TESI DOCTORAL - La Salle

Appendix C. Experiments on hierarchical consensus architectures
A.5 (i.e. CSPA, EAC, HGPA, MCLA, ALSAD, KMSAD and SLSAD), employing
cluster ensembles of the sizes corresponding to the four diversity scenarios described
in appendix A.4 —which basically boils down to compiling the clusterings output by
|dfA| = {1, 10, 19, 28} clustering algorithms. In all cases, the real running times correspond
to an average of 10 independent runs of the whole RHCA, in order to obtain
representative real running time values (recall that the mini-ensemble components
change from run to run, as they are randomly selected). For a description of the
computational resources employed in or experiments, see appendix A.6.
– How are results presented? Both the real and estimated running times of the
serial and parallel implementations of the RHCA variants are depicted by means of
curves representing their average values.
C.2.1 Iris data set
For starters, let us analyze the results corresponding to the Iris data collection. In this
case, each diversity scenario corresponds to a cluster ensemble of size l =9, 90, 171 and 252,
respectively. The left and right columns of figure C.1 present the estimated and real running
times of several variants of the serial implementation of the RHCA on this data set across
the four diversity scenarios. It can be observed that, as the size of the cluster ensemble
grows, there appear RHCA variants more computationally efficient than flat consensus
(especially when the MCLA and KMSAD consensus functions are employed). However,
there are no significant differences between the running times of the fastest RHCA variant
and flat consensus, probably due to the small size of this data set and of the associated
cluster ensembles. For this reason, the inaccuracies of the running time prediction based
on SERTRHCA are of little importance in practice.
Figure C.2 presents the estimated and real running times of the parallel implementation
of the RHCA in the four diversity scenarios analyzed. According to PERTRHCA, the
parallel RHCA variants with the s = 2/lowest b and s = 3/highest b configurations yield
the maximum computational efficiency —except for the lowest diversity scenario, where flat
consensus is correctly designated to be the fastest option. If these predictions are compared
to the real running times presented on the right column of figure C.2, it can be observed
that, as the diversity level grows, they maintain their accuracy as regards the identification
of the fastest consensus architecture for most consensus functions. However, in the case the
prediction strategy fails to identify the fastest RHCA variant, we make, in terms of absolute
running time penalization, a perfectly assumable error, as the real running times of parallel
RHCA are below one second for the particular case of this data set.
C.2.2 Wine data set
In this section, we present the estimated and real running times of the serial and parallel
implementations of RHCA on the Wine data collection. As aforementioned, this experiment
has been replicated across four diversity scenarios that, in the case of this data set, correspond
to cluster ensembles of size l =45, 450, 855 and 1260. Thus, notice that considerably
large cluster ensembles are obtained in this case, especially if compared to those of the Iris
data collection. This is due to the fact that the Wine data set has a much richer dimensional
diversity as regards the distinct object representations generated (approximately five times
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