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4.3. Selection-based self-refining
%of
experiments
relative %
φ (NMI) gain
Consensus function
CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
9.1 9.1 0 16.7 36.4 27.6 0
2.1 0.2 – 2.6 1.8 1.3 –
Table 4.14: Percentage of experiments where either the top quality self-refined consensus
clustering solution or λref better the best cluster ensemble component, and relative φ (NMI)
gain percentage with respect to it, averaged across the twelve data collections.
Consensus function
CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
%of
experiments
100 95.4 95 100 100 100 95.4
relative %
φ
118.7 100.7 118.3 114.9 116.1 112.5 107.4
(NMI) gain
Table 4.15: Percentage of experiments where either the top quality self-refined consensus
clustering solution or λref better the median cluster ensemble component, and relative
φ (NMI) gain percentage with respect to it, averaged across the twelve data collections.
age relative φ (NMI) gain of 112.7%. These figures indicate that the selection-based consensus
self-refining yields better results –when compared to the MEC– than its consensus-based
counterpart, where the two aforementioned percentages reduced to 67.7% and 91%, respectively.
As a summarization of this analysis of the selection-based consensus self-refining proposal,
we can conclude that, firstly, it constitutes a fairly good approach as far as the
obtention of a high quality partition of the data is concerned. When compared to the
consensus-based self-refining procedure put forward in section 4.1, it can be observed that,
while the relative quality gains introduced by the self-refining process itself are smaller in
selection-based consensus self-refining, the top quality clustering results obtained are superior
to those yielded by consensus-based self-refining. We believe that these phenomena
are both due to the differences in the quality of the clustering solution that constitutes
the starting point of the self-refining process —in the case of consensus-based self-refining,
this reference is a previously derived consensus clustering λc, which typically is a poorer
data partition than the maximum φ (ANMI) cluster ensemble component λref (see figures in
appendices D.1 and D.2 for a quick visual comparison). This fact makes selection-based
self-refining even a more attractive alternative, all the more since no previous consensus
process execution is required —with the obvious computational savings this implies.
4.3.2 Evaluation of the supraconsensus process
As regards the performance of the supraconsensus function proposed by (Strehl and Ghosh,
2002), we have conducted a twofold evaluation. On one hand, we have analyzed the percentage
of experiments in which the highest quality and the clustering solution selected
via supraconsensus coincide. On the other hand, we have measured the relative percentage
φ (NMI) loss derived from a suboptimal consensus solution selection, using the top quality
clustering solution as a reference (i.e. the one that should be selected by an ideal supracon-
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