TESI DOCTORAL - La Salle

C.3. Estimation of the computationally optimal DHCA
Figure C.20 depicts the estimated and real execution times of fully parallel DHCA variants
and flat consensus. The patterns presented in both columns of this figure (estimated
running times on the left column, real execution times on the right) reveal the same behaviour
observed on the previous data sets. That is, all DHCA variants have comparable
running times, which would make running time estimations unnecessary as far as the election
of the fastest DHCA variant is concerned. However, this estimation is necessary to
decide whether hierarchical consensus is faster that its flat alternative, which occurs in all
the diversity scenarios but in the lowest diversity one.
C.3.4 Ionosphere data set
In this section, the results of estimating the execution times of DHCA are compared to their
real counterparts across four diversity scenarios on the Ionosphere data collection. The cluster
ensemble sizes corresponding to these diversity scenarios are l =97, 970, 1843 and 2716,
respectively.
Firstly, figure C.21 depicts the estimated and real execution times considering the fully
serial implementation of deterministic hierarchical consensus architectures. In this case,
SERTDHCA is a fairly good estimator of SRTDHCA, and it constitutes a good base for
predicting the least time consuming consensus architecture. Notice that, when consensus
clusterings are built by means of the MCLA consensus function, flat consensus execution
becomes impossible (given the computational resources employed in our experiments, see
appendix A.6), so its hierarchical counterpart becomes a feasible alternative. Moreover, if
hierarchical consensus is implemented by means of the DHCA variant defined by an ordered
list of diversity factors arranged in decreasing cardinality order, notable computation time
savings can be obtained.
And secondly, as far as the fully parallel DHCA implementation is concerned (see figure
C.22), the following observations can be made: i) PERTDHCA is a pretty accurate estimator
of PRTDHCA, ii) there are no significant differences between the running times of the
distinct variants of DHCA, and iii) flat consensus is more computationally costly than its
hierarchical counterpart in all but one of the diversity scenarios considered.
C.3.5 WDBC data set
In this section, let us analyze the results corresponding to the WDBC data collection. In
this case, each diversity scenario corresponds to a cluster ensemble of size l = 113, 1130, 2147
and 3164, respectively. In first place, the left and right columns of figure C.23 present the
estimated and real running times of the variants of the serial implementation of the DHCA
on this data set across the four diversity scenarios.
It can be observed that the proposed methodology yields a pretty good estimation
of the real running time of DHCA variants. This allows the user to make well-grounded
decisions regarding the most efficient hierarchical consensus architectures. For this data set,
flat consensus is the computationally optimal architecture except in the highest diversity
scenario —except when the EAC consensus function is employed.
In second place, figure C.24 depicts the results corresponding to the parallel implementation
of DHCA. The same conclusions drawn for the previous data collections are also
applicable in the WDBC data set. That is, running times are almost independent of the
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