TESI DOCTORAL - La Salle

4.2. Flat vs. hierarchical self-refining
the 30% and 60% of the whole cluster ensemble, i.e. λc30 and λc60. Moreover, notice that
supraconsensus selects λc30 as the final consensus clustering solution (that is, it performs
correctly).
In other cases, supraconsensus fails to select the highest quality consensus clustering
solution. See, for instance, that supraconsensus selects the non-refined consensus clustering
solution λc yielded by the flat consensus architecture based on the EAC consensus function
as the optimal one, whereas the refined clusterings λc40, λc50 and λc60 attain higher φ (NMI)
values (leftmost boxplot chart on the second row of figure 4.1). Furthermore, notice that
in some minority cases, the self-refining procedure introduces no or little improvement,
as when it is applied on the consensus solution output by the RHCA using the ALSAD
consensus function —central column boxplot on the fifth row of figure 4.1.
Last, notice that the boxplot corresponding to the refining of the consensus clustering
solution output by the flat consensus architecture using MCLA –leftmost boxplot on the
fourth row– only presents the φ (NMI) values corresponding to the cluster ensemble E. This
is due to the fact that, for this particular consensus function and diversity scenario, flat
consensus is not executable with our computational resources —see appendix A.6. Moreover,
as all self-refining consensus processes in our experiments have been conducted using a
flat consensus architecture, the self-refining of the consensus clustering solutions output by
RHCA and DHCA are not computed from λc40 forth due to memory limitations when using
the MCLA consensus function. However, recall from chapter 3 that hierarchical consensus
architectures would allow the computation of consensus clustering solutions in situations
where flat consensus is not executable.
A deeper and more quantitative evaluation of the proposed consensus self-refining procedure
requires analyzing two of its facets. Firstly, it is necessary to evaluate the self-refining
process in itself, answering questions such as: i) how often does the self-refining process yield
a higher quality consensus clustering solution than the non-refined one? ii) to which extent
are the top quality self-refined consensus clustering solutions better than their non-refined
counterpart? iii) how do the best self-refined consensus clustering solutions compare to
the cluster ensemble components? or iv) does the self-refining procedure reduce the differences
between the quality of the consensus clustering solutions output by distinct consensus
architectures? The answers to these questions are presented in section 4.2.1.
And secondly, given a set of self-refined consensus clustering solutions, a supraconsensus
function capable of blindly selecting the highest quality self-refined solution is required. Its
performance can be evaluated in terms of i) the percentage of occasions the supraconsensus
function selects the highest quality consensus solution, and ii) the quality loss degree due
to the supraconsensus selection of suboptimal consensus clustering solutions. These aspects
are evaluated in section 4.2.2.
4.2.1 Evaluation of the consensus-based self-refining process
As regards the evaluation of the self-refining process, we have firstly analyzed the percentage
of self-refining experiments in which at least one of the self-refined consensus clustering
solutions attains a φ (NMI) with respect to the ground truth that is higher than the one
achieved by the consensus clustering solution available prior to self-refinement. The results
presented in table 4.2, which correspond to an average across all the data sets for each
consensus architecture and consensus function, reveal that the proposed self-refining proce-
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