TESI DOCTORAL - La Salle

Chapter 2. Cluster ensembles and consensus clustering
strength between the ith and the jth objects. The authors base these consensus functions
on the proved suitability of using similarity measures as object features in classification
problems (Kalska, 2005). Thus, the consensus clustering solution is obtained by applying
standard clustering algorithms on the pairwise object co-association matrix. In particular,
the hierarchical average-link, single-link and k-means clustering algorithms are applied,
giving rise to the ALSAD, SLSAD and KMSAD consensus functions. Notice that these
consensus functions, despite being based on partitioning the object co-association matrix
(just like EAC, for instance), differ from these in that the contents are not interpreted as
measures of similarity between objects, but rather as attributes in a new feature space.
2.2.8 Consensus functions based on cluster centroids
The time and memory scalability problems derived from combining clusterings of large data
sets is the principal motivation of several works that tackle the consensus clustering problem
following a centroid-based approach (Hore, Hall, and Goldgof, 2006; Nguyen and Caruana,
2007). The underlying rationale consists of representing the cluster ensemble components
in terms of the centroids of their clusters, instead of label vectors. By doing so, storage
inconveniences are alleviated, as the number of clusters k is usually much lower than the
number of objects n. In (Hore, Hall, and Goldgof, 2006), moreover, the authors highlight
that the parallelization of the cluster ensemble construction process would dramatically
decrease its time complexity. As regards the creation of the consensus clustering solution,
it is based on computing the average centroid of each cluster, after disambiguating them
by means of the Hungarian algorithm. Furthermore, that work introduced the possibility
of discarding bad clusters from the cluster ensemble at consensus clustering creation time.
In (Nguyen and Caruana, 2007), three iterative consensus functions were presented and
empirically compared with other eleven clustering combiners in a complete experimental
study. The proposal in that work derived the consensus clustering solution in terms of the
centroids of its clusters. Although the proposed consensus functions are capable of combining
clusterings with a variable number of clusters, all the individual partitions contained
in the hard cluster ensembles used in the experiments have the same number of clusters
for simplicity. The first consensus function proposed in this work, called Iterative Voting
Consensus (IVC), is based on recursively computing the centroids of the consensus solution
clusters, and assigning each object to the nearest cluster, which is determined in terms
of the Hamming distance. This procedure is iterated until the centroids of the consensus
clustering solution reach a stable state. The second proposal (named Iterative Probabilistic
Voting Consensus or IPVC), is a variant of IVC in which objects are iteratively assigned
to consensus clusters in terms of their distance with respect to the objects that have been
previously assigned to them. And in the third proposed consensus function, Iterative Pairwise
Consensus or IPC, objects are iteratively reassigned to consensus clusters according to
their similarity as measured by the pairwise object co-association matrix.
2.2.9 Consensus functions based on correlation clustering
Recently, the connection between the late-emerging problem of correlation clustering and
consensus clustering was exploited for deriving novel consensus functions capable of determining
the most natural number of clusters (Gionis, Mannila, and Tsaparas, 2007). In
that work, the cluster ensemble is modeled as a graph resembling a pairwise object co-
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