TESI DOCTORAL - La Salle

7.1. Hierarchical consensus architectures
make the execution of traditional one-step (aka flat) consensus processes (in which the whole
cluster ensemble is input to the consensus function at once) very costly or even unfeasible
when conducted on highly populated cluster ensembles. For this reason, the application of
a divide-and-conquer strategy on the cluster ensemble –which gives rise to the hierarchical
consensus architectures (HCA) proposed in chapter 3– constitutes an alternative to classic
flat consensus that, besides leaving out none of the l cluster ensemble components, is also
naturally parallelizable, making it even more computationally appealing.
In particular, two types of hierarchical consensus architectures have been proposed:
random and deterministic HCA. Both architectures differ in the way the user intervenes in
their design. In random HCA, the user selects the size (b) of the mini-ensembles intermediate
consensus processes are conducted, which, together with the cluster ensemble size l
determines the number of stages of the consensus architecture. Compared to them, deterministic
HCA provide a more modular approach to consensus clustering, as clusterings of
the same nature are combined at each stage of the hierarchy. In fact, our first approach to
hierarchical consensus architectures dealt with deterministic HCA (Sevillano et al., 2007a),
although it was solely focused on the analysis of the quality of the consensus clusterings
obtained, not on its computational aspect.
Extensive experiments have proven that their computational efficiency is highly dependent
on the characteristics of the consensus function employed for combining the clusterings
(in particular, it depends on how its time complexity scales with the number of clusterings
combined). For instance, flat consensus based on the EAC consensus function is more efficient
than any hierarchical architecture, whereas a rather opposite behaviour is observed
when MCLA is used.
Moreover, we have observed that HCAs become faster than flat consensus when operating
on highly populated cluster ensembles, regardless of whether their fully serial or parallel
implementation is considered (except when the EAC consensus function is employed). Expectably,
the fully parallel version of HCAs outperforms flat consensus (often by a large
margin), even when small cluster ensembles are employed. An additional interesting feature
of hierarchical consensus architectures is that they provide a means for obtaining a
consensus clustering solution in scenarios where the complexity of flat consensus makes its
execution impossible (for a given set of computational resources).
Given the fact that multiple specific implementation variants of a HCA exist, and that
their time complexities can differ largely, it seems necessary to provide the user with tools
that allow to predict, for a given consensus clustering problem, which is the most computationally
efficient one. In this sense, a simple methodology for estimating their running time
–and thus, selecting which is the least time consuming– has also been proposed. Despite
its simplicity, the proposed methodology is capable of achieving an accuracy close to 80%
when predicting the fastest serially implementated HCA variant, while this percentage goes
down to nearly 50% in the parallel implementation case. This difference is caused by the
fact that, in the parallel case, the running time estimation is more sensitive to random
deviations of the measured running times the estimation is based upon, as it often ends up
depending on a single execution time sample. However, the impact of incorrect predictions,
when measured in running time overheads with respect to the truly fastest HCA variant,
is well below 10 seconds in a vast majority of the experiments conducted —of course, the
relative importance of such deviations will ultimately depend on the time requirements of
the specific application the HCA is embedded in.
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