TESI DOCTORAL - La Salle

φ (NMI)
0.8
0.78
0.76
0.74
0.72
0 100 200 300
clustering index
(a) Decreasingly ordered
φ (NMI) (wrt ground truth)
Chapter 4. Self-refining consensus architectures
φ (ANMI)
0.8
0.75
0.7
0.65
0 100 200 300
clustering index
(b) φ (ANMI) values wrt the
toy cluster ensemble
Figure 4.2: Decreasingly ordered φ (NMI) (wrt ground truth) values of the 300 clusterings
included in the toy cluster ensemble (left), and their corresponding φ (ANMI) values (wrt the
toy cluster ensemble) (right).
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 8.8 14.5 17.8 12 6.7 8.9 12.1
RHCA 6.3 26.6 24.7 27.3 8.6 8.4 16.9
DHCA 15.9 27 22.9 19.6 9.4 11 8.7
Table 4.10: Relative percentage φ (NMI) losses due to suboptimal self-refined consensus clustering
solution selection by supraconsensus, averaged across the twelve data collections.
ground truth. Notice how the monotonic decreasing behaviour of φ (NMI) –figure 4.2(a)– is
not strictly observed in φ (ANMI) (see figure 4.2(b), where a fifth order fitting red dashed
curve is overlayed for comparison). In fact, the clustering attaining the maximum φ (ANMI)
is the one with the fiftieth largest φ (NMI) . Thus, in practice, φ (ANMI) seems to constitute
a means for identifying good clustering solutions, but not the best one. For this reason,
it seems that requiring φ (ANMI) (E, λc) to select the one self-refined consensus clustering
solution of highest quality is a far too restrictive constraint, which leads to the slightly
disappointing results presented in table 4.9.
In order to evaluate the influence of the apparent lack of precision of the supraconsensus
function, we have measured the relative percentage φ (NMI) loss derived from a suboptimal
consensus solution selection, using the top quality consensus clustering solution as a reference
(i.e. the one that should be selected by an ideal supraconsensus function). The results,
which are presented in table 4.10, show that the impact of the modest selection accuracy
of the supraconsensus function leads to an average relative φ (NMI) loss of 14.9%.
To conclude, it can be asserted that, while the proposed consensus self-refining procedure
introduces notable gains as regards the quality of consensus clustering solutions, there
still exists room for taking full advantage of its performance, as the entirely unsupervised
selection of the highest quality consensus solution is not a fully solved problem yet.
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