TESI DOCTORAL - La Salle

Chapter 7. Conclusions
of-the-art consensus funtions employed, both in terms of the quality of the consensus clusterings
they yield and their computational complexity, and the most relevant conclusions
drawn are enumerated next. As regards the consensus functions for hard cluster ensembles,
we have observed that, in general terms, the EAC and HGPA consensus functions deliver,
by far, the poorest quality consensus clusterings. We believe that the low performance of
EAC is due to the fact that it was originally devised for consolidating clusterings with a very
high number of clusters into a consensus partition with a smaller number of clusters (Fred
and Jain, 2005). However, in our experiments, both the cluster ensemble components and
the consensus clustering have the same number of clusters, which probably has a detrimental
effect on the quality of the consensus partitions obtained by the evidence accumulation
approach.
From a computational standpoint, the HGPA and MCLA consensus functions are applicable
on larger data collections than the rest, as their complexity is linear with the number
of objects n. However, the execution time of MCLA is penalized when it is executed on
large cluster ensembles, as its time complexity is quadratic with l (the number of cluster
ensemble components). As regards the soft consensus functions, VMA constitutes the most
attractive alternative, as it yields pretty high quality consensus clusterings while being fast
to execute, thanks to the simultaneous execution of the cluster disambiguation and voting
procedures. A rather opposite behaviour is shown by the soft versions of the EAC and
HGPA consensus functions: the former is notably time consuming, while the latter outputs
really poor quality consensus clusterings.
Let us get critical for a while: possibly one of the major sources of criticism for this
work refers to the rather unrealistic assumption (though not uncommon in the literature)
that the number of clusters the objects must be grouped into (referred to as k) isaknown
parameter. In practice, however, the user seldom knows how many clusters should be found,
so it becomes a further indeterminacy to deal with.
In this work, all the clusterings involved in any process (i.e. the cluster ensemble components
and the consensus clusterings) have the same number of clusters, which coincides
with the number of true groups in the data, defined by the ground truth that constitutes
the gold standard for ultimately evaluating the quality our results. By doing so, we have
also disregarded a common diversity factor employed in the creation of cluster ensembles,
which often contain clusterings with different numbers of clusters (often chosen randomly).
However, we would like to highlight at this point that not many of the consensus functions
found in the literature are capable of estimating the correct number of clusters in
the data set, thus making it necessary to specify the desired value of k as one of their parameters.
Quite obviously, two of the clearest future research directions of this work are i)
estimating the number of clusters of the consensus clustering solution, and ii) adapting the
proposed consensus functions for dealing with cluster ensemble components with distinct
numbers of clusters. The achievement of these goals would constitute the ultimate step
towards a fully generic approach to robust clustering based on cluster ensembles.
7.1 Hierarchical consensus architectures
As regards the computational efficiency of consensus processes, the fact that their space and
time complexities usually scale linearly or quadratically with the cluster ensemble size can
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