Reviews in Computational Chemistry Volume 18

The terminology associated with clustering is extensive, with many terms
used to describe the same thing (reflecting the separate development of clustering
methods within a multitude of disciplines). Clusters can be overlapping or
nonoverlapping; if a compound occurs in more than one cluster, the clusters
are overlapping. At one extreme, each compound is a member of all clusters to
a certain degree. An example of this is fuzzy clustering in which the degree of
membership of an individual compound is in the range 0 to 1, and the total
membership summed across all clusters is normally required to be 1. This
scheme contrasts with crisp clustering in which each compound’s degree of
membership in any cluster is either 0 or 1. At the other extreme, is the situation
wherein each compound is a member of exactly one cluster, in which case the
clusters are said to be nonoverlapping. Intermediate situations sometimes
occur, where compounds can be members of several, though not of all, clusters.
The majority of clustering methods used on chemical data sets generate
crisp, nonoverlapping clusters, because analysis of such clusters is relatively
simple.
If a data set is analyzed in an iterative way, such that at each step a pair
of clusters is merged or a single cluster is divided, the result is hierarchical,
with a parent–child relationship being established between clusters at each
successive level of the iteration. The successive levels can be visualized using
a dendrogram, as shown in Figure 1. Each level of the hierarchy represents a
partitioning of the data set into a set of clusters. In contrast, if the data set is
analyzed to produce a single partition of the compounds resulting in a set of
clusters, the result is then nonhierarchical. Note that the term partitioning
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Introduction 3
Figure 1 An example of a hierarchy (dendrogram) generated from the clustering of eight
items (shown numbered 1–8 across the bottom). The top (root) is a single cluster
containing all eight items. The vertical positions of the horizontal lines joining pairs of
items or cluster indicate the relative similarities of those pairs. Items 1 and 2 are the most
similar and clusters [8,3,1,2] and [4,5,6,7] are the least similar. The dotted horizontal
line represents a single partition containing the four clusters [8], [3,1,2], [4,5], and [6,7].