TESI DOCTORAL - La Salle

4.2. Flat vs. hierarchical self-refining
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 8.3 0 0 0 25 23.9 8.3
RHCA 8.3 0 0 16.7 28.3 23.8 4
DHCA 16.7 0 0.1 16.6 16.7 18.2 8.3
Table 4.4: Percentages of experiments in which the best (non-refined or self-refined) consensus
clustering solution is better than the best cluster ensemble component, averaged across
the twelve data collections.
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 2.7 – – – 3.5 1.1 0.1
RHCA 2.5 – – 1.7 4.2 1 0.1
DHCA 3.3 – 2.2 1.4 1.4 1.2 0.8
Table 4.5: Relative percentage φ (NMI) gains between the best (non-refined or self-refined)
consensus clustering solution and the best cluster ensemble component, averaged across the
twelve data collections.
all the results presented correspond to an average across all the experiments conducted on
the twelve unimodal data collections.
As regards the first issue, table 4.4 presents the percentage of experiments where the
highest quality consensus clustering solution (either refined or non-refined) is better than the
BEC (i.e. it attains a φ (NMI) that is higher than that of the cluster ensemble component that
best describes the group structure of the data in terms of normalized mutual information
with respect to the given ground truth). In average, this happens in a 10.6% of the conducted
experiments, which is a frequency of occurence 100 times higher than what was obtained
when non-refined clustering solutions were considered (see table 3.14 in chapter 3). Again,
this result reveals the notable consensus improvement introduced by the proposed selfrefining
procedure. Moreover, notice the poor results obtained with the EAC and the
HGPA consensus functions, which were already reported to be the worst performing ones
in chapter 3.
Moreover, the relative percentage φ (NMI) gains between the top quality consensus clustering
solution and the BEC are presented in table 4.5, attaining a modest average increase
of 1.8%. However, recall that this figure was as low as 0.6% when the non-refined consensus
clustering solution was considered (see table 3.15 in section 3.4), which indicates that the
consensus self-refining procedure introduces again notable quality improvements.
If this comparison is now referred to the median ensemble component, it can be observed
that, in average, the best (non-refined or self-refined) consensus clustering solution attains
a φ (NMI) that is higher than that of the cluster ensemble component that has the median
normalized mutual information with respect to the given ground truth in a 67.7% of the
experiments conducted (see table 4.6). Recall that this percentage was 53.1% when the
consensus clustering solution prior to self-refining was compared to the MEC —see table
3.12 in section 3.4.
If the degree of improvement between the best (non-refined or self-refined) consensus
clustering solutions that attain a higher φ (NMI) than the MEC is measured in terms of
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