Cluster single-linkage

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... 

Fig. 30.8. Dissimilar objects A and X are chained together in a cluster obtained by single linkage.

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]). 

Compute the distances between all clusters using complete linkage, single linkage, average linkage, or other methods. 

Single linkage, nearest neighbor — uses the distance between the two closest samples in the different clusters. 

There are a variety of ways to compute distances between data points and clusters in hierarchical clustering. A few are shown in Figure 9.7. The single-linkage method... 

Allen, F. H., Doyle, M. J., and Taylor, R. / Automated conformational analysis from crystallographic data. 1. A symmetry-modified single-linkage clustering algorithm for three-dimensional pattern recognition. Acta Cryst. B47, 29-40 (1991). 

Hierarchical algorithms are characterized by the construction of a tree-like structure. A single linkage algorithm starts with placing in the first cluster the two nearest points. At the next stage, a third point joins the already formed cluster of two if its shortest distance to the members of the first cluster is smaller than to any other point. 

Single linkage, the distance is defined as the minimum distance between any two clusters, where s,t defines the two clusters and xsj defines the entity in cluster s and xtj in cluster t. 

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