Cluster multivariate methods

Multivariate chemometric techniques have subsequently broadened the arsenal of tools that can be applied in QSAR. These include, among others. Multivariate ANOVA [9], Simplex optimization (Section 26.2.2), cluster analysis (Chapter 30) and various factor analytic methods such as principal components analysis (Chapter 31), discriminant analysis (Section 33.2.2) and canonical correlation analysis (Section 35.3). An advantage of multivariate methods is that they can be applied in... 

Preliminary data analysis carried out for the spectral datasets were functional group mapping, and/or hierarchical cluster analysis (HCA). This latter method, which is well described in the literature,4,9 is an unsupervised approach that does not require any reference datasets. Like most of the multivariate methods, HCA is based on the correlation matrix Cut for all spectra in the dataset. This matrix, defined by Equation (9.1),... 

Among the multivariate methods the most important are principal components analysis (PCA), factor analysis, cluster analysis and the pattern recognition method, from which only PCA will be briefly described below. PCA is used to find such a system of new variables, called principal components (PC), which explains the variation of a given data set in a more convenient way than the original system of variables, e.g. xl9...,Xj,...,xm. The greater convenience of PC consists mainly in a reduction of dimensions, m, in which the data were originally described, because the PC variables are chosen so that only two or three of them should be sufficient to characterize the variation of the data. The PC are linear combinations of the original variables, xj9 used to characterize the set of objects,... 

The following examples demonstrate the usefulness of multivariate methods in the evaluation of field ecological data and laboratory multispecies toxicity tests. In each of the examples, several multivariate techniques were used — generally Euclidean and cosine distances (Figure 11.29), principal components, and nonmetric clustering and association analysis. 

To find patterns in data and to assign samples, materials, or, in general, objects, to those patterns, multivariate methods of data analysis are applied. Recognition of patterns, classes, or clusters is feasible with projection methods, such as principal component analysis or factor analysis, or with cluster analysis. To construct class models for classification of unknown objects, we will introduce discriminant analyses. 

Chatfield and Collins (1980), in the introduction to their chapter on cluster analysis, quote the first sentence of a review article on cluster analysis by Cormack (1971) The availability of computer packages of classification techniques has led to the waste of more valuable scientific time than any other statistical innovation (with the possible exception of multiple-regression techniques). This is perhaps a little hard on cluster analysis and, for that matter, multiple regression but it serves as a note of warning. The aim of this book is to explain the basic principles of the more popular and useful multivariate methods so that readers will be able to understand the results obtained from the techniques and, if interested, apply the methods to their own data. This is not a substitute for a formal training in statistics the best way to avoid wasting one s own valuable scientific time is to seek professional help at an early stage. 

Exploratory analysis of spectral data by PCA, PLS, cluster analysis, or Kohonen mapping tries to get an insight into the spectral data structure and into hidden factors, as well as to find clusters of similar spectra that can be interpreted in terms of similar chemical structures. Classification methods, such as LDA. PLS, SIMCA, KNN classification, and neural networks, have been used to generate spectral classifiers for an automatic recognition of structural properties from spectral data. The multivariate methods mostly used for spectra prediction (mainly NMR. rarely IR) are neural networks. Table 6 contains a summary of recent works in this field (see Infrared Data Correlations with Chemical Structure). 

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. 

Techniques for multivariate input analysis reduce the data dimensionality by projecting the variables on a linear or nonlinear hypersurface and then describe the input data with a smaller number of attributes of the hypersurface. Among the most popular methods based on linear projection is principal component analysis (PCA). Those based on nonlinear projection are nonlinear PCA (NLPCA) and clustering methods. 

Use of multivariate approaches based on classification modelling based on cluster analysis, factor analysis and the SIMCA technique [98,99], and the Kohonen artificial neural network [100]. All these methods, though rarely implemented, lead to very good results not achievable with classical strategies (comparisons, amino acid ratios, flow charts) and, moreover it is possible to know the confidence level of the classification carried out. 

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... 

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