Chemometrics supervised techniques

In a related paper Herrador and Gonzalez [144] described the application of PCA and CA and of two supervised techniques, LDA and back-propagated ANN on Al, Ba, Ca, Cu, K, Mg, Mn, and Zn data obtained from commercial Spanish tea samples. A minitorch ICP-AES instrument was used for the determinations. The characterization of three classes of tea was achieved. In a paper that expands previous research described in reference [47], trace metal concentrations measured by ICP-AES and ICP-MS were employed by Moreda-Pineiro et al. [145] for a more elaborated chemometric treatment on 85 samples of tea of Asian, African, commercial, and unknown origin. Seventeen elements (Al, Ba, Ca, Cd, Co, Cr, Cu, Cs, Mg, Mn, Ni, Pb, Rb, Sr, Ti, V, and Zn) were determined. In addition to the techniques employed in the already mentioned papers (PCA, CA, LDA), soft independent modeling (SIM) of class analogy was also applied. The latter method resulted in the totally correct (100 percent) classification of Chinese teas. 

Once the data are prepared, they can be explored chemometrically with techniques as PCA, rPCA, PP, and clustering. These enable visualization of the structure of the data set more specifically, they detect outliers and group similar samples. For several applications, it was confirmed that this approach outperforms the visual comparison of electropherograms. Chemometric techniques can also be apphed to classify samples based on their CE profile. When the classes in the data set are a priori known, supervised classification techniques as EDA, QDA, kNN, CART, PLSDA, SIMCA, and SVM can be used. The choice of techniques will often depend on the preference of the analyst and the complexity of the data. However, when nonlinear classification problems occur, a more complex technique as, for instance, SVM, will be outper-... 

CONTENTS 1. Chemometrics and the Analytical Process. 2. Precision and Accuracy. 3. Evaluation of Precision and Accuracy. Comparison of Two Procedures. 4. Evaluation of Sources of Variation in Data. Analysis of Variance. 5. Calibration. 6. Reliability and Drift. 7. Sensitivity and Limit of Detection. 8. Selectivity and Specificity. 9. Information. 10. Costs. 11. The Time Constant. 12. Signals and Data. 13. Regression Methods. 14. Correlation Methods. 15. Signal Processing. 16. Response Surfaces and Models. 17. Exploration of Response Surfaces. 18. Optimization of Analytical Chemical Methods. 19. Optimization of Chromatographic Methods. 20. The Multivariate Approach. 21. Principal Components and Factor Analysis. 22. Clustering Techniques. 23. Supervised Pattern Recognition. 24. Decisions in the Analytical Laboratory. 

Fig. 5. An example of a scores plot as one might obtain in a principal components analysis. Distinct clustering or grouping of NMR spectra is observed in this type of plot, where the discrimination results from the analyzed metric used (e.g., principal components). The distance between samples (r ) within groups is used by many supervised methods to further describe and improve class or group separation. There are different chemometric techniques that can be used to identify outliers, or to provide a group assignment.

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... 

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