TESI DOCTORAL - La Salle

3.2. Random hierarchical consensus architectures
observed (figures 3.5(a) and 3.5(b)), it can be noticed that i) SERTRHCA is again a pretty
accurate estimation of SRTRHCA, andii) for several consensus functions (in fact, all but
EAC) there exists at least one RHCA variant that is more computationally efficient that
flat consensus. In general terms, the difference between the running times of the fastest
RHCA variant and flat consensus is small, although in the case of the MCLA consensus
function, the execution of flat consensus (i.e. b = l = 570) is six times as costly as the
fastest RHCA variant (the one with b = 20).
Three main conclusions can be drawn at this point: firstly, increasing the size of the
cluster ensemble makes hierarchical consensus architectures a computationally competitive
alternative to flat consensus. Secondly, it is necessary to predict accurately which is the
fastest RHCA variant (i.e. the specific value of the mini-ensembles size b) soastoobtain
significant execution time savings. And thirdly, the computational optimality of a particular
RHCA variant is local to the consensus function employed.
As regards the estimated and real running times of the fully parallel RHCA implementation,
depicted in figures 3.5(c) and 3.5(d), we can conclude that, again, PERTRHCA is a
good indicator of the most computationally efficient RHCA variant. Furthermore, notice
that the differences between the running times of flat consensus and the optimal RHCA are
beyond one order of magnitude for most consensus functions, which highlights the interestingness
of RHCA in computational terms, as well as the need for being able to predict
which is the least time consuming consensus architecture.
Diversity scenario |df A| =19
The results corresponding to the third diversity scenario (i.e. cluster ensembles of size
l = 1083 using |dfA| = 19 randomly chosen clustering algorithms) are presented in figure
3.6. In this case, the mini-ensembles size sweep is b = {2, 3, 4, 5, 6, 8, 9, 26, 27, 541, 1083}.
As regards the serial implementation of the RHCA –whose estimated and real running
times are presented in figures 3.6(a) and 3.6(b), respectively–, a few observations must be
made. Firstly, notice that the curves in figure 3.6(a) present a high degree of resemblance
to the ones in figure 3.6(b), which indicates that SERTRHCA is a notably accurate predictor
of SRTRHCA. Again, we would like to highlight the fact that our main interest is that
the former is a good predictor of the location of the minima of the latter, a goal which is
pretty successfully achieved in this case. Secondly, notice the influence of the consensus
function employed for conducting the clustering combination on the running time of the
RHCA. Whereas most of them yield a similar running time pattern (i.e. they have a
more or less pronounced minimum around b =26orb = 27), two consensus functions
stand out for their particular behaviour: i) when the EAC consensus function is employed,
flat consensus is faster than any serial RHCA variant, and ii) when consensus is created
by means of the MCLA consensus function, the space complexity requirements of MCLA
make flat consensus not executable, as this is the only consensus function (among the ones
employed in this work) whose complexity scales quadratically with the cluster ensemble size
(see appendix A.5).
If the estimated and real parallel RHCA implementation running times are evaluated
(see figures 3.6(c) and 3.6(d)), it can be observed that, whatever the consensus function
employed, there always exists at least one parallel RHCA variant which performs more
efficiently than flat consensus. Moreover, notice that just like in the previous diversity
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