TESI DOCTORAL - La Salle

φ (NMI)
1
0.8
0.6
0.4
0.2
0
CSPA
E
RHCA
DHCA
flat
φ (NMI)
1
0.8
0.6
0.4
0.2
0
EAC
E
RHCA
DHCA
flat
φ (NMI)
1
0.8
0.6
0.4
0.2
0
HGPA
E
RHCA
DHCA
flat
φ (NMI)
Chapter 3. Hierarchical consensus architectures
1
0.8
0.6
0.4
0.2
0
MCLA
E
RHCA
DHCA
flat
φ (NMI)
1
0.8
0.6
0.4
0.2
0
ALSAD
E
RHCA
DHCA
flat
φ (NMI)
1
0.8
0.6
0.4
0.2
0
KMSAD
E
RHCA
DHCA
flat
φ (NMI)
1
0.8
0.6
0.4
0.2
0
SLSAD
E
RHCA
DHCA
flat
Figure 3.24: φ (NMI) of the consensus solutions yielded by 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 = 1596.
given consensus architecture, the HGPA, MCLA and KMSAD consensus functions have the
highest quality variability, due to the existence of some random underlying process in their
consensus generation procedures (e.g. the random initialization of k-means in the KM-
SAD consensus function). In contrast, the qualities of the consensus clusterings output by
those consensus architectures based on CSPA, EAC, ALSAD and SLSAD show very small
(or even null) variations. As regards the inter-consensus architecture quality divergences,
those based on the HGPA and ALSAD consensus functions show the most disparate results,
whereas in other cases (e.g. CSPA, EAC, MCLA or KMSAD) statistically equivalent qualities
are yielded by the three consensus architectures. And last, as far as the robustness of
the consensus clustering solutions is concerned, notice that the EAC, ALSAD, KMSAD and
SLSAD based consensus architectures yield the highest quality clustering results, getting
pretty close to the top-quality component of the cluster ensemble E, being,inmostcases,
better than the 75% of the clusterings contained in it.
Comparison across diversity scenarios and data collections
So as to provide the reader with a global comparative view of the consensus architectures in
terms of the quality of the consensus clustering solutions they yield, we have compiled the
φ (NMI) values obtained across all the experiments conducted on the twelve unimodal data
collections in each diversity scenario, representing them in the boxplots depicted in figure
3.25. Recall that, when comparing boxplots, non-overlapping boxes notches indicate that
the medians of the compared magnitudes differ at the 5% significance level.
A twofold qualitative analysis can be made in view of these results. The first aspect of
study is an intra-consensus function comparison among consensus architectures. A quick
inspection of any of the rows of figure 3.25 reveals that the optimality of consensus architectures
is a property that is local to the consensus function applied. When the clustering
combination process is based on the CSPA consensus function, the three consensus architectures
yield pretty similar quality consensus solutions (as the boxes have a notable overlap),
although DHCA tends to attain slightly higher φ (NMI) values —a similar pattern is observed
in the boxplots presented in the column corresponding to the EAC consensus function. In
contrast, flat consensus architectures yield higher quality consensus than their hierarchical
counterparts when they are based on the HGPA clustering combiner. The analysis of the
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