TESI DOCTORAL - La Salle

3.4. Flat vs. hierarchical consensus
of the consensus function employed, and that such differences are, in all cases, statistically
significant. As far as the hierarchical consensus architectures are concerned, notice that the
fastest DHCA variant (DRA) is more computationally efficient than its RHCA counterpart
(which has s = 2 stages and mini-ensembles of size b = 28), except when consensus processes
are conducted by means of the EAC and SLSAD consensus functions —in this case, statistically
equivalent running times are attained by both HCA. If these results are contrasted
with the predicted computationally optimal consensus architectures presented in tables 3.4
and 3.10, a single prediction error is detected (flat consensus turns out to be faster than the
DRA DHCA variant when consensus is conducted by MCLA), which reinforces the notion
that the proposed computationally optimal consensus architecture prediction methodology
performs pretty well.
Figure 3.15(b) presents the running times of the fully parallel optimal hierarhical consensus
architectures and flat consensus. As in the serial case, it can be noticed that flat
consensus tends to be more efficient than RHCA and DHCA. The only exception occurs
when consensus is conducted by means of the MCLA consensus function —which is due
to the fact that it is the only combiner the computational complexity of which increases
quadratically with the size of the cluster ensemble. Last but not least, it is to note that,
as opposed to what was observed in the serial implementation, the fastest RHCA is less
time consuming than the most efficient DHCA variant, and the running time differences
between them are statistically significant. The reason for this lies in the fact that this
specific RHCA variant has s = 2 stages and consensus is conducted on mini-ensembles of
size b = 7, whereas the DHCA variant consists of three consensus stages, in one of which
consensus are built on larger mini-ensembles of size |dfD| = 14, which is responsible for the
higher computational cost of parallel DHCA in this case.
Diversity scenario |df A| =10
The results corresponding to the experiments conducted in the second diversity scenario
(i.e. cluster ensembles generated by the compilation of the clusterings output by |dfA| =10
randomly selected clustering algorithms, giving rise to cluster ensembles of size l = 570) are
presented in figure 3.16. In particular, figure 3.16(a) depicts the execution time boxplots
of the serial implementation of hierarchical consensus architectures. The first noticeable
situation is that, in contrast to what was observed in the lowest diversity scenario, the
computationally optimal RHCA variant (s =2andb =20orb = 285 depending on the
consensus function employed) is faster than its DHCA counterpart (DAR). This is due to the
fact that the rise of the algorithmic diversity factor (from |dfA| =1to|dfA| = 10) entails an
increase of the computational cost of one of the DHCA stages that exceeds the increment
of the complexity of the RHCA caused by the same factor. Meanwhile, regarding the
computational efficiency of flat consensus, two opposed behaviours are observed depending
on the consensus function employed: while being faster than any hierarchical architecture
when consensus are built using the CSPA and EAC consensus functions, one-step consensus
is slower when the remaining clustering combiners are employed. Moreover, the differences
between the running times of these consensus architectures is statistically significant at the
5% significance level in all cases.
Figure 3.16(b) presents the results corresponding to the fully parallel implementation
of consensus architectures. In this case, flat consensus is at least four times more computationally
costly than the DHCA and RHCA variants. Moreover, the optimal RHCA
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