TESI DOCTORAL - La Salle

Appendix C. Experiments on hierarchical consensus architectures
behaviour, as flat consensus is the fastest option regardless of the diversity scenario. That is,
as already observed in sections C.2.5 and C.3.5, the time complexity behaviour of consensus
architectures is local to the consensus function employed for combining the clusterings.
As regards the computational complexity of the parallel implementation of HCA (see
figure C.33), it can be observed that these become much faster than flat consensus as soon
as the size of the cluster ensemble is increased. As in the previous data collection, the
running times of parallel RHCA and DHCA are pretty similar.
Consensus quality comparison
As far as the quality of the consensus clustering solutions obtained by the distinct consensus
architectures, figure C.34 depicts the corresponding φ (NMI) boxplots. Again, performances
are highly local to the consensus function employed: in this case, those consensus architectures
based on the EAC, HGPA and SLSAD consensus functions give rise to the lowest
quality consensus clusterings. If the three consensus architectures are compared, it can
be observed that RHCA and flat consensus tend to perform quite similarly, while worse
clustering solutions are generally obtained from DHCA. Notice that the highest robustness
to clustering indeterminacies (i.e. consensus clustering solutions of comparable quality to
the cluster ensemble components of highest φ (NMI) ) are obtained from the RHCA and flat
consensus architectures based on MCLA, ALSAD and KMSAD.
C.4.3 Glass data set
In this section, we present the running times and quality evaluation (by means of φ (NMI)
values) of the consensus clustering processes implemented by means of the serial and parallel
RHCA DHCA implementations and flat consensus on the Glass data collection. The cluster
ensembles sizes corresponding to the four diversity scenarios in which our experiments are
conducted are l =29, 290, 551 and 812.
Running time comparison
Figure C.35 presents the boxplot charts that represent the running times of the three implemented
consensus architectures, considering the entirely serial implementation of the
hierarhical ones. As in the previous data collections, flat consensus is the fastest option
in the lowest diversity scenario, whereas hierarchical consensus architectures become more
computationally efficient as soon as the size of the cluster ensemble increases —for all but
the EAC consensus function. which again highlights the interest of structuring consensus
processes in a hierarchical manner as a means for i) reducing their time complexity when
they are to be conducted on large cluster ensembles, and ii) obtaining a consensus clustering
solution when the execution of flat consensus becomes unfeasible (e.g. when the MCLA
consensus function is employed in the highest diversity scenario).
The computational complexity of the consensus architectures presents a very similar
behaviour when the parallel implementation of hierarchical versions is studied (see figure
C.36). In this case, though, the differences between the running times of flat and hierarchical
consensus architectures is even larger.
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