TESI DOCTORAL - La Salle

3.2. Random hierarchical consensus architectures
SERT RHCA (sec.)
PERT RHCA (sec.)
10 0
10 −1
s : number of stages
5 4 3 3 2 2 1
2 3 4 6 7 28 57
b : mini−ensemble size
(a) Serial estimated running time
5
10
4 3 3 2 2 1
0
s : number of stages
10 −1
2 3 4 6 7 28 57
b : mini−ensemble size
(c) Parallel estimated running time
CSPA
EAC
HGPA
MCLA
ALSAD
KMSAD
SLSAD
CSPA
EAC
HGPA
MCLA
ALSAD
KMSAD
SLSAD
SRT RHCA (sec.)
PRT RHCA (sec.)
10 0
10 −1
s : number of stages
5 4 3 3 2 2 1
2 3 4 6 7 28 57
b : mini−ensemble size
(b) Serial real running time
5
10
4 3 3 2 2 1
0
s : number of stages
10 −1
2 3 4 6 7 28 57
b : mini−ensemble size
(d) Parallel real running time
CSPA
EAC
HGPA
MCLA
ALSAD
KMSAD
SLSAD
CSPA
EAC
HGPA
MCLA
ALSAD
KMSAD
SLSAD
Figure 3.4: Estimated and real running times of the serial RHCA on the Zoo data collection
in the diversity scenario corresponding to a cluster ensemble of size l = 57.
variants. Figures 3.4(c) and 3.4(d) present their counterparts for the parallel RHCA implementation.
The lower horizontal axis of each chart presents the mini-ensembles size b of
each RHCA variant, and the superior horizontal axis indicates the corresponding number
of stages s of the RHCA. Notice, for instance, that s =1forb = 57, which corresponds to
flat consensus.
If the estimated and real execution times of the serial implementation of the RHCA are
analyzed separately (figures 3.4(a) and 3.4(b)), it can be observed that flat consensus is
faster than any RHCA variant regardless of the consensus function employed. This is due
to the small size of the cluster ensemble (l = 57) in this low diversity scenario, which makes
any hierarchical consensus architecture slower than its one-step counterpart.
Moreover, the visual comparison of figures 3.4(a) and 3.4(b) shows that SERTRHCA is
a fairly accurate estimation of SRTRHCA. However, it is to notice that our goal is not
to predict the exact value of SRTRHCA, but to use SERTRHCA to predict where the real
running time will attain its minimum value —which is equivalent to determining the most
computationally efficient RHCA variant, a goal that is perfectly accomplished in this case.
Figures 3.4(c) and 3.4(d) depict the estimated and real running times of the fully
parallel implementation of the same RHCA variants as before. The observation of these
charts reveals that PERTRHCA succeeds notably in predicting the location of the minima
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