Supervised classification, chemometrics

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-... 

In terms of chemometrics, the concepts presented here fall into the category of supervised classification methods, because it must be known beforehand which group each specimen falls into. Unsupervised training methods also exist, in which samples are grouped based solely on the characteristics of the data. In order to use the methods presented here, the additional information, in other words, which samples belong to which group, must be known beforehand. It is conceivable, however, that that information could be derived from an unsupervised classification scheme and then applied to the supervised scheme. 

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. 

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. 

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. 

Technometrics. Vol. 17, pp. 103-109. ISSN 0040-1706 Meissen, W. Wehrens, R. Buydens, L. (2006). Supervised Kohonen networks for classification problems. Chemometrics and Intelligent Laboratory Systems. Vol. 83, pp. 99-113. ISSN 0169-7439... 

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],... 

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