TESI DOCTORAL - La Salle

3.4. Flat vs. hierarchical consensus
of objects in the collection, as they employ object co-association matrices as a basic
element of their consensus processes.
– regarding which type of hierarchical consensus architecture (RHCA or DHCA) is
more computationally efficient, little can be said apriori, as it depends on the specific
configurations of the hierarhical architectures, i.e. their number of stages and the
sizes of the mini-ensembles.
– using the MCLA consensus function penalizes those architectures with large miniensembles,
as its time complexity depends quadratically on this factor.
Comparison across diversity scenarios and data collections
Aiming to reveal the existence of any global computational superiority pattern between
the two hierarchical consensus architecture variants, besides confirming the hypotheses put
forward earlier, we have compiled the real running times of the assumedly computationally
optimal RHCA and DHCA variants and of flat consensus in each diversity scenario using
each consensus function, across the twelve data collections employed in these experiments.
This process has been replicated for both the fully serial and parallel implementations
of hierarchical consensus architectures, and as a result, the running time boxplot charts
presented in figures 3.19 and 3.20 have been obtained.
For starters, figure 3.19 presents the running times corresponding to the entirely serial
implementation of the computationally optimal RHCA and DHCA variants and flat consensus.
Notice the notable height of the boxes in the boxplots, caused by the fact that they
represent running times of the consensus architectures across data collections with fairly
distinct characteristics (i.e. number of objects and clusters). Nevertheless, the focus of this
analysis should be placed on detecting relative differences between the boxes corresponding
to the three consensus architectures. In general terms, it can be observed how flat consensus
becomes gradually slower than hierarchical consensus as the size of the cluster ensembles
grows (i.e. as the cardinality of the algorithmic diversity factor |dfA| is increased). As reported
earlier, consensus architectures based on the EAC consensus function constitute the
only exception to this rule. As regards the comparison between the running times of RHCA
and DHCA, the most significant differences are observed when the ALSAD and SLSAD
consensus functions are employed —in these cases, the random HCA variants are faster
than their deterministic counterparts, a trend that becomes more apparent as the cluster
ensembles size grows. Finally, notice that, in absolute terms, consensus architectures based
on the HGPA, MCLA and CSPA consensus functions are faster than those employing the
EAC, ALSAD, KMSAD and SLSAD clustering combiners.
And secondly, the execution time boxplots corresponding to flat consensus and the fully
parallel implementation of consensus architectures are depicted in figure 3.20. As in the serial
case, the use of the HGPA, MCLA and CSPA consensus functions gives rise, in general,
to faster consensus architectures than when consensus clustering solutions are generated by
means of the EAC, ALSAD, KMSAD and SLSAD clustering combiners. Moreover, the superiority
of hierarchical architectures in front of flat consensus becomes manifest in diversity
scenarios with |dfA| ≥10, depending on the consensus function employed. As regards the
comparison between RHCA and DHCA, a wide spectrum of behaviours is observed. When
consensus is built upon the CSPA, EAC, HGPA and KMSAD consensus functions, little significant
differences between both hierarchical architectures are detected. Meanwhile, RHCA
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