Average linkage hierarchical clustering

Science (North-Holland), Amsterdam, 1986, pp. 289-301. Divisive vs. Agglomerative Average Linkage Hierarchical Clustering. 

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... 

FIGURE 6.6 Dendrogram from hierarchical cluster analysis (average linkage) of n = 20 standard amino acids. Distance measure used was dTANi (Equation 6.5) calculated from eight binary substructure descriptors. Four structure pairs with identical descriptors merge at a distance of zero. Clustering widely corresponds to the chemist s point of view. 

Other hierarchical algorithms are also known, such as that using the average linkage option. In this algorithm, the first set of clusters is done in the same way as previously described. However, the addition of the third element to a cluster considers the average distance to the elements in the previously formed cluster, and the distance between clusters is the average distance from points in the first cluster and the second cluster. 

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