TESI DOCTORAL - La Salle

Appendix C. Experiments on hierarchical consensus architectures
tation of hierarchical architectures are presented in figure C.30. It can be observed that
flat consensus gradually moves from being the optimal consensus architecture in the lowest
diversity scenario to being the slowest in the highest diversity one. Compared to the serial
implementation, the running time differences between RHCA and DHCA are less significant
in this case —except when the ALSAD consensus function is the base of the consensus
architecture.
Consensus quality comparison
As regards the quality of the consensus clustering solutions yielded by each consensus architecture
as a function of the consensus function employed and the diversity scenario, the
results obtained are presented in figure C.31. A few observations can be made: firstly, if
the results obtained by the seven consensus functions are compared, it is to notice that
fairly different performances are obtained: for instance, HGPA gives rise to pretty poorer
quality consensus than the remaining consensus functions, as none of the boxes exceeds the
φ (NMI) =0.6 level. Moreover, these relative performances are maintained across the different
diversity scenarios. Secondly, the variability of the quality of the consensus clustering
solutions can be evaluated by observing figure C.31(d), as the depicted boxplots corresponds
to ten independent runs of the consensus clustering processes on the same cluster ensemble.
Notice that the major differences are observed in the HGPA, MCLA and KMSAD consensus
functions, which, as aforementioned, contain some random parameters that makes their
performance vary (largely, as in HGPA or slightly, as in MCLA) from run to run. Thirdly,
the relative comparison of the quality of the consensus solutions yielded by the the two HCA
and flat consensus is local to the consensus function employed. Whereas DHCA seems to
give rise to better consensus clustering solutions when the CSPA, ALSAD and KMSAD
consensus functions are employed, it tends to be outperformed by RHCA flat consensus
when clusterings are combined by EAC or HGPA. Last, notice that the highest level of
similarity between the top-quality cluster ensemble components and consensus clustering
solutions correspond to DHCA based on the CSPA consensus function.
C.4.2 Wine data set
This section presents the comparison between flat consensus and the computationally optimal
consensus architectures in terms of CPU execution time and normalized mutual information
between the ground truth and the consensus clustering solution yielded by each
one of them. On this data collection, the cluster ensemble sizes corresponding to the four
diversity scenarios are l =45, 450, 855 and 1260.
Running time comparison
As regards the execution times of the fully serial implementations of the estimated optimal
RHCA and DHCA variants and flat consensus, a double evolutive behaviour can be
observed —see figure C.32. Firstly, those consensus architectures using the CSPA, HGPA,
MCLA, ALSAD, KMSAD and SLSAD consensus functions follow the same evolution pattern
observed, for instance, in the Iris data collection (i.e. the larger the cluster ensemble,
the more efficient hierarhical architectures become compared to flat consensus). In contrast,
the consensus architectures based on the EAC consensus function present a fairly different
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