Reviews in Computational Chemistry Volume 18

Progress in Clustering Methodology 23
or k-means method). The nature of the rough-distance measure used can guarantee
that the canopies will be sufficiently broad to encompass all candidates
for the ensuing full-distance measure. These ideas to speed up nearestneighbor
searches are similar to the earlier use of bounds on the distance
measure, as discussed by Murtagh. 27
Comparative Studies on Chemical Data Sets
Much of the use of clustering for chemical applications is based on the
similar property principle. 107 This principle, which holds in many, but certainly
not all, structure–property relationships, states that compounds with
similar structure are likely to exhibit similar properties. Clustering on the basis
of structural descriptors is thus likely to group compounds having similar
properties. However, there exist many different clustering methods, each
having its own particular characteristics that are likely to affect the composition
of the resultant clusters. Consequently, there have been several comparative
studies on the performance of different clustering methods when
applied to chemical data sets. The first such studies were conducted by
Willett and Rubin 5,108–110 in the early 1980s. These studies were highly
influential in the subsequent implementation of clustering methods in
commercial and in-house software systems used by the pharmaceutical
industry. Over 30 hierarchical and nonhierarchical methods were tested on 10
small data sets for which certain properties were known. Clustering was conducted
using 2D fingerprints as compound representations. The leave-one-out
approach (based on the similar property principle) was used to compare the
results of different clustering methods by predicting the property of each
compound (as the average of the property of the other members of the cluster)
and correlating it with the actual property. High correlations indicate that
compounds with similar properties have been clustered together. The results
indicated that the Ward hierarchical method gave the best overall performance.
But, this method was not well suited to processing large data sets due
to the requirement for random access to the fingerprints. The Jarvis–Patrick
nonhierarchical method results were almost as good and, because it does not
require the fingerprints to be in memory, it became the recommended method.
In the early 1990s, a subsequent study by Downs, Willett, and Fisanick 46
compared the performance of the Ward and group-average agglomerative
methods, the minimum-diameter divisive hierarchical method, and the
Jarvis–Patrick nonhierarchical method when using dataprints of calculated
physicochemical properties. In this assessment, a data set was used that was
considerably larger than those used in the original studies. 108–110 The results
highlighted the poor performance of the Jarvis–Patrick method in comparison
with the hierarchical methods. The hierarchical methods all had similar levels
of performance with the minimum-diameter method being slightly better for
small numbers of clusters. Brown and Martin 20 then investigated the same