TESI DOCTORAL - La Salle

Chapter 4
Self-refining consensus
architectures
As described in chapter 3, our proposal for building clustering systems robust to the inherent
indeterminacies that affect the clustering problem consists of i) creating a cluster ensemble
E composed of a large number of individual partitions generated by the use of as many
diversity factors (e.g. clustering algorithms, object representations, etc.) as possible, ii)
deriving a unique clustering solution λc upon that cluster ensemble through the application
of a consensus clustering process.
As mentioned earlier, the use of such a large cluster ensemble entails two negative consequences.
The first one refers to the fact that the construction of the consensus clustering
solution can become costly or even unfeasible, as the space and time complexity of consensus
functions scales up linearly or even quadratically with the size of the cluster ensemble.
In order to overcome such difficulty, in chapter 3 we put forward the concept of hierarchical
consensus architectures, which are based on applying a divide-and-conquer approach
to consensus clustering. Moreover, by means of a simple running time estimation methodology,
the user is capable of deciding apriori, with a notable degree of accuracy, which
is the most computationally efficient consensus architecture for solving a given consensus
clustering problem.
The other main downside to the use of large cluster ensembles is the negative bias induced
on the quality of the consensus clustering solution λc by the expectable presence
of poor1 individual clusterings in E, caused by the somewhat indiscriminate generation of
cluster ensemble components that our proposal indirectly encourages. In order to overcome
this inconvenience, we propose a simple consensus self-refining process that, in a fully unsupervised
manner, allows to improve the quality of the derived consensus clustering solution
λc. Moreover, an additional benefit derived from this automatic consensus refining procedure
is the uniformization of the quality of the consensus clustering solutions yielded by
distinct consensus architectures, which allows selecting the most appropriate one based on
1 By good quality clustering solutions we refer to those partitions that reflect the true group structure
of the data. Provided that we evaluate our clustering results by means of an external cluster validity index
–normalized mutual information (φ (NMI) ) with respect to the ground truth, i.e. an allegedly correct group
structure of the data–, the highest quality clustering results will be those attaining a φ (NMI) close to 1,
whereas the φ (NMI) values associated to poor quality partitions will tend to zero, as φ (NMI) ∈ [0, 1] by
definition (Strehl and Ghosh, 2002).
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