TESI DOCTORAL - La Salle

3.4. Flat vs. hierarchical consensus
CPU time (sec.)
CPU time (sec.)
8
7
6
5
4
8
7
6
5
4
3
2
1
0
CSPA
RHCA
DHCA
flat
CSPA
RHCA
DHCA
flat
CPU time (sec.)
CPU time (sec.)
1.4
1.2
1
0.8
0.6
0.4
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
EAC
RHCA
DHCA
flat
EAC
RHCA
DHCA
flat
CPU time (sec.)
CPU time (sec.)
9
8
7
6
5
4
HGPA
RHCA
DHCA
flat
CPU time (sec.)
8
7.5
7
6.5
6
5.5
5
4.5
4
MCLA
RHCA
DHCA
flat
CPU time (sec.)
8
7
6
5
4
3
2
1
ALSAD
RHCA
DHCA
flat
(a) Serial implementation running time
8
6
4
2
0
HGPA
RHCA
DHCA
flat
CPU time (sec.)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
MCLA
RHCA
DHCA
flat
CPU time (sec.)
8
7
6
5
4
3
2
1
0
ALSAD
RHCA
DHCA
flat
(b) Parallel implementation running time
CPU time (sec.)
CPU time (sec.)
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
0
KMSAD
RHCA
DHCA
flat
KMSAD
RHCA
DHCA
flat
CPU time (sec.)
CPU time (sec.)
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
0
SLSAD
RHCA
DHCA
flat
SLSAD
RHCA
DHCA
flat
Figure 3.17: Running times of the computationally optimal RHCA, DHCA and flat consensus
architectures on the Zoo data collection for the diversity scenario corresponding to
a cluster ensemble of size l = 1083.
3.5 and 3.11) are at least eight times faster than flat consensus –see figure 3.17(b)– attaining
very similar execution times (being statistically equivalent when the HGPA, ALSAD and
SLSAD consensus functions are employed). This is quite logical provided that DHCA has 3
stages, building consensus on mini-ensembles of sizes |dfA| = 19, |dfD| = 14, and |dfR| =5,
while the fastest RHCA has two or three stages (depending on the consensus function employed)
where consensus is built on mini-ensembles of size b =26orb = 27. At the end of
the day, the number of stages and the mini-ensembles sizes of DHCA and RHCA are conterbalanced,
yielding, as mentioned earlier, pretty similar running times. Notice, however,
that when consensus are built using the MCLA consensus function, RHCA is penalized
with respect to DHCA, given the larger size of its mini-ensembles and the aforementioned
quadratic dependence of this consensus function running time with this factor.
Diversity scenario |df A| =28
A very similar behaviour to the one just reported is observed when the size of the cluster
ensembles is increased. Indeed, in the highest diversity scenario, i.e. the one corresponding
to the use of the |dfA| = 28 clustering algorithms of the CLUTO toolbox for creating cluster
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