The user knows if the model can or cannot be used for a certain compound. In some cases a warning is given, recommending expert opinion. In all cases the reasons for the reliability is given, and it can be evaluated in a transparent way. 

So now we have done a moderately thorough job of investigating the relationship between the calculus approach to least squares and the matrix algebra approach, based on their chemometrics. But the original purpose of this chapter was stated to be an investigation of the relationship between Chemometrics and Statistics. What does our discussion here have to do with that Come back and read the exciting conclusion in our next chapter. 

Despite the broad definition of chemometrics, the most important part of it is the application of multivariate data analysis to chemistry-relevant data. Chemistry deals with compounds, their properties, and their transformations into other compounds. Major tasks of chemists are the analysis of complex mixtures, the synthesis of compounds with desired properties, and the construction and operation of chemical technological plants. However, chemical/physical systems of practical interest are often very complicated and cannot be described sufficiently by theory. Actually, a typical chemometrics approach is not based on first principles—that means scientific laws and mles of nature—but is data driven. Multivariate statistical data analysis is a powerful tool for analyzing and structuring data sets that have been obtained from such systems, and for making empirical mathematical models that are for instance capable to predict the values of important properties not directly measurable (Figure 1.1). 

In terms of computer-based and chemometric approach, additional improvements were also needed in mathematical models for chromatography and in method development, in order to help identifying the correct type of model and the adequate experimental parameters then, application to high volume of generated data is possible. 

IR instruments are available in filter-based, grating-based, and FT-based models. The usual approach is to use a full-spectrum model to ascertain the working wavelengths for a particular reaction, then to apply simpler filter instruments to the process. This works where one, two, or three discrete wavelengths may be used for the analysis. If complex, chemometric models are used, and full-spectrum instruments are needed. 

Frake et al. compared various chemometric approaches to the determination of the median particle size in lactose monohydrate with calibration models constrncted by MLR, PLS, PCR or ANNs. Overall, the ensuing models allowed mean particle sizes over the range 20-110/tm to be determined with an error less than 5 pm, which is comparable to that of the laser light diffraction method nsed as reference. Predictive ability was similar for models based on absorbance and second-derivative spectra this confirms that spectral treatments do not suppress the scattering component arising from differences in particle size. 

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