TESI DOCTORAL - La Salle

Appendix C. Experiments on hierarchical consensus architectures
experiment is conducted.
For starters, figure C.7 presents the estimated and real exectution times of several variants
of the fully serial implementation of RHCA. If the estimated and real running times are
compared, it can be observed that it is possible to accurately predict the real execution time
of serial RHCA variants which, at the same time, allows the precise prediction of the most
computationally efficient RHCA variant —the ultimate goal of the proposed methodology.
Figure C.8 depicts the estimated and real running times of the parallel RHCA implementation
across the sweep of values of b for all four diversity scenarios. In comparison to
what is observed in other data sets, PERTRHCA is a better estimator of PRTRHCA in this
case. Moreover, as the diversity of the cluster ensemble grows, the computational savings
derived from employing the fastest RHCA instead of flat consensus are noteworthy (especially
for the HGPA, CSPA, ALSAD and SLSAD consensus functions). Last, note that
flat consensus is not executable in the three of the four diversity scenarios if consensus is
obtained by means of MCLA, due to the large size of the mini-ensembles b.
C.2.5 WDBC data set
In this section, we present the results of estimating the execution times of the serial and
parallel RHCA implementations on the WDBC data collection. According to the four
diversity scenarios generated by employing |dfA| =1, 10, 19 and 28 clustering algorithms
for generating the cluster ensembles, these contain l = 113, 1130, 2147 and 3164 individual
partitions.
The estimated and real running times corresponding to the serial implementation of
RHCA are depicted in figure C.9. As observed in the remaining data collections, SERTRHCA
is a fairly accurate estimator of SRTRHCA, which allows predicting the fastest consensus
architecture with a high precision. Notice that, as already noted in other collections, RHCA
becomes a competitive option as the size of the cluster ensemble grows, except when the EAC
consensus functions is employed. Notice that, for the most diverse scenarios, all consensus
architectures are highly costly (in terms of execution time), so being able to predict which
is the fastest can lead to important computation savings.
As regards the fully parallel implementation of RHCA, the estimated and real running
times corresponding to the four aforementioned diversity scenarios are presented in figure
C.10. Despite the estimation of the real execution time is not as accurate as in the serial
case, PERTRHCA is a reasonable predictor of the fastest consensus architecture in most
cases.
C.2.6 Balance data set
This section presents the estimated and real execution times of multiple variants of random
hierarchical consensus architectures on the Balance data collection, both in its serial and
parallel versions. The low cardinality of the dimensional diversity factor of this data set
gives rise to relatively small cluster ensembles in the four diversity scenarios, which are
equal to l =7, 70, 133 and 196 in this case.
Firstly, figure C.11 depicts the estimated and real running times of the serial RHCA
implementation in the four diversity scenarios. As already observed in the previous data
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