Supervised chemometric analysis

Table 7.1 Authentication of the geographical origin of virgin olive oil samples comparative results of SEXIA expert system, neural networks and the supervised chemometric procedure of stepwise linear discriminant analysis. Samples collected in the regions of Jaen (Spain)...

Table 7.2 Authentication of mono varietal virgin olive oils comparative results of fuzzy logic algorithms (Calvente and Aparicio, 1995) and the supervised chemometric procedure of linear discriminant analysis. Chemical compounds used linolenic acid, 24-methylen-cycloarthanol sterol and copaene hydrocarbon...

For the example in Fig. 2, the Fourier transformed NMR spectra (variables or descriptors being intensity as a function of frequency) were utilized for the creation of the data matrix D. It should be noted that many different descriptors can be used to create D, with the descriptor selection depending on the analysis method and the information to be extracted. For example, in the spectral resolution methods (Section 6), the desired end result is the determination of the true or pure component spectra and relative concentrations present within the samples or mixtures [Eq. (4)]. For this case, the unmodified real spectra Ij co) are commonly used for the chemometric analysis. In contrast, for the non-supervised and supervised methods described in Sections 3 and 4, the classification of a sample into different categories is the desired outcome. For these types of non-supervised and supervised methods the original NMR spectrum can manipulated or transformed to produce new descriptors including... 

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. 

Since 1992 a variety of related but much more powerful data-handling strategies have been applied to the supervised analysis of PyMS data. Such methods fall within the framework of chemometrics the discipline concerned with the application of statistical and mathematical methods to chemical data.81-85 These methods seek to relate known spectral inputs to known targets, and the resulting model is then used to predict the target of an unknown input.86... 

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.

When a supervised analysis is mentioned in the pharmaceutical industry, it often refers to a concentration prediction using a chemometric model. By nature, the objective of the analysis is not to identify the ingredients of the sample, as they are all known. Rather, the aim is to predict their concentrations in the sample. 

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. 

These various chemometrics methods are used in those works, according to the aim of the studies. Generally speaking, the chemometrics methods can be divided into two types unsupervised and supervised methods(Mariey et al., 2001). The objective of unsupervised methods is to extrapolate the odor fingerprinting data without a prior knowledge about the bacteria studied. Principal component analysis (PCA) and Hierarchical cluster analysis (HCA) are major examples of unsupervised methods. Supervised methods, on the other hand, require prior knowledge of the sample identity. With a set of well-characterized samples, a model can be trained so that it can predict the identity of unknown samples. Discriminant analysis (DA) and artificial neural network (ANN) analysis are major examples of supervised methods. 

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... 

Mass spectrometry and chemometric methods cover very diverse fields Different origin of enzymes can be disclosed with LC-MS and multivariate analysis [45], Pyrolysis mass spectrometry and chemometrics have been applied for quality control of paints [46] and food analysis [47], Olive oils can be classified by analyzing volatile organic hydrocarbons (of benzene type) with headspace-mass spectrometry and CA as well as PC A [48], Differentiation and classification of wines can similarly be solved with headspace-mass spectrometry using unsupervised and supervised principal component analyses (SIMCA = soft independent modeling of class analogy) [49], Early prediction of wheat quality is possible using mass spectrometry and multivariate data analysis [50],... 

In contrast to exploratory data analysis that mostly uses unsupervised learning, supervised learning involves developing models from data that are paired with a desired set of outcomes, which are used to guide the estimation of the models. In chemometrics. 

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