Reviews in Computational Chemistry Volume 18

Hierarchy level selection methods provide useful guidance in selecting
reasonable partitions from hierarchies where the underlying structure of the
data set is unknown. They are, however, a compromise in that they compare
entire partitions with each other rather than individual clusters. In disciplines
outside of chemistry, there is an increasing awareness that such global comparisons
can mask comparative differences in local densities. For example, the
situation in Figure 5 shows three clusters (below the dendrogram) that cannot
be retrieved by using a conventional straight horizontal line across the dendrogram
(such as that shown in Figure 1). Using a straight line can include either
item 8 with cluster [3,1,2] but merge [4,5] with [6,7], or keep [4,5] and [6,7]
separate but maintain 8 as a singleton. What may be required for the selection
of the ‘‘best,’’ nonoverlapping clusters from different partitions is a stepped (or
segmental) horizontal line, which is illustrated by the dotted line across the
dendrogram in Figure 5. No solution to deciding which is the best selection
of nonoverlapping clusters appears to have been published to date, but there
are examples of methods that are moving toward a solution. One such example
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Progress in Clustering Methodology 27
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Figure 5 An illustration of how a stepped hierarchy partition can extract particular
clusters (clusters [8,1,2,3], [4,5], and [6,7], as shown below the hierarchy).
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