Multivariate statistical analysis cluster analyses

Gas chromatography (GC)-MS coupled with multivariate statistical analysis proved valuable in verifying the authenticity of Echinacea species (Lienert et al, 1998). Similar root extracts could be grouped, based on the identified compounds from the GC-run, by principal component and cluster analysis. The correct grouping of the Echinacea species (i.e., purpurea, angustifolia, and pallida) was not influenced by the extraction method or by the aging process of the roots. 

Evidence of the appHcation of computers and expert systems to instmmental data interpretation is found in the new discipline of chemometrics (qv) where the relationship between data and information sought is explored as a problem of mathematics and statistics (7—10). One of the most useful insights provided by chemometrics is the realization that a cluster of measurements of quantities only remotely related to the actual information sought can be used in combination to determine the information desired by inference. Thus, for example, a combination of viscosity, boiling point, and specific gravity data can be used to a characterize the chemical composition of a mixture of solvents (11). The complexity of such a procedure is accommodated by performing a multivariate data analysis. 

Hierarchical Cluster Analysis (HCA) is a multivariate statistical method that can be used assign groundwater samples or monitoring sites to distinct categories (hydrochemical facies). HCA offers several advantages over other methods of... 

The compositional data was analyzed by multivariate statistics using 24 well-acquired elements (i.e., measured in all samples), free of contamination and dilution effects. These included Al, Ti, V, Cr, Mn, Fe, Co, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf and Ta. The log-transformed data with various treatments of the raw data, was analyzed by hierarchical cluster analysis, discriminant analysis and principal component analysis. 

The data processing of the multivariate output data generated by the gas sensor array signals represents another essential part of the electronic nose concept. The statistical techniques used are based on commercial or specially designed software using pattern recognition routines like principal component analysis (PCA), cluster analysis (CA), partial least squares (PLSs) and linear discriminant analysis (LDA). 

Marco, V R., Young, D. M., Turner, D. W. Commun. Statist. - Simula. 16 (1987) 485 Mardia, K.V, Kent, J.T., Bibby, J.M. Multivariate Analysis, Academic Press, London, 1979, pp. 191 Massart, D.L., Kaufman, L. The Interpretation of Analytical Data by the Lise of Cluster Analysis, Wiley, New York, 1983... 

The application of methods of multivariate statistics (here demonstrated with examples of cluster analysis, multivariate analysis of variance and discriminant analysis, and principal components analysis) enables clarification of the lateral structure of the types of feature change within a test area. 

In soil science, the empirical description of soil horizons predominates. Only a few applications of statistical methods in this scientific field are described. SCHEFFER and SCHACHTSCHABEL [1992] give an example for the classification of different soils into soil groups using cluster analysis. They claim the objectivity of the results to be one advantage of multivariate statistical methods. 

Principal component analysis is a popular statistical method that tries to explain the covariance structure of data by means of a small number of components. These components are linear combinations of the original variables, and often allow for an interpretation and a better understanding of the different sources of variation. Because PCA is concerned with data reduction, it is widely used for the analysis of high-dimensional data, which are frequently encountered in chemometrics. PCA is then often the first step of the data analysis, followed by classification, cluster analysis, or other multivariate techniques [44], It is thus important to find those principal components that contain most of the information. 

There are several books on pattern recognition and multivariate analysis. An introduction to several of the main techniques is provided in an edited book [19]. For more statistical in-depth descriptions of principal components analysis, books by Joliffe [20] and Mardia and co-authors [21] should be read. An early but still valuable book by Massart and Kaufmann covers more than just its title theme cluster analysis [22] and provides clear introductory material. 

There are many other statistical models which can be used for the evaluation of DICE studies. Inclusion of not only a group factor, but also a time factor in the experiment methods of the analysis of variance (ANOVA) can be applied to find expression changes within the temporal course of the protein expression or to find interactions between the group and time factor. Several multivariate statistical methods are of use, too. Spots with similar expression profiles can be grouped by cluster analysis or, on the other hand, new spots can be assigned to existing groups by the methods of discriminant analysis. 

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