Dendrograms

Often the result of hierarchical clustering is presented in the form of a dendrogram (sometimes called a tree diagram ). The objects are organised in a row, according 

Multi-way Analysis With Applications in the Chemical Sciences 

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Fig. 9. (a) Single-link clusteriag process and (b) corresponding connection dendrogram (14). Reprinted with permission. 

Figure 8.5 Example dendrogram representing an hierarchical clustering of a set of seven compounds.

Fig. 3. Relationships within a family of transporters of nitrogenous compounds. The dendrogram is based on the alignments shown in Fig. 2. See legend of Fig. 2.

Fig. 30.7. Dendrograms for the data of Tables 30.3-30.7 (a) average linkage (b) single linkage (c) complete linkage.

In hierarchical clustering one can obtain any number of clusters K,lhierarchical clustering, with the difference that there K is defined a priori by the user. The question then arises which A -clustering is significant. To introduce the problem let us first consider a technique that was proposed for the non-hierarchical method MASLOC [27], which selects so-called robust clusters. 

P.J. Lewi, H. Moereels and D. Adriaensen, Combination of dendrograms with plots of latent variables. Application of G-protein coupled receptor sequences. Chemom. Intell. Lab. Syst., 16 (1992) 145-154. 

Figure 11.3 Positive ion FIESMS spectra of crude cell extracts from Escherichia coli HB101 (A), Bacillus sphaericus DSM 28 (B), and Bacillus licheniformis NTCC 10341 (C). (D) A pseudo-3D plot of the first three discriminant functions (DF1-3) obtained from positive ion whole-cell DIESMS spectra of seven Bacillus subtilis strains (a-g) (E) the corresponding abridged dendrogram obtained from the same information as in D. (Adopted from Vaidyanathan et al.57)...

Due to the mainly qualitative nature of PCA, DFA, and HCA, the role of PyMS in microbiology has been somewhat restricted. For example, using these clustering methods, the use of PyMS to identify microorganisms can be a subjective process because it relies on the interpretation of complex scatter plots and dendrograms. Furthermore the qualitative nature of PCA, DFA, and FICA prevents the application of PyMS to quantitative microbial analysis, while limitations also arise from batch-to-batch variation of PyMS data.80... 

It is possible to treat dendrograms according to graph-theoretical principles (Frank and Todeschini [1994]). However, in general, the results of clustering are evaluated qualitatively and taken as a basis of extensive studies on data structure. 

FIGURE 16-4 Evolutionary relationships between DNA sequences of GABAa receptors and glycine receptors. The dendrogram is based on literature data for human cDNAs, provided by Tim Hales and Ewen Kirkness, analyzed by Ziwei Chen, Kui Yang and Richard Olsen. 

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