Cluster tree analysis

Hierarchical cluster analysis (HCA) and the closely related tree cluster analysis (TCA) provide a simple view of distances between samples, often viewed in a tree-like structure called a dendrogram (see Fig. 6a as an example). These types of analyses methods allow for the development of quick and simple classification schemes. Distances are calculated between all samples within the data set where the data parameters are the coordinates in a multidimensional variable parameter space (of dimension Mvar)- The general distance... 

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

Fig. 4.3. Dendrogram resulting from cluster analysis containing 91 spectra from 15 tree species (see also Table 4.2). Cluster analysis was done on first derivatives over the spectral range 380 cm-1 to 1700 cm-1). The distance matrix was calculated using Euclidean distance and Ward s algorithm was applied for clustering. Spectra were measured after decomposition of carotenoid molecules with 633 nm irradiation. For example, spectra of each species are shown in Fig. 4.1. Reprinted with permission from [52]...

Cluster analysis (CA) performs agglomerative hierarchical clustering of objects based on distance measures of dissimilarity or similarity. The hierarchy of clusters can be represented by a binary tree, called a dendrogram. A final partition, i.e. the cluster assignment of each object, is obtained by cutting the tree at a specified level [24],... 

Unsupervised learning methods - cluster analysis - display methods - nonlinear mapping (NLM) - minimal spanning tree (MST) - principal components analysis (PCA) Finding structures/similarities (groups, classes) in the data... 

Graphical methods in connection with pattern recognition algorithms, i.e. geometrical or statistical methods, e.g. minimum spanning tree or cluster analysis, are more powerful methods for explorative data analysis than graphical methods alone. 

In this passage we demonstrate that comparable results may also be obtained when other methods of unsupervised learning, e.g. the non-hierarchical cluster algorithm CLUPOT [COOMANS and MASSART, 1981] or the procedure of the computation of the minimal spanning tree [LEBART et al., 1984], which is similar to the cluster analysis, are applied to the environmental data shown above. 

The second cluster analysis involved attaching twice as much importance to the interaction term than to any of the other 12 attributes. We obtained basically the same cluster tree as with the first method, with only a few modifications some cluster breakups were more severe than before, indicating more cluster-to-cluster distinctiveness, and some were less severe. Inspection of the tree indicated that there were either two clusters, in which case one cluster was approximately twice as big as the other cluster, or there were three clusters, with the larger cluster subdivided into two clusters. (See Figure 4.) Further examination of spatial plots revealed no clear separation of cluster, whether the number of clusters was designated two or three (Figures 5a and b),... 

In order to understand the relation between the embedding result and the functionality of proteins, we have shown some proteins with their known functionalities (Fig. 23, the functionalities are due to http //aaa-proteins.uni-graz.at/AAA/Tree.html). As can be seen easily, the proteins cluster in the nMDS result share similar functions. Clustering can be done by the popular hierarchical clustering analysis, but the relations among obtained clusters is often hard to recognize. This is especially true when there are several uppermost clusters. However, the nMDS result clearly shows us the relations among clusters. There are two big branches. One consists of meiosis/mitochondria and cell division cycle/centrosome/ER homotypic fusion. The other consists... 

Linear regression analysis has pitfalls. There is always the possibility of chance correlations. Hence, we opted to analyze the data using an alternate statistical method, namely cluster analysis. The data were scaled so that each of the descriptors ranged in value between 0 and 1. Minimal tree spanning methods was employed in the determination of clusters (24). 

Fig. 23 Classification of the NSAID dataset based on three-dimensional autocorrelation descriptors, a) Hierarchical clustering analysis (HCA). The dark gray cluster includes the COX-2-selective drugs, b) Visualization of the minimal spanning tree (MST). The longest connections are drawn as dotted lines in order to derive classes of compounds.

Exploratory modeling using modem statistical modeling techniques such as generalized additive modeling (GAM) (15), cluster analysis, and tree-based modehng (TBM) to reveal structure in the data and initially select explanatory covariates. 

FIGURE 5.2 Trees A and B show the results of a hierarchical cluster analysis of the same data. Tree B has been reordered. Dendrogram A is equivalent to Dendrogram B. Rotating an internal branch does not affect the topology of a tree. If Tree A or Tree B were cut at the position of the dashed line (a height of 1.0), each tree would produce three equivalent clusters. That is, the members in each of these three branches are the same. 

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