cluster to which it belongs, compared to the same measure computed for the next
closest cluster (see Sect. 4.7.3.7). Silhouette widths range from À1 to 1 and can be
averaged over all objects of a partition.
We shall use the function silhouette() of package cluster. The documentation file of this function provides a formal definition of a silhouette width. In
short, the larger the value is, the better the object is clustered. Negative values
suggest that the corresponding objects may have been placed in the wrong cluster.
At each fusion level, the average silhouette width can be used as a measure of the
quality of the partition (Rousseeuw quality index): compute silhouette widths
measuring the intensity of the link of the objects to their groups, and choose the
level where the within-group mean intensity is the highest, that is, the largest average
silhouette width. A barplot is drawn (Fig. 4.11).
0
5
10
15
20
25
30
0.0
0.1
0.2
0.3
Silhouette-optimal number of clusters
k (number of clusters)
Average silhouette width
optimum
2
Fig. 4.11 Barplot showing the average silhouette widths for k ¼ 2 to 29 groups. The best partition
by this criterion is the one with the largest average silhouette width, i.e., in two groups. The second
best, in 4 groups, and the third best, in 6 groups, are more interesting from an ecological point of
view
4.7 Interpreting and Comparing Hierarchical Clustering Results
81