TESI DOCTORAL - La Salle

Chapter 4. Self-refining consensus architectures
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 90.4 63.6 70 77.25 80 76.9 90
RHCA 85.7 83.2 97 94.2 73.4 76.5 82.4
DHCA 91.1 78.5 98 88.5 89.8 88.1 67.8
Table 4.2: Percentages of self-refining experiments in which one of the self-refined consensus
clustering solutions is better than its non-refined counterpart, averaged across the twelve
data collections.
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 16.5 273.3 53.3 14.9 9.8 16.1 433.4
RHCA 10.9 157.1 294779.8 200.8 14.1 15.1 205.6
DHCA 24.5 66.4 152450.9 79.9 38.4 30.9 224.9
Table 4.3: Relative φ (NMI) gain percentage between the top quality self-refined consensus
clustering solutions with respect to its non-refined counterpart, averaged across the twelve
data collections.
dure performs pretty successfully, giving rise to at least one self-refined consensus clustering
solution that improves the consensus clustering available prior to refining in an average 83%
of the experiments conducted.
Moreover, we have also computed the relative φ (NMI) percentage gain between the nonrefined
and the top quality self-refined consensus clustering solution —considering only
those experiments where self-refining yields a better clustering solution, i.e. the 83% of
the total. The results presented in table 4.3, which again correspond to an average across
all the data sets for each consensus architecture and consensus function, reveal that the
proposed self-refining procedure performs in an overwhelmingly successful manner, giving
rise to an average relative percentage φ (NMI) gain of 21386% across all the experiments
conducted. This exceptionally large figure is due to the fact that, although seldom, extremely
poor quality consensus clustering solutions are available prior to self-refining in some cases.
In particular, this situation is found when the HGPA consensus function is employed for
refining the consensus clustering solutions yielded by hierarchical consensus architectures
on the WDBC and BBC data collections (see, for instance, figure D.10 in appendix D).
Despite its exceptionality, this fact introduces a large bias on the averaged values of φ (NMI)
gains. However, if this kind of artifact is ignored, relative φ (NMI) gains between 10% and
430% are consistently obtained in all cases, which gives an idea of the suitability of the
proposed self-refining procedure for bettering consensus clustering solutions.
Besides comparing the top quality self-refined consensus clustering solution with its
non-refined counterpart, we have also contrasted its quality with respect to the highest and
median φ (NMI) components of the cluster ensemble E, referred to as BEC (best ensemble
component) and MEC (median ensemble component), respectively. Using the quality of
these two components as a reference, we have evaluated i) the percentage of experiments
where the maximum φ (NMI) (either refined or non-refined) 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. Again,
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