TESI DOCTORAL - La Salle

C.4. Computationally optimal RHCA, DHCA and flat consensus comparison
C.4 Computationally optimal RHCA, DHCA and flat consensus
comparison
In this section, we compare those random and deterministic hierarchical consensus architectures
deemed to be computationally optimal against classic flat consensus in terms of two
factors: i) their execution times, and ii) the quality of the consensus clustering solutions
they yield. This twofold comparison is intended to determine under which conditions any
the aforementioned consensus architectures outperforms the others, not only in terms of
their computational efficiency, but also as far as their perfomance for the construction of
robust clustering systems is concerned.
This comparison has been conducted across the following eleven unimodal data collection:
Iris, Wine, Glass, Ionosphere, WDBC, Balance, MFeat, miniNG, Segmentation, BBC
and PenDigits. For each data set, ten independent experiments have been conducted on four
diversity scenarios. Each diversity scenario is characterized by the use of cluster ensembles
generated by applying a certain number of clustering algorithms |dfA| = {1, 10, 19, or 28}.
In each experiment, the CPU time required for executing either the whole hierarchical consensus
architecture or flat consensus is measured, and the quality of the consensus clustering
solution is evaluated in terms of its normalized mutual information φ (NMI) with respect the
ground truth.
From a visualization perspective, both the execution times and the φ (NMI) values are
presented by means of their respective boxplots —each of which comprises the ten independent
experiments conducted on each diversity scenario for each data collection. When
comparing boxplots, notice that non-overlapping boxes notches indicate that the medians
of the compared running times differ at the 5% significance level, which allows a quick
inference of the statistical significance of the results.
C.4.1 Iris data set
In this section, the running time and consensus quality comparison experiments are conducted
on the Iris data collection. The four diversity scenarios correspond to cluster ensembles
of sizes l =9, 90, 171 and 252.
Running time comparison
Figure C.29 presents the running times of the allegedly computationally optimal RHCA
and DHCA variants (considering their serial implementation) and flat consensus. Due to
the relatively small cluster ensembles on this data set, it can be observed that flat consensus
is the fastest option in most cases, regardless of the diversity scenario and the consensus
function employed. The only exceptions occur when consensus are built using the MCLA
consensus function in the two highest diversity scenarios –in these cases, DHCA turns out to
be the most efficient consensus architecture–, as this is the only consensus function the time
complexity of which grows quadratically with the size of the cluster ensemble l. Amongthe
hierarchical consensus architectures, DHCA tends to outperform RHCA in computational
terms, except when the ALSAD consensus function is employed (although the differences
between RHCA and DHCA are in general minor).
The execution times corresponding to flat consensus and the entirely parallel implemen-
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