Linkage clustering method

Table 9.3 A comparison of the single-linkage, complete-linkage and average-linkage cluster methods using the data in Table 92 The figures in parentheses indicate the distance between the clusters as they are formed In this particular case Ward s clustering follows the same order of cluster formation as the group average method.

In single-linkage clustering methods, the distance between two clusters is determined from the two closest objects in different clusters (shortest intercluster distance). 

The cluster method Between-groups linkage, interval Euclidean distance. Transform Values-standardize Range 0-1. 

As the distance measure can be combined with various linkage rules, the results of CA are different the unraveled pattern depends on the methods used. If all techniques provide the same pattern, the clustering, the classification can be accepted, otherwise it is not clear why the given linkage rule or distance measure provides acceptable/explainable groupings. Except using Mahalanohis distance, all clustering methods require standardization of data. 

Single linkage methods have a tendency to chain together ill-defined clusters (see Fig. 30.8). This eventually leads to include rather different subjects (A to X of Fig. 30.8) into the same long drawn-out cluster. For that reason one sometimes... 

An example of an application is shown in Fig. 30.10. This concerns the classification of 42 solvents based on three solvatochromic parameters (parameters that describe the interaction of the solvents with solutes) [13]. Different methods were applied, among which was the average linkage method, the result of which is shown in the figure. According to the method applied, several clusterings can be found. For instance, the first cluster to split off from the majority of solvents consists of solvents 36, 37, 38, 39, 40, 41, 42 (t-butanol, isopropanol, n-butanol. 

There exist several methods of hierarchical clustering which use diverse measures of distance or similarity, respectively, e.g., single linkage, complete linkage, average linkage, centroid linkage, and Ward s method (Sharaf et al. [1986], Massart et al. [1988], Otto [1998] Danzer et al. [2001]). 

Hierarchical cluster analysis (Section 6.4)—with the result represented by a dendrogram—is a complementary, nonlinear, and widely used method for cluster analysis. The distance measure used was dTANi (Equation 6.5), and the cluster mode was average linkage. The dendrogram in Figure 6.6 (without the chemical structures) was obtained from the descriptor matrix X by... 

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