TESI DOCTORAL - La Salle

1.4. Clustering indeterminacies
The other major source of indeterminacy is the selection of the particular clustering
algorithm to apply. In this sense, there are several critical questions that must be answered:
– what type of algorithm should we apply? Hierarchical or partitional? Hard or soft?
– once the type of clustering algorithm is selected, which specific clustering algorithm
should be applied?
– how should the parameters of the clustering algorithm be tuned?
– in how many clusters should the data objects be grouped?
As far as the selection of the type of clustering algorithm is concerned, it depends on
the desired shape of the clustering solution. In any case, it is worth noting that soft and
hierarchical clustering algorithms can be regarded as a generalization of their hard and
partitional counterparts, as the latter can always be obtained from the former.
Moreover, it is a commonplace that no universally superior clustering algorithm exists,
as most of the proposals found in the literature have been designed to solve particular
problems in specific fields (Xu and Wunsch II, 2005), thus being able to outperform the
other existing algorithms in a concrete context, but not in others (Jain, Murty, and Flynn,
1999). This fact has been theoretically analyzed and demonstrated by the impossibility
problem in (Kleinberg, 2002). Thus, unless some domain knowledge enables clustering
practitioners to choose a specific algorithm, this selection is often made blindly to a large
extent.
Once the algorithm is chosen, its parameters must be set. Again, this is not a trivial
choice, as they largely determine its behaviour. Several examples concerning the sensitivity
of some popular clustering algorithms to their parameter tuning are easy to find in the
literature: for instance, there is no universal method for identifying the initial centroids
of k-means. The EM clustering algorithm is highly sensitive to the selection of its initial
parameters and the effect of a singular covariance matrix, as it can converge to a local
optimum (Xu and Wunsch II, 2005). In combinatorial search based clustering, there exist
no theoretic guidelines to select the appropriate and effective parameters, while the selection
of the graph Laplacians is a major issue that affects the performance of spectral clustering
algorithms, just like it happens in kernel-based clustering algorithms as regards selecting
the width of the Gaussian kernels (Xu and Wunsch II, 2005).
And finally, one has to decide the number of clusters k into which the objects must be
grouped, as many clustering algorithms (e.g. partitional) require this value to be passed as
one of their parameters. Unfortunately, in most cases the number of classes in a data set
is unknown, so it is one more parameter to guess about. Moreover, determining which is
the ‘correct’ number of clusters in a data set is an open question: in some cases, equally
satisfying (though substantially different) clustering solutions can be obtained with different
values of k for the same data, proving that the right value of k often depends on the scale
at which the data is inspected (Chakaravathy and Ghosh, 1996).
Notwithstanding, there exist several practical procedures for determining the most suitable
value of k. Possibly, the most intuitive approach consists in visualizing the data set on
a two-dimensional space, although this strategy is of little use for complex data sets (Xu and
Wunsch II, 2005). Additionally, relative cluster validity indices (such as the Davies-Bouldin
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