TESI DOCTORAL - La Salle

3.5. Discussion
separate clustering processes on each type of features (employing well-established clustering
algorithms designed to that end), and subsequently combining the resulting clustering
solutions by means of consensus functions. Thus, this divide and conquer consensus clustering
proposal is aimed to deal with objects composed of multi-type features, rather than
a means for reducing the overall time complexity of consensus processes.
In this chapter, two versions of hierarchical consensus architectures have been proposed.
In each one of them, one of the two factors that define the topology of the architecture are
prefixed, i.e. the number of stages (in deterministic HCA) or the size of the mini-ensembles
(in random hierarchical consensus architectures). Structuring the whole consensus clustering
task as a set of partial consensus processes that take place in successive stages gives
the user the chance to apply different consensus functions across the hierarchy —a possibility
that, to our knowledge, remains unexplored. Moreover, the decomposition of a classic
one-step problem into a set of smaller instances of the same problem naturally allows its parallelization
—provided that sufficient computational resources are available. At this point,
we would like to highlight the fact that, though posed in the context of the robust clustering
problem, hierarchical consensus architectures are applicable to any consensus clustering
task involving large cluster ensembles.
From a practical perspective, we have presented a simple running time estimation
methodology that, for a given consensus clustering problem, allows a fast and pretty accurate
prediction of which is the computationally optimal consensus architecture. However,
the reasonably good performance of the proposed methodology could be further improved
by means of a more complex (probably statistical) modeling of the consensus running times
which constitute the basis of the estimation.
Based on these predictions, we have presented an experimental study in which the flat
and the fastest hierarchical consensus architectures are, firstly, compared in terms of their
execution time. Such comparison has taken into account the most and least computationally
costly HCA implementations (i.e. fully serial and parallel), so as to provide a notion of the
upper and lower bounds of the time complexity of hierarchical consensus architectures.
One of the most expectable conclusions drawn from the conducted experiments is that the
computational optimality of a given consensus architecture is local to the consensus function
F employed for combining the clusterings. In particular, as far as the execution time of
hierarchical consensus architectures is concerned, the main issue to take into account is
the dependence between the time complexity of F and the size of the mini-ensembles upon
which consensus is conducted. For instance, the use of consensus functions the complexity
of which scales quadratically with the number of clusterings consensus is created upon (e.g.
MCLA) clearly favours hierarchical consensus architectures. In contrast, flat consensus
is more efficient than the fastest serial hierarchical consensus architectures even in high
diversity scenarios when consensus functions such as EAC are employed.
Besides analyzing their computational aspects, we have also compared hierarchical and
flat consensus architectures in terms of the quality of the consensus clustering solutions
they yield. In this sense, inter-consensus architecture variability is highly dependent on the
characteristics of the cluster ensemble and the consensus function employed. For instance,
hierarchical and flat consensus architectures based on the CSPA, EAC, ALSAD and SLSAD
consensus functions yield pretty similar quality consensus clusterings, whereas greater variances
are observed when the remaining consensus functions are used. Moreover, in general
terms, we have observed that consensus architectures based on EAC and HGPA typically
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