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3.3 Tree Clustering 6 1

d(ui,uj)= min 11~-~ll. (3-3a)
xetui.y€wj
The norm Ilx - yll is evaluated using any of the metrics described in section 2.2.
Unless explicitly stated otherwise we will use the Euclidian norm.
The single linkage rule produces a chaining effect and is therefore adequate for
clusters with filamentary shape.
Consider the globular data of Figure 3.4a. If we apply the single linkage rule no
reasonable clustering solution is attained and the schedule graph increases
smoothly to the uninteresting one cluster solution as shown in Figure 3.7. On the
contrary, if we apply this rule to the filamentary data of Figure 3.4b, a clear two-
cluster solution consistent with the visual clustering is obtained, as shown in Figure
3.8.

Figure 3.7. Single linkage clustering of globular data. (a) Dendrogram; (b)
Clustering schedule graph.

Figure 3.8. Single linkage clustering of filamentary data. (a) Dendrogram; (b)
Clustering schedule graph.