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fuzzy consensus clustering solutions (Dimitriadou, Weingessel, and Hornik, 2002; Punera
and Ghosh, 2007; Sevillano, Alías, and Socoró, 2007b).
Regardless of whether the cluster ensemble is hard or soft, combining the results of
several clustering processes has multiple applications, a good description of which can be
found in (Strehl and Ghosh, 2002). In a nutshell, consensus clustering is useful for:
– knowledge reuse: in some scenarios, one may want to create a partition of a set of
objects, but the access to the original data may be restricted due to copyright or privacy
reasons (customer databases are the most prototypical examples of this type of
situation). However, if a set of legacy partitions of the data exist (e.g. segmentations
of a customer database based on distinct criteria –such as residence, purchasing patterns,
age, etc.), consensus clustering provides a means for reconciling the knowledge
contained in those legacy clusterings.
– distributed clustering: due to security or operational reasons, there exist situations in
which the data to be clustered is scattered across different locations. In this context,
as an alternative to gathering and processing all the data at one site –which can be
unfeasible, for instance, due to storage costs–, the data available at each location
would be subject to a clustering process, and the label vectors obtained would be
combined by means of consensus clustering, yielding a consolidated classification of
the data.
– robust clustering: in this case, the goal is to obtain a consensus clustering solution
that improves the quality of the component clusterings, based on the fact that if the
distinct clustering processes disagree, combining their outcomes may offer additional
information and discriminatory power, thus obtaining a combined better clustering
closer to a hypothetical true classification (Pinto et al., 2007).
It is in this latter application that consensus clustering can be more clearly regarded as
the unsupervised counterpart of classifier committees, as the objective of both strategies is to
combine the outcomes of several classification processes aiming to improve the quality of the
component classifiers (Dietterich, 2000). However, the purely symbolic nature of the labels
returned by unsupervised classifiers makes consensus clustering a more challenging task.
Possibly due to this fact, consensus clustering has historically been far less popular than
classifier committees, and it has only began to draw considerable attention of researchers
during the last decade.
In the quest for obtaining good quality consensus clustering solutions, the design of
both the cluster ensemble and the consensus function are of critical importance. Although
having a cluster ensemble is always necessary in order to conduct consensus clustering, some
works focus mainly on the design of the consensus function, relegating the construction of
the cluster ensemble, and vice versa. Given the importance of both elements, we split the
revision of the related work in this field into two separate parts, devoting section 2.1 to the
previous work regarding the construction of cluster ensembles and section 2.2 to overview
the existing approaches to the design of consensus functions.
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