Chemometrics unsupervised techniques

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 More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR.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. 

Pattern Recognition. The application of computers to build descriptive or predictive models (i.e., find patterns) of information from input datasets. The techniques of pattern recognition overlap those used in statistics, chemometrics, and data mining, and include data display, description, and reduction, unsupervised methods such as cluster analy-... 

In complex systems where the number of groups to be separated during classification becomes larger, the performance of simple unsupervised methods (Section 3) degrades, requiring the use of more sophisticated supervised chemometric techniques. Additionally, in fields such a process NMR where there is a need for quantifying a component, the use of supervised methods becomes necessary. The different supervised methods described in the sections below have all been utilized in the chemometric analysis of NMR data for classification and/or quantitation. Examples utilizing these different techniques are discussed in Section 5. 

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. 

In chemometrics we are very often dealing not with individual signals, but with sets of signals. Sets of signals are used for calibration purposes, to solve supervised and unsupervised classification problems, in mixture analysis etc. All these chemometrical techniques require uniform data presentation. The data must be organized in a matrix, i.e. for the different objects the same variables have to be considered or, in other words, each object is characterized by a signal (e.g. a spectrum). Only if all the objects are represented in the same parameter space, it is possible to apply chemometrics techniques to compare them. Consider for instance two samples of mineral water. If for one of them, the calcium and sulphate concentrations are measured, but for the second one, the pH values and the PAH s concentrations are available, there is no way of comparing these two samples. This comparison can only be done in the case, when for both samples the same sets of measurements are performed, e.g. for both samples, the pH values, and the calcium and sulphate concentrations are determined. Only in that case, each sample can be represented as a point in the three-dimensional parameter space and their mutual distances can be considered measures of similarity. 

After applying the appropriate pre-processing, different chemometric techniques can be applied according to the aim of the study. Pattern recognition is one of the chemometric methods most used in analytical chemistry and this is true for separations data. Pattern recognition can be generally divided into two classes exploratory data analysis and unsupervised and supervised pattern recognition (Otto, 2007 Brereton, 2007). 

Statistical Analysis and Reporting Methods for statistical analysis of metabonomics data sets include a variety of supervised and unsupervised multivariate techniques (Holmes et al., 2000) as well as univariate analysis strategies. These chemometric approaches have been recently reviewed (Holmes and Antti, 2002 Robertson et al., 2007), and a thorough discussion of these is outside the scope of this chapter. Perhaps the best known of the unsupervised multivariate techniques is principle component analysis (PCA) and is widely... 

Daszykowski M. From Projection Pursuit to other unsupervised chemometric techniques. 1 Chemometr 2007 21 270-9. 

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