Chemometrics

Chemometrics has been defined as the chemical discipline that uses mathematical and statistical methods to design or select optimal measurement procedures and experiments and to provide maximum chemical information by analysing chemical data (Kowalski, 1978) It is a relatively new discipline that assists with (i) the planning of experiments, and (ii) the manipulation and interpretation of large data sets. Some aspects of chemometrics can be done using an appropriate speadsheet but the majority of applications require the use of dedicated software. The fundamental principles of most of the processes involved in chemometrics are those of statistics. You are therefore advised to become familiar with the material in Chapters 40 and 41 before proceeding. 

Once the experimental work has been completed you then need to consider how to interpret the results, i.e. how to maximize the chemical information inherent in the data. Initial attempts are often centred around plotting the data, to visualize trends and to allow conclusions to be drawn. The simplest form of data visualization is simply to tabulate the results (Chapter 38). As an example, if a class of students has determined the melting point of naphthalene, it is a relatively simple matter to tabulate the data (see Table 43.1). One possibility for the data is then to calculate the mean and standard deviation. Another approach would be to plot the data as a histogram, as in Fig. 43.1, so we are then able to make a visual interpretation of the quality of this univariate (one-variable) data. 

However, what if we had more than one variable to consider In other words, we have multivariate data. For example, what if we want to identify trends in the properties of a range of organic molecules The variables we might want to consider could be melting point, boiling point, Mt, solubility in a solvent and vapour pressure. We can, of course, tabulate the data, as before, but this does not allow us to consider any trends in the data. To do this we need to be able to plot the data. However, once we exceed three variables (which we need to be able to plot in three dimensions) it becomes impossible to produce a straightforward plot. It is in this context that chemometrics offers a solution, reducing the dimensionality to a smaller number of dimensions and hence the ability to display multivariate data. The most important technique in this context is called principal component analysis (PCA). 

Annual Review of Physical Chemistry Chemical Physics Chemical Physics Letters International Journal of Quantum Chemistry 

Journal of Chemical Physics Journal of Computational Chemistry Journal of Molecular Structure/Theochem Journal of Physical Chemistry Reviews in Computational Chemistry Theoretica Chimica Acta 

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Chemometrics is a convenient mathematical tool for developing QSRR or scaling laws that can be embedded in process models. It is somewhat analogous to Wei and Kuo s treatment in that it contracts system dimensions through a projective transformation. Each lump is a linear combination of all original variables. The widely used principal component analysis (PCA) and partial least squares (PLS) are two examples of chemometric modeling. 

Kohonen network Conceptual clustering Principal Component Analysis (PCA) Decision trees Partial Least Squares (PLS) Multiple Linear Regression (MLR) Counter-propagation networks Back-propagation networks Genetic algorithms (GA) 

The following sections present a more detailed description of the methods mentioned above. An overview of machine learning techniques in chemistry is given in Chapter IX, Section 1 in the Handbook. 

Chemometrics is the discipline which deals wdth the application of statistical and, in a more general sense, of mathematical methods to chemical data. Chemometric methods are used for the extraction of chemical information from chemical data. 

To enable the application of electronic data analysis methods, the chemical structures have to be coded as vectors see Chapter 8). Thus, a chemical data set consists of data vectors, where each vector, i.e., each data object, represents one chemical structure. 

Throughout this section x and y are vectors whose components are denoted as Xj,. . and Yi. y , respectively x is the mean of the components of x, y the mean for y. Data matrices are denoted as X and Y, respectively. 

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Soc. 1974, 96, 4S34--i842. pi3] D. Weininger, SMILES - a language for molecules and reactions, in Handbook of Chemoinformatics, J. Gasteiger (Ed.) Wiley-VCH, Weinheim, 2003, Chapter 11, Section 3. pi4] G. M. Crippen, T.F. Havel, Distance geometry and molecular conformations, in Chemometrics Research Studies Series 15 D. Bawden (Ed.), Research Studies Press (Wiley), New York, 1988. 

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

B.G.M. Vandeginste, L.M.C. Buydens, S. De Jong, P.J. Lewi, J. Smeyers-Verbeke, D.L. Massart, Handbook of Chemometrics and Qualimetrics, Elsevier Science, Amsterdam, 1998. 

M. Otto, Chemometrics. Statistics and Computer Application in Analytical Chemistry. Wiley-VCH, Weinheim, 1998. 

M. Otto, Chemometrie Statistik und Computereinsatz in der Analytik, WHey-VCH, Weinheim, 1997 M. Otto, Chemometrics. Statistics and Computer Application in Analytical Chemistry, Wiley-VCH, Weinheim, 1998. 

M. J. Adams, Chemometrics in Analytical Spedroscopy, The Royal Society of Chemistry, Cambridge,... 

K. R. Beebe, R. J. Pell, M.B. Seasholtz, Chemometrics A Pradical Guide, John WOey Sons, New York, 1998. 

J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics Part A, Elsevier, Amsterdam, 1997. 

Drewry D H and S S Young 1999. Approaches to the Design of Combinatorial Libraries. Chemometrics in Intelligent Laboratory Systems 48 1-20. 

Jurs P C1990. Chemometrics and Multivariate Analysis in Analytical Chemistry. In Lipkowitz K B and D B Boyd (Editors) Reviews in Computational Chemistry Volume 1. New York, VCH Publishers, pp. 169-212. 

History and Objectives of Quantitative Drug Design. In Hansch C, P G Sammes and J B lor (Editors) Comprehensive Medicinal Chemistry Volume 4. Oxford, Pergamon Press, pp. 1-31. emd H van de 1995. Chemometric Methods in Molecular Design. Weinheim, VCH Publishers. 

Note These equations are from Doming, S. N. Morgan, S. L. Experimental Design A Chemometric Approach. Elsevier Amsterdam, 1987, and pseudo-three-dimensional plots of the response surfaces can be found in their figures 11.4, 11.5, and 11.14. The response surface for problem (a) also is shown in Color Plate 13. 

Deming, S. N. Morgan, S. L. Experimental Design A Chemometric Approach. Elsevier Amsterdam, 1987. 

Morgan, E. Chemometrics Experimental Design. John Wiley and Sons Chichester, England, 1991. 

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