TESI DOCTORAL - La Salle

4.4. Discussion
have experimentally proved that it is very likely to obtain a refined consensus clustering
solution of higher quality than the original one.
The main difference between our two proposals lies in the origin of the clustering employed
as a reference for creating the select cluster ensemble. In the first proposal, referred
to as consensus-based self-refining, this initial clustering is the consensus clustering solution
λc resulting from a previous consensus process run on the whole cluster ensemble. In our
second proposition, the starting point of the refining process is one of the components of
the cluster ensemble, which is selected using an average normalized mutual information
criterion —giving rise to what we call selection-based self-refining.
Unfortunately, the optimal configuration of this self-refining procedure –e.g. the size
of the select cluster ensemble, or the consensus function employed for creating the refined
clustering solutions– is local to each particular experiment. This inconvenience, which
is by no means new in the consensus clustering literature, can be tackled by means of
a supraconsensus function that, in a blind manner, selects the highest quality clustering
solution among a bunch of them, created using distinct self-refining configurations. However,
the application of one of the most extended supraconsensus function (the one proposed in
(Strehl and Ghosh, 2002)) in our experiments has yielded little disappointing results, as it
is capable of selecting the highest quality clustering solution in a relatively low percentage
of the experiments conducted. Moreover, alternative supraconsensus functions based on
average normalized mutual information gave rise to even poorer selection accuracies (not
reported here due to the limited interest of the results obtained), which suggests that it
is necessary to conduct further research in order to devise novel supraconsensus functions
capable of satisfying such a restrictive constraint as the one imposed here —i.e. selecting,
among a set of clustering solutions, the top quality one in a fully unsupervised fashion.
As aforementioned, the concepts of consensus self-refining and supraconsensus functions
are closely related. In fact, supraconsensus is originally presented in (Strehl and Ghosh,
2002) as a means for selecting the best consensus clustering solution among a bunch of
them, created using different consensus functions. Therefore, it seems logical to consider
the application of supraconsensus not on a set of previously derived consensus clustering
solutions, but on the cluster ensemble components themselves, so as to select the highest
quality ones.
Some very recent works have dealt with this issue, such as (Gionis, Mannila, and
Tsaparas, 2007), where the BESTCLUSTERING algorithm is defined as a means for identifying
the individual partition that minimizes the number of disagreements with respect to
the remaining components of the cluster ensemble. Nevertheless, no posterior consensus
clustering based refinement process is applied on this presumably high quality cluster ensemble
component, which, as we have experimentally proved, may bring about important
quality gains.
More recently, the use of clustering solution refinement procedures based on consensus
clustering has been studied in (Fern and Lin, 2008) contemporarily to the completion of this
thesis. That work and ours have multiple points in common, such as i) the primary purpose
of avoiding the negative influence of poor clusterings contained in large cluster ensembles
on the quality of the consensus clustering solutions built upon them, ii) the use of one of
the components of the cluster ensemble as the reference partition for creating the reduced
select cluster ensemble, as we propose in selection-based self-refining, iii) the analysis of
the quality of several refined consensus clustering solutions generated upon multiple select
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