|dc.description.abstract||Clustering is a widely used technique, with applications ranging
from data mining, bioinformatics and image analysis to marketing,
psychology, and city planning. Despite the practical importance of
clustering, there is very limited theoretical analysis of the topic.
We make a step towards building theoretical foundations for
clustering by carrying out an abstract analysis of two central
concepts in clustering; clusterability and clustering quality.
We compare a number of notions of clusterability found in the
literature. While all these notions attempt to measure the same
property, and all appear to be reasonable, we show that they are
pairwise inconsistent. In addition, we give the first computational
complexity analysis of a few notions of clusterability.
In the second part of the thesis, we discuss how the quality of a
given clustering can be defined (and measured). Users often need to
compare the quality of clusterings obtained by different methods.
Perhaps more importantly, users need to determine whether a given
clustering is sufficiently good for being used in further data
mining analysis. We analyze what a measure of clustering quality
should look like. We do that by introducing a set of requirements
(`axioms') of clustering quality measures. We propose a number of
clustering quality measures that satisfy these requirements.||en