TESI DOCTORAL - La Salle

Chapter 4. Self-refining consensus architectures
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 67.7 41.7 62.1 25 75 75 66.7
RHCA 72.3 46.4 69.8 81.9 82 83.3 66.6
DHCA 83.3 33.3 69.2 88.2 83.3 83.1 66.7
Table 4.6: Percentage of experiments in which the best (non-refined or self-refined) consensus
clustering solution is better than the median cluster ensemble component, averaged
across the twelve data collections.
Consensus Consensus function
architecture CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
flat 107.4 33.1 82.4 91.1 113.8 109.1 73.3
RHCA 96.6 24 98.7 109.5 118.4 114.3 70.4
DHCA 113.3 25.6 100.2 108.8 118.9 114.7 87.8
Table 4.7: Relative percentage φ (NMI) gain between the best (non-refined or self-refined)
consensus clustering solution and the median cluster ensemble component, averaged across
the twelve data collections.
relative percentage φ (NMI) increase, a notable 91% relative φ (NMI) gain is obtained in average
—see table 4.7 for a detailed view across consensus functions and architectures. Again,
the beneficial effect of self-refining becomes evident if this result is compared to the one
obtained from the analysis of the non-refined consensus clustering solution as, in that case,
the observed relative φ (NMI) gain was 59% (see table 3.13).
Furthermore, we have also measured the ability of the self-refining procedure for uniformizing
the quality of the consensus clustering solutions output by the distinct consensus
architectures. So as to evaluate this issue, we have computed, for each individual experiment,
the average variance of the φ (NMI) values of the non-refined consensus solutions
yielded by the RHCA, DHCA and flat consensus architectures —the smaller the variance,
the more similar φ (NMI) values. This procedure has been repeated for the top quality (either
refined or non-refined) consensus clustering solutions obtained at each experiment. The results
of this analysis are presented in table 4.8. Except for the EAC consensus function,
we can observe a notable reduction in the variance between the φ (NMI) of the consensus
solutions output by the three considered consensus architectures, keeping it below the hundredth
threshold in most cases. In average global terms, variance is dramatically reduced
by an approximate factor of 20, from 0.105 to 0.0056. For this reason, it can be conjectured
that, besides bettering the quality of consensus clustering solutions as already reported, the
proposed self-refining procedure also helps making the quality of the self-refined consensus
clustering solution more independent from the consensus architecture employed —so that
it can be selected following computational criteria solely.
As a conclusion, it can be asserted that the proposed consensus self-refining procedure is
reasonably successful, as, in general terms, it introduces a quality increase that makes selfrefined
consensus clustering solutions closer to the best individual components available
on the cluster ensemble, which would ultimately constitute the goal of robust clustering
systems based on consensus clustering.
It is of paramount importance to notice that, in the analysis of all the previous results,
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