Cluster analysis results

Since the PCA and cluster analysis results were similar for the three sites and since one emission source has been suggested (12) as the source of many of the species detected In Western Washington rain, an analysis of the regional similarities In composition was appropriate. 

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]...

This can be used to automatically analyse single beads with no knowledge of M.Wt Fig. 5.26 shows the cluster analysis result on four single beads that were analysed in triplicate. The TIC traces only show responses that fitted with the isotopic difference criteria and by selecting these peaks , mass spectra are generated depicting the doublets only with the M.Wt values. 

Figure 1. Dendogram of cluster analysis results from phospholipid fatty acid profiles of rhizosphere and nonvegetated soils from the contaminated site. Comparisons of qualitative differences between the groups of microorganisms present in the different samples illustrated the primary clustering of nonvegetated soil samples with Lespedeza cuneata rhizosphere soil samples, and Solidago sp. rhizosphere soil with Firms taeda rhizosphere soil and Paspalum notatum rhizosphere soil samples. Secondary clustering occurred between Firms taeda soil samples and Faspalum notatum soil samples.

The system constants for packed column stationary phases are summarized in Table 8. Classification of their properties by cluster analysis results in the connection dendrogram shown in Figure 4. Stationary phases with similar solvation properties are located next to each other and connected close to the left-hand side of the dendrogram. Stationary phases with no paired descendents are singular phases with properties that cannot be duplicated by other phases from the data set (Table 8). Classification results in six groups with three phases behaving... 

FIGURES Similarity of cluster, analysis results of the physico-chemical (PC) and descriptor space clusters of the ten compounds given in TABLES 3 and 4. 

Spectral features and their corresponding molecular descriptors are then applied to mathematical techniques of multivariate data analysis, such as principal component analysis (PCA) for exploratory data analysis or multivariate classification for the development of spectral classifiers [84-87]. Principal component analysis results in a scatter plot that exhibits spectra-structure relationships by clustering similarities in spectral and/or structural features [88, 89]. 

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. 

Fig. 8.8. Result of cluster analysis of 88 German wines according to Ward s method (Thiel et al. [2004])...

Cluster analysis is important in all situations where homogeneity of data on the one hand and latent structures on the other hand play a significant role in evaluation and interpretation of analytical results. This applies in particular for single objects with extreme properties like outliers, hot spots etc that can easily be recognized being singletons among clusters. 

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. 

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. 

Thus, besides being sensitive to absorbing species on the electrode surface as well as in the solution in the region very close to the surface, it is possible to obtain potential dependent behavior in fine detail. We have applied these techniques to examine the interaction of simple ions such as CN and Ny with polycrystalline electrodes of silver, gold and copper. The observed vibrational spectra can be interpreted with the help of selection rules based on symmetry and analysis of ab-initio SCF wavefunctions of clusters. The results of these studies will be reviewed. 

FIGURE 3.28 Dendrogram resulting from hierarchical cluster analysis of the nri i... 

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