Ae

So, one way of identifying the next fusion is to compute the AEhi statistic for all possible pairs and select the pair which generates the smallest value of this statistic for the next merge. Another way is to use the following updating formula to compute the fusion distances between the new cluster hi and all other objects or clusters g, in the agglomeration table (Table 8.7):

Squared distances are used instead of similarities in eq. 8.10 and in Table 8.7.

Dendrograms for Ward's clustering may be represented along a variety of scales. They all lead to the same clustering topology.

• Fig. 8.11 uses the same scale of squared distances as Table 8.7. This is the solution advocated by Jain & Dubes (1988) and other authors.

• One can easily compute the square roots of the fusion distances of Table 8.7 and draw the dendrogram accordingly. This solution, illustrated in Fig. 8.12a, removes the distortions created by squaring the distances. It is especially suitable when one wants to compare the fusion distances of Ward's clustering to the original distances, either graphically (Shepard-like diagrams, Fig. 8.23) or numerically (cophenetic correlations, Subsection 8.11.2).

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