Cluster dendrogram

Because of the long computing time of distances and the difficulty of evaluating the output dendrogram, cluster analysis is ususally performed with a small number of objects, as in the work of Aishima. However, Ooghe et al. > used cluster analysis with 269 objects in the study of French red wines by their amino acid spectrum. 

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

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. 

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. 

X clust <- hclust (X dist) hierarchical clustering plot (X clust) plots a dendrogram... 

FIGURE 3.24 Dendrogram of fatty acid concentration data from mummies and reference samples. Hierarchical cluster analysis (complete linkage) with Euclidean distances has been applied. 

For comparison also a dendrogram (Figure 3.28) and a nonlinear mapping (NLM) (Figure 3.29) have been performed on the PAH data. Results from these methods show a clear separation of the samples from Linz and Vienna, but not much more details. The clusters in the NLM plots are very similar to the clusters in the PCA score plots. Thus, preserving the distances using two dimensions—the goal of... 

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

Depending on the clustering method, cluster results can be displayed in the form of a dendrogram or in a PCA score plot (Section 3.8.2). Such graphic allows abetter visual impression about the relations between the variables and about the clustering structure. It is thus a suitable tool for selecting the variables. 

An appropriate graphical representation of the result is a tree-like dendrogram (Section 6.4). It allows to determine manually the optimal number of clusters as well as to see the hierarchical relations between different groups of objects. 

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