Cluster analysis grouping

Figure 6. Bivariate plot of logic [Eu/Fe] vs logi0 [Mn/Fe], Samples are plotted by groups as determined by a cluster analysis. Group 1 does not have enough samples to form an ellipse.

Rodriguez, A., Tomas, M.S., Perez, J.J. and Rubio-Martinez, J. (2005) Assessment of the performance of cluster analysis grouping using pharmacophores as molecular descriptors. /. Mol. Struct. (Theochem), 727, 81-87. 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

The aim of cluster analysis is to group together similar objects. 

In dissimilarity-based compound selection the required subset of molecules is identified directly, using an appropriate measure of dissimilarity (often taken to be the complement of the similarity). This contrasts with the two-stage procedure in cluster analysis, where it is first necessary to group together the molecules and then decide which to select. Most methods for dissimilarity-based selection fall into one of two categories maximum dissimilarity algorithms and sphere exclusion algorithms [Snarey et al. 1997]. 

It has been shown that similar conformations that belong to adjacent energy basins separated by high energy barriers are incorrectly grouped together by the straightforward cluster analysis [29]. 

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. 

L. Kaufman and P.J. Rousseeuw, Finding Groups in Data An Introduction to Cluster Analysis. Wiley, New York, 1990. 

Inhomogeneities in data can be studied by cluster analysis. By means of cluster analysis both structures of objects and variables can be found without any pre-information on type and number of groupings (unsupervised learning, unsupervised pattern recognition). 

Methods of cluster analysis may be distinguished into two groups ... 

Rubin, J., Friedman, H. P., A Cluster Analysis and Taxonomy System for Grouping and Classifying Data, IBM Corporation, Scientific Center, New York, 1967. 

Beauchaine, T. P., Beauchaine, R. J. (2002). A comparison of maximum covariance and k-means cluster analysis in classifying cases into known taxon groups. Psychological Methods, 7, 245-261. 

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