TESI DOCTORAL - La Salle

C.2. Estimation of the computationally optimal RHCA
C.2 Estimation of the computationally optimal RHCA
Section 3.2 presents a methodology for selecting the most computationally efficient implementation
variant of random hierarchical consensus architectures. In short, such methodology
consists of estimating the running time of several RHCA variants differing in the
mini-ensembles size b, selecting the one that yields the minimum running time, which is the
one to be truly executed.
So as to validate this procedure, in this section we present the estimated and real running
times of several variants of the fully serial and parallel implementations of RHCA on the
Iris, Wine, Glass, Ionosphere, WDBC, Balance and MFeat unimodal data sets (see appendix
A.2.1 for a description of these collections) 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 RHCA variant. And secondly, we intend to analyze the conditions
under which random hierarchical consensus architectures are computationally advantageous
compared to flat consensus clustering. The experimental design that has been followed is
outlined next.
– What do we want to measure?
i) The time complexity of random hierarchical consensus architectures.
ii) The ability of the proposed methodology for predicting the computationally optimal
RHCA variant, in both the fully serial and parallel implementations.
– How do we measure it?
i) The time complexity of the implemented serial and parallel RHCA variants is
measured in terms of the CPU time required for their execution —serial running
time (SRTRHCA) and parallel running time (PRTRHCA).
ii) The estimated running times of the same RHCA variants –serial estimated running
time (SERTRHCA) and parallel estimated running time (PERTRHCA)– 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 RHCA variant will be successful
in case that both the real and estimated running times are minimized by the
same RHCA 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
RHCA 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.
– How are the experiments designed? All the RHCA variants corresponding to
the sweep of values of b resulting from the proposed running time estimation methodology
have been implemented (see table 3.2). In order to test our proposals under a
wide spectrum of experimental situations, consensus processes have been conducted
using the seven consensus functions for hard cluster ensembles presented in appendix
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