Reviews in Computational Chemistry Volume 18

24 Clustering Methods and Their Uses in Computational Chemistry
clustering methods to compare their performance for compound selection,
using various 2D and 3D fingerprints. Active/inactive data was available for
the compounds in the data sets used, so assessment was based on the degree to
which clustering separated active from inactive compounds (into nonsingleton
clusters). Although the Jarvis–Patrick method was the fastest of the methods, it
again gave the poorest results. The results were improved slightly by using a
variant of the Jarvis–Patrick method that uses variable rather than fixed-length
nearest-neighbor lists. 12 Overall, the Ward method gave the best and most
consistent results. The group-average and minimum-diameter methods were
broadly similar and only slightly worse in performance than the Ward method.
The influence of the studies summarized above can be seen in the
methods subsequently implemented by many other researchers for their applications
(see the section on Chemical Applications). One method that was
included in the original assessment studies, but not in the later assessments,
is k-means. This method did not perform particularly well on the small data
sets of the original studies, and the resultant clusters were found to be very
dependent on the choice of initial seeds; hence it was not included in the subsequent
studies. However, k-means is computationally efficient enough to be
of use for very large data sets. Indeed, over the last decade k-means and its
variants have been studied extensively and developed for use in other disciplines.
Because it is being increasingly used for chemical applications, any
future comparisons of clustering methods should include k-means.
How Many Clusters?
A problem associated with the k-means, expectation maximization, and
hierarchical methods involves deciding how many ‘‘natural’’ (intuitively
obvious) clusters exist in a given data set. Determining the number of ‘‘natural’’
clusters is one of the most difficult problems in clustering and to date no
general solution has been identified. An early contribution from Jain and
Dubes 28 discussed the issue of clustering tendency, whereby the data set is analyzed
first to determine whether it is distributed uniformly. Note that randomly
distributed data is not generally uniform, and, because of this, most
clustering methods will isolate clusters in random data. To avoid this problem,
Lawson and Jurs 111 devised a variation of the Hopkins’ statistic that indicates
the degree to which a data set contains clusters. McFarland and Gans 112 proposed
a method for evaluating the statistical significance of individual clusters
by comparing the within-cluster variance with the within-group variance of
every other possible subset of the data set with the same number of members.
However, for large heterogeneous chemical data sets it can be assumed that
the data is not uniformly or randomly distributed, and so the issue becomes
one of identifying the most natural clusters.
Nonhierarchical methods such as k-means and EM need to be initialized
with k seeds. This presupposes that k is a reasonable estimation of the number