TESI DOCTORAL - La Salle

Chapter 2. Cluster ensembles and consensus clustering
2.2.12 Other interesting works on consensus clustering
There exist several works in the literature devoted to the experimental comparison of the
performance of consensus functions, the main interest of which lies in the evaluation of the
quality of the consensus clusterings obtained.
Examples of this include the work by Minaei-Bidgoli, Topchy, and Punch (2004), where
a data resampling scheme was presented as a means for improving the robustness and stability
of the consensus clustering solution. In that work, the EAC, BagClust2, QMI, CSPA,
HGPA and MCLA consensus functions are experimentally compared when operating on
hard cluster ensembles created from bootstrap partitions on several artificial and real data
collections. The main conclusion drawn is that, as expected, there exists no universally superior
consensus function, as each consensus function explores the data set in different ways,
thus its efficiency greatly depends on the existing structure in the data set. Another extensive
and interesting performance comparison between several consensus functions operating
on small hard cluster ensembles is presented in (Kuncheva, Hadjitodorov, and Todorova,
2006). Recently, the application of consensus clustering as a means for avoiding the obtention
of suboptimal clustering solutions when applying non-parametric clustering algorithms
on text document collections is tackled in both (Gonzàlez and Turmo, 2008a) and (Gonzàlez
and Turmo, 2008b). These works compared i) the performance of several non-parametric
clustering algorithms across six text corpora, and ii) the quality of the consensus clustering
solution when it is built –using some of the consensus functions presented in (Gionis,
Mannila, and Tsaparas, 2007)– upon homogeneous and heterogeneous cluster ensembles.
In most of these inter-consensus functions comparisons, the evaluation of their computational
complexity is often given marginal importance, although it becomes a critical aspect
when it comes to their application in practice, especially when dealing with large data
collections or cluster ensembles containing many partitions. This is the main motivation
behind the data sampling strategy proposed in (Greene and Cunningham, 2006; Gionis,
Mannila, and Tsaparas, 2007). The proposal of the latter work is the SAMPLING algorithm,
which consists of performing a sufficient subsampling of the objects in the data set –thus
constructing the consensus clustering solution on a reduced cluster ensemble–, and the subsequent
extension of the combined clustering solution on those objects that have been left
out of the subsampling process. The time complexity of these two processes is linear with
the data set size, which can lead to relevant time savings when dealing with large data
collections.
Another variant of the consensus clustering problem is the weighted combination of
clusterings, which constitutes the central point of (Gonzàlez and Turmo, 2006). The idea
behind weighted consensus clustering is the possibility of giving more relevance to some
components of the cluster ensemble, as they may better describe the structure of the data
set. Thus, it makes sense to combine clusterings in a weighted manner, emphasizing the
contribution of those components deemed as the best ones in the ensemble. Besides designing
consensus functions capable of combining weighted partitions, it is necessary to devise
strategies for setting the proper weight of each individual clustering, which is not trivial in
an unsupervised scenario. In this work, hypergraph-based (Strehl and Ghosh, 2002) and
probabilistic (Topchy, Jain, and Punch, 2004) consensus functions are modified so as to
handle weighted partitions. Moreover, the best weighting scheme is determined by creating
differently weighted cluster ensembles, and subsequently selecting the best option in an
unsupervised manner through the maximization of a scoring function. Moreover, this con-
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