Reviews in Computational Chemistry Volume 18

Introduction 5
is, it is a top-down approach. If, at each split, only one descriptor is used to
determine how the cluster is split, the method is monothetic; otherwise, more
descriptors (typically all available) are used, and the method is polythetic.
Nonhierarchical methods encompass a wide range of different techniques
to build clusters. A single-pass method is one in which the partition
is created by a single pass through the data set or, if randomly accessed, in
which each compound is examined only once to decide which cluster it should
be assigned to. A relocation method is one in which compounds are moved
from one cluster to another to try to improve on the initial estimation of the
clusters. The relocating is typically accomplished based on improving a cost
function describing the ‘‘goodness’’ of each resultant cluster. The nearestneighbor
approach is more compound centered than are the other nonhierarchical
methods. In it, the environment around each compound is examined
in terms of its most similar neighboring compounds, with commonality
between nearest neighbors being used as a criterion for cluster formation. In
mixture model clustering the data are assumed to exist as a mixture of densities
that are usually assumed to be Gaussian (normal) distributions, since their
densities are not known in advance. Solutions to the mixture model are
derived iteratively in a manner similar to the relocation methods. Topographic
methods, such as use of Kohonen maps, typically apply a variable cost function
with the added restriction that topographic relationships are preserved so
that neighboring clusters are close in descriptor space. Other nonhierarchical
methods include density-based and probabilistic methods. Density-based, or
mode-seeking, methods regard the distribution of descriptors across the data
set as generating patterns of high and low density that, when identified, can be
used to separate the compounds into clusters. Probabilistic clustering generates
nonoverlapping clusters in which a compound is assigned a probability, in the
range 0 to 1, that it belongs to the chosen cluster (in contrast to fuzzy clustering
in which the clusters are overlapping and the degree of membership is not
a probability).
Having now provided a broad overview of clustering methodology, we
next focus on the ‘‘classical’’ methods, which include hierarchical and singlepass,
relocation, and nearest-neighbor nonhierarchical techniques. The classification
we have described in Figure 2 is one that is commonly used by many
scientists; however, it is just one of many possible classifications. Another way
to differentiate between clustering techniques is to consider parametric and
nonparametric methods. Parametric methods require distance-based comparisons
be made. Here access to the descriptors is required (typically given as
Euclidean vectors), rather than just a proximity matrix derived from the
descriptors. Parametric methods can be further organized into generative
and reconstructive methods. Generative methods, including mixture model,
density-based, and probabilistic techniques, try to match parameters (e.g.,
cluster centers, variances within and between clusters, and mixing coefficients
for the descriptor distributions) to the distribution of descriptors within the
data set. Reconstructive methods, such as relocation and topographic, are