TESI DOCTORAL - La Salle

3.4. Flat vs. hierarchical consensus
results obtained when the MCLA consensus function is employed as the basis of consensus
architectures must be made with care, as flat consensus is not executable when it must
be conducted on large cluster ensembles. For this reason, the boxplots presented in the
MCLA column only reflect the φ (NMI) values corresponding to those experiments where the
three consensus architectures are executable. In these cases, the best consensus clustering
solutions are obtained by the flat and DHCA consensus architectures. A greater degree of
evenness between consensus architectures is observed in the consensus functions that treat
object similarity as object features, i.e. ALSAD, KMSAD and SLSAD —notice the large
overlap between boxes. However, whereas DHCA yields slightly lower quality consensus
clustering solutions than the RHCA and flat consensus architectures when the ALSAD and
KMSAD consensus functions are employed, it is the flat consensus approach that attains
the lowest φ (NMI) values among the SLSAD based consensus architectures.
And secondly, if an inter-consensus functions comparison is conducted, we can conclude
that the excellent performance of the EAC consensus function on the Zoo data collection
apparently constitutes an exception to the rule, as –together with HGPA and SLSAD–
it yields the lowest φ (NMI) values (i.e. the poorest consensus clustering solutions) when
the results obtained across all the data sets and diversity scenarios are compiled. In contrast,
CSPA, MCLA, ALSAD and KMSAD tend to yield comparatively better consensus
clustering solutions in a global perspective.
Following a more quantitative perspective, we have compared the quality of the consensus
clustering solutions yielded by the three consensus architectures with the components
of the cluster ensemble consensus is conducted upon. In particular, this comparison has
taken into account the cluster ensemble components of median and maximum φ (NMI) with
respect to the ground truth (referred to as the median ensemble component, orMEC,and
best ensemble component, or BEC, respectively). This comparison makes sense inasmuch we
focus the application of consensus clustering as a means for becoming robust to the inherent
indeterminacies that affect the clustering problem. More specifically, the higher the φ (NMI)
of the consensus clustering solution with respect to that of the cluster ensemble components,
the higher robustness is achieved. The median and maximum φ (NMI) components are used
as a summarized reference of the quality of the cluster ensemble contents.
For this reason, we have evaluated i) the percentage of experiments in which the consensus
clustering solution attains a higher φ (NMI) than the MEC and the BEC, and ii)
the relative percentage φ (NMI) variation between the median and the best cluster ensemble
components and the consensus clustering solution.
As regards the first issue, table 3.12 presents the percentage of experiments (considering
all data sets in the highest diversity scenario) where the consensus clustering solution is better
than the median normalized mutual information cluster ensemble component (MEC). It
can be observed that the average percentage of experiments (considering all data sets in the
highest diversity scenario) where the consensus clustering solution is better than the MEC
is 53.1%, which indicates than in more than the half of the experiments, consensus yields a
clustering solution better than the one located halfway of the cluster ensemble components.
When the relative percentage φ (NMI) gains between consensus clustering solutions and the
MEC are computed, a reasonable average of 59% gain is obtained —see table 3.13 for a
detailed presentation of the results per consensus function and consensus architecture.
If such comparison is referred to the cluster ensemble component that best describes the
group structure of the data in terms of normalized mutual information with respect to the
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