TESI DOCTORAL - La Salle

Appendix C. Experiments on hierarchical consensus architectures
C.3 Estimation of the computationally optimal DHCA
The methodology for selecting the most computationally efficient implementation variant
of deterministic hierarchical consensus architectures presented in section 3.3 –consisting of
estimating the running time of several DHCA variants differing in the order diversity factors
are associated to the stages of the hierarchical consensus architecture, selecting the one that
yields the minimum running time, which is the one to be truly executed– has been applied
on the Iris, Wine, Glass, Ionosphere, WDBC, Balance and MFeat unimodal data sets (see
appendix A.2.1 for a description of these collections).
In these experiments, the fully serial and parallel implementations of DHCA variants
have been considered across the four experimental diversity scenarios employed in this work
—see appendix A.4. The objective of this experiment is twofold: firstly, we seek to verify
whether the proposed strategy succeeds in predicting the most computationally efficient
DHCA variant. And secondly, we intend to analyze the conditions under which deterministic
hierarchical consensus architectures are computationally advantageous compared to flat
consensus clustering. We have followed the experimental design outlined next.
– What do we want to measure?
i) The time complexity of deterministic hierarchical consensus architectures.
ii) The ability of the proposed methodology for predicting the computationally optimal
DHCA variant, in both the fully serial and parallel implementations.
iii) The predictive power of the proposed methodology based on running time estimation
vs the computational optimality criterion based on designing the DHCA
according to a decreasing diversity factor cardinality order, in both the fully
serial and parallel implementations.
– How do we measure it?
i) The time complexity of the implemented serial and parallel DHCA variants is
measured in terms of the CPU time required for their execution —serial running
time (SRTDHCA) and parallel running time (PRTDHCA).
ii) The estimated running times of the same DHCA variants –serial estimated running
time (SERTDHCA) and parallel estimated running time (PERTDHCA)– are
computed by means of the proposed running time estimation methodology, which
is based on the measured running time of c = 1 consensus clustering process. Predictions
regarding the computationally optimal DHCA variant will be successful
in case that both the real and estimated running times are minimized by the
same DHCA variant, and the percentage of experiments in which prediction is
successful is given as a measure of its performance. In order to measure the
impact of incorrect predictions, we also measure the execution time differences
(in both absolute and relative terms) between the truly and the allegedly fastest
DHCA variants in the case prediction fails. This evaluation process is replicated
for a range of values of c ∈ [1, 20], so as to measure the influence of this factor
on the prediction accuracy of the proposed methodology.
iii) Both computationally optimal DHCA variants prediction approaches are compared
in terms of the percentage of experiments in which prediction is successful,
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