Data Analysis Classification

Other methods consist of algorithms based on multivariate classification techniques or neural networks they are constructed for automatic recognition of structural properties from spectral data, or for simulation of spectra from structural properties [83]. Multivariate data analysis for spectrum interpretation is based on the characterization of spectra by a set of spectral features. A spectrum can be considered as a point in a multidimensional space with the coordinates defined by spectral features. Exploratory data analysis and cluster analysis are used to investigate the multidimensional space and to evaluate rules to distinguish structure classes. 

Spectral features and their corresponding molecular descriptors are then applied to mathematical techniques of multivariate data analysis, such as principal component analysis (PCA) for exploratory data analysis or multivariate classification for the development of spectral classifiers [84-87]. Principal component analysis results in a scatter plot that exhibits spectra-structure relationships by clustering similarities in spectral and/or structural features [88, 89]. 

Often the goal of a data analysis problem requites more than simple classification of samples into known categories. It is very often desirable to have a means to detect oudiers and to derive an estimate of the level of confidence in a classification result. These ate things that go beyond sttictiy nonparametric pattern recognition procedures. Also of interest is the abiUty to empirically model each category so that it is possible to make quantitative correlations and predictions with external continuous properties. As a result, a modeling and classification method called SIMCA has been developed to provide these capabihties (29—31). 

Ball, G. H and Hall, D. J., Isodata, a novel method of data analysis and pattern classification, NTIS Report AD699616 (1965). 

Neural networks are helpful tools for chemists, with a high classification and interpretation capacity. ANNs can improve and supplement data arrangements obtained by common multivariate methods of data analysis as shown by an example of classification of wine (Li-Xian Sun et al. [1997]). 

Frank IE, Friedman JH (1989) Classification oldtimers and newcomers. J Chemom 3 463 Frank IE, Todeschini R (1994) The data analysis handbook. Elsevier, Amsterdam... 

Exploratory data analysis shows the aptitude of an ensemble of chemical sensors to be utilized for a given application, leaving to the supervised classification the task of building a model to be used to predict the class membership of unknown samples. 

Recently, introductory books about chemometrics have been published by R. G. Brereton, Chemometrics—Data Analysis for the Laboratory and Chemical Plant (Brereton 2006) and Applied Chemometrics for Scientists (Brereton 2007), and by M. Otto, Chemometrics—Statistics and Computer Application in Analytical Chemistry (Otto 2007). Dedicated to quantitative chemical analysis, especially using infrared spectroscopy data, are A User-Friendly Guide to Multivariate Calibration and Classification (Naes et al. 2004), Chemometric Techniques for Quantitative Analysis (Kramer 1998), Chemometrics A Practical Guide (Beebe et al. 1998), and Statistics and Chemometrics for Analytical Chemistry (Miller and Miller 2000). 

In this example, we apply D-PLS (PLS discriminant analysis, see Section 5.2.2) for the recognition of a chemical substructure from low-resolution mass spectral data. This type of classification problems stood at the beginning of the use of multivariate data analysis methods in chemistry (see Section 1.3). 

A great variety of different methods for multivariate classification (pattern recognition) is available (Table 5.6). The conceptually most simply one is fc-NN classification (Section 5.3.3), which is solely based on the fundamental hypothesis of multivariate data analysis, that the distance between objects is related to the similarity of the objects. fc-NN does not assume any model of the object groups, is nonlinear, applicable to multicategory classification, and mathematically very simple furthermore, the method is very similar to spectral similarity search. On the other hand, an example for a rather sophisticated classification method is the SVM (Section 5.6). 

Plots of melting point against optical purity are commonly referred to as phase-composition diagrams. The direct proportionality of melting point with heat of fusion has also been employed to construct similar plots based on thermal analysis data. The classification of racemic modifications into three different types with regard to their crystal packing (32) can be made based on the overall shape of these plots as follows ... 

From the outset acoustic chemometrics is fully dependent upon the powerful ability of chemometric full spectrum data analysis to elucidate exactly where in the spectral range (which frequencies) the most influential information is found. The complete suite of chemometric approaches, for example PCA, PLS regression, SIMCA (classification/discrimination) are at the disposition of the acoustic spectral data analyst there is no need here to delve further into this extremely well documented field. (See Chapter 12 for more detail.)... 

Figure 7 Wastewater classification on the basis of toxicological results (data analysis of 13 Russian regions).

Fig. 4. Application of bioinformatics tools to 2D-DIGE data analysis. Proteome data consisting of the normalized spot intensity values are exported from the image analysis software and their correlation with clinicopathological data examined. Using informatics tools including clustering algorithms and machine-learning methods, a novel cancer classification based on proteome data is established, and key proteomic features and proteins corresponding to biomarker candidates are identified.

Eigenvectors reduce the dimensionality of the data matrix when the rank of the covariance matrix is E < V, so that V — E eigenvalues vanish, or when some eigenvectors are not significant, the use of some classification methods with the scores on the first eigenvectors, instead of the original variables, can avoid singular matrices or/and noticeably speed up data analysis. 

Thus, the use of univariate criteria is advisable only when the number of variables is very large, or in a preliminary data analysis, because sometimes it is possible to find one or two variables that give enough information to solve the classification problem. In this way, Van der Greef et al. showed that Rhone and Bordeaux wines are almost completely separated in the plane of the masses 300 and 240. 

Bisani, M. L., Clementi, S. Chemometrics in Food Chemistry Classification of Camomiles from Central Italy, in Food Research and Data Analysis (Martens, H., Russwurm, H., eds.), p. 428, Applied Science Publ., Barking 1983... 

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