Dendrogram diagram

The typical output of hierarchical cluster methods is a so-called dendrogram, a treelike diagram which is very useful for discussing several possible results of the clustering process. For an illustration see Fig. 5-13 the underlying example will be explained in Section 5.3.4. 

As indicated, agglomerative methods start with single objects or pairs of objects step by step clusters are formed which are finally united in one cluster. Divisive methods, on the other hand, start from the one cluster of all objects and divide it step by step. One drawback of the commonly used agglomerative methods is that clusters formed may not be broken up in a subsequent step. With certain algorithms this sometimes leads to so-called inversions in the dendrogram, i.e. crossing lines in the diagram. 

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... 

The bidimensional methods of representation most used by multivariate techniques are direct methods, such as matricial dispersion diagrams, and icon plots based on histograms, profiles or stars projection approach techniques, that represent observations in the new variables obtained, and which fulfil a specific objective (principal components, canonical variables, etc.) and dendrograms that inform about the similarity of observations or variables (Krzanowski 1988). 

From this extremely simple example, the basic steps involved in cluster analysis and the value of the technique in classification are evident. The final dendrogram. Figure 3(c), clearly illustrates the similarity between the different samples. The original raw tabulated data have been reduced to a pictorial form which simplifies and demonstrates the structure within the data. It is pertinent to ask, however, what information has been lost in producing the diagram and... 

PCs). The obtained clustering dendrogram is reproduced in Figure 29.10. In this type of diagram, the most similar compounds clustered together at the lowest levels. 

Plot the dendrogram (A dendrogram is a tree diagram used to illustrate the output of clustering analysis) and carry out analysis to compare the means across various clusters. 

Fig. 2.3. Example of a similarity diagram (dendrogram) from cluster analysis (after Reibnegger ef a/. 1993, with permission of Buttenvorth-Heinemann).

Dworzanski et al. (2010) used this approach for phylogenomic analysis of isolates from poisonous food samples. The results of their analysis are shown as the upper diagram in Fig. 5.10 and are contrasted with a dendrogram obtained by cluster analysis of the DDH data, lower diagram, for the same strains. 

Dendrogram or branched diagram is a diagram showing the relationships of items arranged like the branches of a tree. 

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