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Chapter 4. Self-refining consensus architectures
Consensus function
CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
54.5 28.2 10.3 69.6 81.8 82 65.4
Table 4.12: Percentage of self-refining experiments in which one of the self-refined consensus
clustering solutions is better than the selected cluster ensemble component reference λref,
averaged across the twelve data collections.
Consensus function
CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
26.9 9.1 20.8 15.2 15.5 11.4 7.8
Table 4.13: Relative φ (NMI) gain percentage between the top quality self-refined consensus
clustering solutions with respect to the maximum φ (ANMI) cluster ensemble component,
averaged across the twelve data collections.
creation uses a previously derived consensus clustering solution (it was 83%). This is due to
the fact that the cluster ensemble component selection usually results in using a reference
clustering λref of higher quality than the consensus clustering solution λc.
Secondly, in those experiments where self-refined consensus solutions are better than
λref, we have measured the relative degree of improvement achieved (quantified in terms
of relative percentage φ (NMI) increase). The results, presented in table 4.13, show notable
quality improvements, averaging a 15.2% relative φ (NMI) gain across all data sets and consensus
functions. These quality gains obtained are much smaller than those obtained on the
self-refining experiments based on a previously derived consensus clustering solution (see
section 4.2), again due to the superior quality of the reference clustering the self-refining
procedure is based upon.
Next, the maximum and median φ (NMI) components of the cluster ensemble E –referred
to as BEC (best ensemble component) and MEC (median ensemble component), respectively–
are compared to either the top quality self-refined consensus clustering solution or λref,
(depending on which has the largest φ (NMI) with respect to the ground truth). As in the
previous section, we have evaluated i) the percentage of experiments where the maximum
φ (NMI) consensus clustering solution attains a higher quality to that of the BEC and MEC,
and ii) the relative percentage φ (NMI) variation between them and the top quality consensus
clustering solution. Once more, all the results presented correspond to an average across
all the experiments conducted on the twelve unimodal data collections.
On one hand, table 4.14 presents the aforementioned magnitudes referred to the best
cluster ensemble component. In average, the highest quality clustering (either λref or one
of the self-refined consensus solutions) is better that the BEC in a 14.1% of the conducted
experiments, achieving an average relative percentage φ (NMI) gain of 1.6%. It is important
to notice that these results are pretty similar to those obtained when self-refining is based
on a previously derived consensus clustering solution (see section 4.2), as these percentages
were equal to 10.6% and 1.8%, respectively.
On the other hand, table 4.15 presents the results of the same experiment, but referred
to the median ensemble component (or MEC). In this case, the selection and self-refining
procedure yields clusterings better than the MEC in 98% of the occasions, attaining an aver-
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