Mathematical pattern-recognition techniques

Progress in chemometrics has made a number of new statistical techniques available, which are increasingly being used. This concerns both new supervised and unsupervised (or pattern recognition ) techniques. Chemometrics was dehned about 25 years ago as the chemical discipline which uses mathematical, statistical and related techniques to design optimal measurement procedures and experiments, and to extract maximum relevant information from chemical data. The science of chemometrics has been developed to promote applications of statistics in analytical, organic and medicinal chemistry. 

PCA involves a mathematical procedure that transforms a number of correlated variables into a smaller number of uncorrelated variables called principal components (PCs). PCA can reduce the dimensionality of multidimensional space while yet retaining a large amount of the original information in the data. For example, two-dimensional data may be transformed into one-dimensional data, as shown in Figure 11.3. The first PC accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. Moreover, PCA is one of the unsupervised pattern recognition techniques, and therefore provides results unbiased by human input. 

H. C. Andrews, Introduction to Mathematical Techniques in Pattern Recognition, Wiley-Interscience, New York, 1972. 

Advanced mathematical and statistical techniques used in analytical chemistry are often referred to under the umbrella term of chemometrics. This is a loose definition, and chemometrics are not readily distinguished from the more rudimentary techniques discussed in the earlier parts of this chapter, except in terms of sophistication. The techniques are applied to the development and assessment of analytical methods as well as to the assessment and interpretation of results. Once the province of the mathematician, the computational powers of the personal computer now make such techniques routinely accessible to analysts. Hence, although it would be inappropriate to consider the detail of the methods in a book at this level, it is nevertheless important to introduce some of the salient features to give an indication of their value. Two important applications in analytical chemistry are in method optimization and pattern recognition of results. 

Relevant examples of the use of classification techniques range from the simple to the complex. Schaper et al. (1985) developed and used a very simple classification of response methodology to identify those airborne chemicals which alter the normal respiratory response induced by C02. At the other end of the spectrum, Kowalski and Bender (1972) developed a more mathematically based system to classify chemical data (a methodology they termed pattern recognition). 

The mathematical techniques employed in pattern recognition permit rapid and efficient identification of relationships and key aspects that otherwise might remain hidden in the large mass of numbers. Since the data base was not well characterized we set the following objectives for the interpretive study ... 

The field-desorption spectra of several aldoses and ketoses ionized by attachment of potassium ions led to the identification of the characteristic fragments formed by loss of small molecules, and related secondary ion analysis was carried out on various purine and pyrimidine nucleosides. Also in the nucleoside field a set of mathematical procedures has been applied to the spectra derived from 125 compounds and has led to pattern recognition and interpretation. Underivatized nucleosides have been studied by a method based on pulsed laser and fission fragment-induced desorption, and also by a chemical ionization technique dependent on a direct exposure probe. ... 

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