Cluster analysis parameters

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

Fig. 37.2. Principal components loading plot of 7 physicochemical substituent parameters, as obtained from the correlations in Table 37.5 [39,40]. The horizontal and vertical axes account for 46 and 31%, respectively, of the correlations. Most of the residual correlation is along the perpendicular to the plane of the diagram. The line segments define clusters of parameters that have been computed by means of cluster analysis.

Usually one cannot expect a unique solution for cluster analysis. The result depends on the used distance measure, the cluster algorithm, and the chosen parameters often... 

There is no one best cluster analysis method (see Table 6.2 for an overview). The variability in the methods and in the parameters demands some discipline of the user to avoid that cluster analysis is applied under different conditions until the desired result is obtained. 

Cluster analysis is simply a method to group entities, for which a number of properties or parameters exist, by similarity [292, 308-313]. Various distance measurements are used, and the analysis is performed in a sequential manner, reducing the number of clusters at each step. Such a procedure has been described for use in drug design and environmental engineering research as a way to group substituents that have the most similarity when various combinations of the electronic, steric, and statistically derived parameters are considered. 

The multivariate techniques which reveal underlying factors such as principal component factor analysis (PCA), soft Independent modeling of class analogy (SIMCA), partial least squares (PLS), and cluster analysis work optimally If each measurement or parameter Is normally distributed In the measurement space. Frequency histograms should be calculated to check the normality of the data to be analyzed. Skewed distributions are often observed In atmospheric studies due to the process of mixing of plumes with ambient air. 

Fig. 3.20 Hierarchical cluster analysis with euclidean distance of the autoscaled variables applied to voltammetric parameters recorded for mineral and pigment specimens studied here. From data in Table 3.2 (a) including greenish natural umber and (b) excluding this pigment [139]...

Pattern recognition can be classified according to several parameters. Below we discuss only the supervised/unsupervised dichotomy because it represents two different ways of analyzing hyperspectral data cubes. Unsupervised methods (cluster analysis) classify image pixels without calibration and with spectra only, in contrast to supervised classifications. Feature extraction methods [21] such as PCA or wavelet compression are often applied before cluster analysis. 

Fig. 4.4. Influence of carotenoid pre-resonant Raman contributions on cluster analysis result. The dendrogram was obtained using the same parameters as in the one displayed in Fig. 4.3. However, the spectra of the used data set were obtained without decomposing carotenoid before the Raman experiments. The species sallow, horse-chestnut and large-leaved linden form a distinct cluster due to the intense carotenoid contribution. The corresponding spectra are shown in Fig. 4.5 traces a, c and e. Reprinted with permission from [52]...

Fig. 5.4. Raman imaging of a HeLa cell incubated for 28 h with Phe-d5. (A) Hierarchical cluster analysis image with five clusters. Univariate images of (B) nucleotides (770-790cm 1), (C) phospholipids (700-730cm 1), (D) Phe-d5 (950-965cm-1), (E) Phe-h5 (995-1, 005 cm-1), and (F) Phe-d5/Phe-h5 ratios (950-965 cm-1 region divided by the 995-1,005 cm-1 region). Image acquisition parameters Exposure time ls/pixel, step size 0.47pm/pixel, field of view 15 x 15 pm2 (reprinted with permission from [30]. Copyright 2008 American Chemical Society)...

In a study of the fluorescence properties of the Brazil Block seam (Parke Co., IN), a somewhat different approach was used. In this case, about a hundred individual spectra were taken on a variety of fluorescing liptinite macerals. Although the macerals from which the spectra were tkane were not identified at the time of measurement, photomicrographs in both normal white-light and fluorescent light were taken for documentation. The spectral parameters for each spectrum were calculated and these data were subjected to cluster analysis to test the degree to which the... 

Fig. 13. Cluster analysis of a batch of 64 acoustic emissions obtained from a stressed sample of polypropylene + 40% calcium carbonate. Parameters maximum amplitude, variance, and median frequency. The bounds of each cluster are indicated in the mapped projection...

Chemometric methods such as analysis of correlation coefficients, cluster analysis or neural network analysis are used, for example, in the classification of fragments of glass on the basis of their elemental composition or refractive index. Such methods allow the test material to be classified into the appropriate group of products on the basis of the measured parameter. 

The principal component analysis of the structural parameters, supported by the cluster analysis, classified fullerenes into five groups. The periodic table of fullerenes was built on the structural parameters, the principal component analysis and the cluster analysis. The conclusion reached by Torrens is that the preriodicity of fullerene properties is not general. Torrens168 171 also studied the periodic properties of carbon nanotubes as well. 

The parameter fitting step requires the specification of the number of hidden states, which, whenever the hidden states should be metastable states, is in general not apriori known. One policy to overcome this problem is to assume a sufficient large number of hidden states, perform the parameter fitting and conduct a further aggregation of the resulting transition matrix. This can be done by Perron cluster cluster analysis (PCCA), e.g., by the spectral properties of the resulting transition matrix T as proposed in the transfer operator approach (we will illustrate this procedure on an example in the next section), see [11] for details. 

Hierarchical cluster analysis (HCA) and the closely related tree cluster analysis (TCA) provide a simple view of distances between samples, often viewed in a tree-like structure called a dendrogram (see Fig. 6a as an example). These types of analyses methods allow for the development of quick and simple classification schemes. Distances are calculated between all samples within the data set where the data parameters are the coordinates in a multidimensional variable parameter space (of dimension Mvar)- The general distance... 

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