TESI DOCTORAL - La Salle

Appendix D. Experiments on self-refining consensus architectures
As regards the performance of the supraconsensus function, the generally small quality
variations among the non-refined and self-refined consensus clustering solutions gives
relative importance to the lack of precision of supraconsensus in most cases. Again, the
only exceptions to this behaviour occur in the refining of the consensus clustering solutions
output by RHCA and DHCA when EAC is employed. In these cases, the supraconsensus
function erroneously selects the non-refined consensus clustering solution λc as the final
clustering solution, although higher quality self-refined partitions are available.
D.1.4 Ionosphere data set
The application of the consensus-based self-refining procedure on the Ionosphere data collection
yields the φ (NMI) boxplots presented in figure D.4. On this collection, self-refining
introduces quality gains in a few cases, such as the refining of the consensus clustering
output by i) RHCA and DHCA using HGPA, or ii) flat consensus architecture and RHCA
based on the SLSAD consensus function. In the remaining cases, the self-refining procedure
brings about little (if any) quality gains.
As regards the selection accuracy of the supraconsensus function, it consistently selects
a good quality clustering solution, if not the highest quality one.
D.1.5 WDBC data set
Figure D.5 presents the φ (NMI) boxplots corresponding to the application of the consensusbased
self-refining procedure on the WDBC data set.
Fairly distinct results are obtained depending on the consensus function employed. For
instance, when consensus is based on EAC and SLSAD, self-refining brings about nothing.
In contrast, spectacular quality gains are obtained on the hierarchically derived consensus
clusterings that employ HGPA. In the remaining cases, more modest φ (NMI) increases are
observed.
Last, notice that the supraconsensus function performs pretty accurately, as it selects
good quality clustering solutions in most cases, although it rarely chooses the top quality
one.
D.1.6 Balance data set
The application of the self-refining consensus procedure on the Balance data set yields the
results summarized by the boxplots presented in figure D.6. It can be observed that, for
most consensus functions and consensus architectures, the self-refined consensus clusterings
show higher φ (NMI) values than those of their non-refined counterpart, λc. In some cases,
these quality gains are notable, as, for instance, when consensus self-refining is based on
the SLSAD consensus function on the flat consensus architecture —bottom row of figure
D.5. In other cases, as in MCLA-based self-refining, the achieved φ (NMI) increases are more
modest.
As regards the ability of the supraconsensus function to select the top quality (nonrefined
or refined) clustering solution, it can be observed that it is a hardly occuring event,
which motivates the low percentage selection accuracy reported in section 4.2.2.
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