TESI DOCTORAL - La Salle

1.4. Clustering indeterminacies
executed if the user is not satisfied with the evaluation of the mined patterns. In the case
that clustering is the data mining task of the knowledge discovery process, these important
decisions are often made blindly, due to the unsupervised nature of the clustering problem.
Unfortunately, these decisions determine, to a large extent, the effectiveness of the clustering
task (Jain, Murty, and Flynn, 1999), so they should not be made unconcernedly.
Thus, the obtention of a good quality clustering solution relies heavily on making optimal
(or quasi-optimal) decisions at every stage of the KD process. The doubts that seize
clustering practitioners at the time of making such decisions are caused by what we call
cluster indeterminacies, which mainly localize in the selection of i) the way objects are
represented, and ii) the clustering algorithm to be applied.
As regards the decision on data representation, ideal features should permit distinguishing
objects belonging to different clusters, besides being robust to noise, easy to extract and
interpret (Xu and Wunsch II, 2005). In a blind quest for finding such a data representation,
the clustering practitioner is struck by the following questions:
– how should the objects be represented? Should we stick to their original representation,
select a subset of the original attributes (i.e. feature selection) or transform
them into a new feature space (i.e. feature extraction)?
– if the original data representation is subject to a dimensionality reduction process,
which should be the dimensionality of the reduced feature space?
– if the original data representation is subject to a feature selection process, which
criterion should be followed?
– if feature extraction is applied, which criterion should guide it?
Regrettably, whereas these questions are easy to answer in a supervised classification
scenario (e.g. the optimal feature subset can be chosen by maximizing some function of
predictive classification performance (Kohavi and John, 1998) or by applying a feature
transformation driven by class labels (Torkkola, 2003)), they have no clear nor universal
answer in an unsupervised context. This is due to the fact that, in clustering, the lack of
class labels makes feature selection a necessarily ad hoc and often trial-and-error process (Dy
and Brodley, 2004). Moreover, studies comparing the influence of object representations
based on feature extraction in clustering performance often come up with contradictory
conclusions (Tang et al., 2004; Shafiei et al., 2006; Cobo et al., 2006; Sevillano, Alías, and
Socoró, 2007b).
To illustrate the effect and importance of the data representation clustering indeterminacy,
in the following paragraphs we present experimental evidences that the selection of
a specific object representation can condition the quality of a clustering process to a large
extent. In particular, we have represented the objects contained in the Wine and the miniNG
data collections using multiple data representations: the original attributes (referred
to as baseline) and feature extraction-based representations —obtained by means of Principal
Component Analysis (PCA), Independent Component Analysis (ICA), Non-Negative
Matrix Factorization (NMF) and Random Projection (RP)— on a range of distinct dimensionalities.
Upon each object representation, we have applied a refined repeated bisecting
clustering algorithm based on the correlation similarity measure for obtaining a partition
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