Cluster analysis 412 INDEX

Niederhauser P, Schanz F (1994) Comparison of diatom communities in remote high-mountain lakes using index B and cluster analysis. Hydrobiologia 274 115... 

Of the four different methods of cluster analysis applied, the method of Ward described in the Clustan User Manual (10), worked best when compared to the single-, complete-, or average-linkage methods. Using Ward s method, two clusters, Gn and Gm, are fused when by pooling the variance within two existing clusters the variance of the so formed clusters increases minimally. The variance or the sum of squares within the classes will be chosen as the index h of a partition. 

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. 

Products Index (CPI) database. To aid in reducing the size of a hit list, a Reagent Selector user can filter reagents and sort on properties, availability, presence or absence of functional groups, etc. (Fig. 9.18). Further list reduction can be achieved by clustering the structures by means of a cluster analysis using substructure keys as descriptors. 

In the same way as the a, -separation has been performed, one can proceed to a cr, rr-separation.52 This separation has been used to evaluate the aromaticity of organic molecules and clusters. An index of aromaticity was proposed using a scale based on the bifurcation analysis of the ELF constructed from the separated densities. In principle, the total ELF has no information about tt and cr bonds, it depends only on the total density. Hence, the ELF does not show clear differences between both kinds of bonds. However, the topological analysis over separated densities, ones formed by the rr-orbitals and the other ones formed by the cr-orbitals, yields the necessary information.52 Of course, this is possible only for the molecules which present the cr, tt symmetries, i.e. planar molecules. The bifurcation analysis of the news ELFW and ELFCT can be interpreted as a measure of the interaction among the different basins and chemically, as a measure of electron delocalization.45 In this way, the tt and a aromaticity for the set of planar molecules described in the Scheme 1 has been characterized.52... 

HBi is zero for all hydrocarbons and, therefore, was deleted from analyses of BP. Twelve of the TIs were deleted for the analysis of the 140 hydrocarbons as well. These indexes included the third- and fourth-order chain connectivity indexes, which were zero for all chemicals, the fourth- and sixth-order bond and valence corrected cluster connectivity indexes, which were perfectly correlated with the simple cluster connectivity indexes (r = 1.0), and and which were perfectly correlated with 7 for hydrocarbons. 

The critical indices estimated from these relations fall into the admissible ranges of variation P = 0.39-0.40, V = 0.8-0.9, and t = 1.6-1.8, determined in terms of the percolation model for three-dimensional systems. The researchers [7] noted that not only numerical values but also the meanings of these values coincide. Thus the index P characterises the chain structure of a percolation cluster. The 1/p value, which serves as the index of the first subset of the fractal percolation cluster in the model considered [7], also determines the chain structure of the cluster. The index v is related to the cellular texture of the percolation cluster. The 2/df index of the second subset of the fractal percolation cluster is also associated with the cellular structure. By analogy, the index t defines the large-cellular skeleton of the fractal percolation cluster. The relationship between the critical percolation indices and the fractal dimension of the percolation cluster for three-dimensional systems and examples of determination of these values for filled polymers are considered in more detail in the book cited [7]. Thus, these critical indices are universal and significant for analysis of complex systems, the behaviour of which can be interpreted in terms of the percolation theory. 

Figure 12.17 Carbon K-edge X-ray absorption spectra of (a) a calcined H-ZSM-5 (ZSM-5-C) sample and (c) steamed H-ZSM-5 (ZSM-5-S) sample, obtained from a cluster analysis performed after 150 min time-on-stream. Cluster index for (b) ZSM-5-C and...

Retention index data can be employed to recognize molecular structures of unknown monofunctional compounds. This was principally demonstrated by Huber and Reich C113, 2373. Retention data of 199 compounds on ten different stationary phases were utilized for cluster analysis, KNN--classifications and the computation of classifiers with the learning machine. The minimum number of stationary phases was only two for the classification of aromatic compounds, four for alcohols and 13 for aldehydes and ketones. A two-step classification procedure was developed. 

Ampe, F., Miambi, E. (2000). Cluster analysis, richness and biodiversity indexes derived from denaturing gradient gel electrophoresis fingerprints of bacterial communities demonstrate that traditional maize fermentations are driven by the transformation process. International Journal of Food Microbiology, 60, 91-97. 

Besides the applications of the electrophilicity index mentioned in the review article [40], following recent applications and developments have been observed, including relationship between basicity and nucleophilicity [64], 3D-quantitative structure activity analysis [65], Quantitative Structure-Toxicity Relationship (QSTR) [66], redox potential [67,68], Woodward-Hoffmann rules [69], Michael-type reactions [70], Sn2 reactions [71], multiphilic descriptions [72], etc. Molecular systems include silylenes [73], heterocyclohexanones [74], pyrido-di-indoles [65], bipyridine [75], aromatic and heterocyclic sulfonamides [76], substituted nitrenes and phosphi-nidenes [77], first-row transition metal ions [67], triruthenium ring core structures [78], benzhydryl derivatives [79], multivalent superatoms [80], nitrobenzodifuroxan [70], dialkylpyridinium ions [81], dioxins [82], arsenosugars and thioarsenicals [83], dynamic properties of clusters and nanostructures [84], porphyrin compounds [85-87], and so on. 

Technische Universitat Wien Does latent class analysis, short-time Fourier transform, fuzzy clustering, support vector machines, shortest path computation, bagged clustering, naive Bayes classifier, etc. (http //cran.r-project.org/ web/packages/el071/index.html)... 

Universite Libre de Bruxelles Toolbox for the analysis of biological networks, clusters, classes, and pathways (http //rsat.bigre.ulb.ac.be/rsat/index neat. html)... 

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