axis(1,
k.best,
paste("optimum", k.best, sep = "\n"),
col = "red",
col.axis = "red")
points(k.best,
max(ng),
pch = 16,
col = "red",
cex = 1.5)
Hint In addition to the search for the solutions meeting the two criteria, the code above
highlights in green the solutions where there are significant indicator species in
the k clusters (object ng). In the Doubs data set, it is the case only in the 2- and 3cluster solutions.
Only the partition in two clusters, simply contrasting the upstream and
downstream sites, fully meets the two criteria. However, a partition in three or
four clusters, allowing the discovery of more subtle structures, would be an
acceptable choice despite the absence of positive differential species (i.e., a
species that is more frequent in a given group than in others) for some groups.
4.7.3.7 Silhouette Plot of the Final Partition
In our example, the silhouette-based, matrix correlation-based and IndVal-based
criteria do not return the same solution; these are, ranging from k ¼ 2 to k ¼ 6. A
good compromise seems to be k ¼ 4. Let us select this number for our final group
diagnostics. We can select the Ward clustering as our final choice, since this method
produced four well-balanced (not equal-sized, but without outliers) and welldelimited groups.
We can now proceed to examine if the group memberships are appropriate (i.e.,
no or few objects apparently misclassified). A silhouette plot is useful here
(Fig. 4.14).
4.7 Interpreting and Comparing Hierarchical Clustering Results
87
k.best,
paste("optimum", k.best, sep = "\n"),
col = "red",
col.axis = "red")
points(k.best,
max(ng),
pch = 16,
col = "red",
cex = 1.5)
Hint In addition to the search for the solutions meeting the two criteria, the code above
highlights in green the solutions where there are significant indicator species in
the k clusters (object ng). In the Doubs data set, it is the case only in the 2- and 3cluster solutions.
Only the partition in two clusters, simply contrasting the upstream and
downstream sites, fully meets the two criteria. However, a partition in three or
four clusters, allowing the discovery of more subtle structures, would be an
acceptable choice despite the absence of positive differential species (i.e., a
species that is more frequent in a given group than in others) for some groups.
4.7.3.7 Silhouette Plot of the Final Partition
In our example, the silhouette-based, matrix correlation-based and IndVal-based
criteria do not return the same solution; these are, ranging from k ¼ 2 to k ¼ 6. A
good compromise seems to be k ¼ 4. Let us select this number for our final group
diagnostics. We can select the Ward clustering as our final choice, since this method
produced four well-balanced (not equal-sized, but without outliers) and welldelimited groups.
We can now proceed to examine if the group memberships are appropriate (i.e.,
no or few objects apparently misclassified). A silhouette plot is useful here
(Fig. 4.14).
4.7 Interpreting and Comparing Hierarchical Clustering Results
87