TESI DOCTORAL - La Salle

Consensus quality comparison
Appendix C. Experiments on hierarchical consensus architectures
As regards the quality of the consensus clustering process, figure C.37 presents the boxplots
depicting the φ (NMI) values of the components of the cluster ensemble E and of the consensus
clustering solutions output by the RHCA, DHCA and flat consensus architectures. On
this data collection, the φ (NMI) differences between the clustering solutions output by the
three distinct consensus architectures are, in general terms, small —except when the EAC
consensus function is employed, as flat consensus is clearly superior in this case. Moreover,
we can observe that ALSAD and SLSAD outstand among the remaining consenus functions
as the top performers.
C.4.4 Ionosphere data set
This section presents the execution times of the computationally optimal RHCA, DHCA
and flat consensus architecture and the φ (NMI) values of the consensus clustering solutions
yielded by them on the Ionosphere data collection. The presented results consider the
experiments conducted across four diversity scenarios, and the cluster ensemble sizes corresponding
to them are l =97, 970, 1843 and 2716, respectively.
Running time comparison
The execution times of flat consensus and the serially implemented RHCA and DHCA are
depicted in the boxplots charts presented in figure C.38. The relative behaviour of the
three consensus architectures is pretty similar to the one observed on the previous data
collections. That is, i) flat consensus becomes slower than its hierarchical counterparts as
the size of the cluster ensemble becomes larger, except when the EAC consensus function is
employed, and ii) RHCA tends to be faster than DHCA when the EAC, ALSAD, SLSAD,
whereas the opposite behaviour is observed in the hypergraph based consensus functions.
The running times obtained in the case the hierarchical consensus architectures are
implemented in an entirely parallel manner are presented in figure C.39. As expected,
RHCA and DHCA become sensibly more efficient than flat consensus. Notice, however,
that notable differences between the running times of the two hierarchical architectures can
be found under certain consensus functions, such as EAC, ALSAD, or SLSAD.
Consensus quality comparison
As far as the quality of the consensus clustering process is concerned, the φ (NMI) boxplots
corresponding to the consensus clustering solutions obtained by the RHCA, DHCA and flat
consensus architectures across the four diversity scenarios on the Ionosphere data collection
are presented in figure C.40. A notably high variability as regards the optimality of the
different consensus architectures is found depending on the consensus function employed.
For instance, DHCA tends to yield the highest quality results when consensus is conducted
by means of SLSAD, flat consensus gives the best consensus clustering solutions derived by
HGPA, and when MCLA is chosen as the clustering combiner, RHCA attains the higher
φ (NMI) values than the remaining consensus architectures. In contrast, marginal quality
differences are observed between the qualities of the consensus clustering solutions derived
by the three consensus architectures when the remaining consensus functions are employed.
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