Opposite to the single linkage approach is complete linkage agglomeration, also called furthest neighbour sorting. In this method, first proposed by S0rensen (1948), the Complete fusion of two clusters depends on the most distant pair of objects instead of the closest. linkage rule Thus, an object joins a cluster only when it is linked (relationship Gc, Section 8.2) to all the objects already members of that cluster. Two clusters can fuse only when all objects of the first are linked to all objects of the second, and vice versa.
Coming back to the ponds of Ecological application 8.2, complete linkage clustering (Fig. 8.3) is performed on the table of ordered similarities of Section 8.2. The pair (212, 214) is formed at S = 0.6 and the pair (431, 432) at S = 0.5. The next clustering step must wait until S = 0.2, since it is only at S = 0.2 that pond 233 is finally linked (relationship Gc) to both ponds 431 and 432. The two clusters hence formed cannot fuse, because it is only at similarity zero that ponds 212 and 214 become linked to all the ponds of cluster (233, 431, 432). S = 0 indicating, by definition, distinct entities, the two groups are not represented as joining at that level.
In the compete linkage strategy, as a cluster grows, it becomes more and more difficult for new objects to join to it because the new objects should bear links with all the objects already in the cluster before being incorporated. For this reason, the growth of a cluster seems to move it away from the other objects or clusters in the analysis. According to Lance & Williams (1967c), this is equivalent to dilating the reference
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