TESI DOCTORAL - La Salle

Chapter 3. Hierarchical consensus architectures
Serial RHCA Parallel RHCA
Dataset % correct ΔRT % correct ΔRT
predictions (sec.) (%) predictions (sec.) (%)
Zoo 72.2 1.11 109.7 54.9 0.10 67.2
Iris 90.4 0.05 26.1 56.7 0.12 102.7
Wine 77.1 0.60 37.8 46.8 0.21 139.5
Glass 74.6 0.49 26.5 25.9 0.26 97.3
Ionosphere 73.1 2.63 16.6 67.8 0.77 110.5
WDBC 63.0 12.11 39.1 38.6 8.17 113.9
Balance 92.4 0.31 29.5 73.2 3.09 87.3
MFeat 83.4 7.02 27.7 76.3 14.41 50.3
average 78.3 3.04 39.1 55.0 3.39 96.1
Table 3.3: Evaluation of the minimum complexity RHCA variant estimation methodology
in terms of the percentage of correct predictions and running time penalizations resulting
from mistaken predictions.
Conclusions regarding the optimal RHCA prediction methodology
As far as the proposed running time estimation methodology is concerned, the following
conclusions are drawn:
– the computation of SERTRHCA and PERTRHCA constitutes a reasonable, simple and
fast means for predicting whether flat or hierarchical consensus must be conducted.
– the selection of computationally suboptimal consensus architectures caused by prediction
errors of the proposed methodology entails a (usually assumable) execution
time overhead.
In order to provide the reader with a more quantitative analysis of the predictive power
of the proposed running time estimation methodology, we have computed the percentage
of experiments –considering the eight data sets over which they have been conducted– the
minimum value of the estimated and real running times is obtained for the same consensus
architecture. If, for a given experiment, both functions are simultaneously minimized, then
our methodology suceeds in determining aprioriwhich is the fastest consensus architecture.
If not, we compute the difference between the real running times of the truly (i.e. the
one that minimizes SRTRHCA or PRTRHCA) and the allegedly (that is, the one minimizing
SERTRHCA or PERTRHCA) computationally optimal consensus architectures, so as to
provide a measure of the impact of choosing a suboptimal consensus configuration both in
absolute and relative terms.
Table 3.3 presents the percentage of experiments where the minima of SERTRHCA
and PERTRHCA predict the most efficient consensus architecture correctly (expressed as
‘% correct predictions’). In this case, SERTRHCA and PERTRHCA have been estimated
upon a single execution (c = 1) of a consensus process on the mini-ensembles of size bij,
i.e. no statistical running time averaging is conducted. Moreover, the difference between
the real running times (ΔRT, measured both in seconds and in relative percentage) of the
truly and the allegedly computationally optimal consensus architectures is also presented,
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