Cluster analysis examples

Finding only the most important scales with respect to the prediction error does not indicate where in the wavenumber domain these features are located. Often it is observed that going from one resolution level to another has dramatic effect on the quality of the multivariate model. In such a case it is possible to perform a systematic search for where in the wavenumber region for the particular scale the important features are approximately localized. The method described here is only applied to the cluster analysis example, however it could have been used for other multivariate modelling techniques also. In cluster analysis, instead of prediction error, the interest is focused on properties such as overlap between clusters, cluster separation, cluster variance etc. In general, some interesting property H is observed to change with respect to the resolution level. 

The dimensionality of a data set is the number of variables that are used to describe eac object. For example, a conformation of a cyclohexane ring might be described in terms c the six torsion angles in the ring. However, it is often found that there are significai correlations between these variables. Under such circumstances, a cluster analysis is ofte facilitated by reducing the dimensionality of a data set to eliminate these correlation Principal components analysis (PCA) is a commonly used method for reducing the dimensior ality of a data set. 

Multiple linear regression is strictly a parametric supervised learning technique. A parametric technique is one which assumes that the variables conform to some distribution (often the Gaussian distribution) the properties of the distribution are assumed in the underlying statistical method. A non-parametric technique does not rely upon the assumption of any particular distribution. A supervised learning method is one which uses information about the dependent variable to derive the model. An unsupervised learning method does not. Thus cluster analysis, principal components analysis and factor analysis are all examples of unsupervised learning techniques. 

Hence there are multiple solutions for the final set of 10000 compounds. The final selection can be diversity driven using for example cluster analysis based on multiple fingerprints [63], hole filling strategies by using scaffold/ring analysis (LeadScope [66], SARVision [66]) or pharmacophore analysis [67, 68]. For a review of computational approaches to diversity and similarity-based selections, see the paper of Mason and Hermsmeier [69] and the references therein. 

Analytical results are often represented in a data table, e.g., a table of the fatty acid compositions of a set of olive oils. Such a table is called a two-way multivariate data table. Because some olive oils may originate from the same region and others from a different one, the complete table has to be studied as a whole instead as a collection of individual samples, i.e., the results of each sample are interpreted in the context of the results obtained for the other samples. For example, one may ask for natural groupings of the samples in clusters with a common property, namely a similar fatty acid composition. This is the objective of cluster analysis (Chapter 30), which is one of the techniques of unsupervised pattern recognition. The results of the clustering do not depend on the way the results have been arranged in the table, i.e., the order of the objects (rows) or the order of the fatty acids (columns). In fact, the order of the variables or objects has no particular meaning. 

Clustering or cluster analysis is used to classify objects, characterized by the values of a set of variables, into groups. It is therefore an alternative to principal component analysis for describing the structure of a data table. Let us consider an example. 

Two examples of unsupervised classical pattern recognition methods are hierarchical cluster analysis (HCA) and principal components analysis (PCA). Unsupervised methods attempt to discover natural clusters within data sets. Both HCA and PCA cluster data. 

A sample may be characterized by the determination of a number of different analytes. For example, a hydrocarbon mixture can be analysed by use of a series of UV absorption peaks. Alternatively, in a sediment sample a range of trace metals may be determined. Collectively, these data represent patterns characteristic of the samples, and similar samples will have similar patterns. Results may be compared by vectorial presentation of the variables, when the variables for similar samples will form clusters. Hence the term cluster analysis. Where only two variables are studied, clusters are readily recognized in a two-dimensional graphical presentation. For more complex systems with more variables, i.e. //, the clusters will be in -dimensional space. Principal component analysis (PCA) explores the interdependence of pairs of variables in order to reduce the number to certain principal components. A practical example could be drawn from the sediment analysis mentioned above. Trace metals are often attached to sediment particles by sorption on to the hydrous oxides of Al, Fe and Mn that are present. The Al content could be a principal component to which the other metal contents are related. Factor analysis is a more sophisticated form of principal component analysis. 

FIGURE 6.2 Representation of multivariate data by icons, faces, and music for human cluster analysis and classification in a demo example with mass spectra. Mass spectra have first been transformed by modulo-14 summation (see Section 7.4.4) and from the resulting 14 variables, 8 variables with maximum variance have been selected and scaled to integer values between 1 and 5. A, typical pattern for aromatic hydrocarbons B, typical pattern for alkanes C, typical pattern for alkenes 1 and 2, unknowns (2-methyl-heptane and meta-xylene). The 5x8 data matrix has been used to draw faces (by function faces in the R-library Tea-chingDemos ), segment icons (by R-function stars ), and to create small melodies (Varmuza 1986). Both unknowns can be easily assigned to the correct class by all three representations. 

In this example different methods of cluster analysis are applied to terpene data from wild growing, flowering Hyptis suaveolens originating from different locations in El Salvador (Grassi et al. 2005) it is a frequently used aromatic and medicinal plant of Central America. The collected plants were hydrodistilled and the resulting... 

It is this diversity of metabolites that presents the most difficult challenge. There are not only a variety of metabolites but they are also dynamic spatially and temporally. To master a universal "omics" approach, one has to have several measurement strategies. For example, a suite of quantitative methods analyzing key metabolites from different biochemical pathways and metabolic "fingerprinting" that compares patterns like multidimensional hierarchical clustering or principal cluster analysis.9... 

In most applications chemometric methods are applied to analytical data in an off-line mode that is, data has already been obtained by conventional techniques and is then applied to a particular chemometric method. Examples of this use are in cluster analysis and in pattern recognition. They are applied to spectroscopic, chromatographic, and other analytical data. 

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