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2.2. Related work on consensus functions
dissociation matrix, and the consensus clustering solution is defined as the one minimizing
the disagreements with respect to the individual partitions contained in the cluster ensemble.
In particular, three consensus functions based on correlation clustering were presented
in this work, which are briefly described next. Firstly, the AGGLOMERATIVE consensus function
results from applying a standard bottom-up procedure for correlation clustering on
cluster ensembles. Resorting to the graph view of the pairwise object distance matrix, the
AGGLOMERATIVE algorithm follows an iterative merging process that joins objects in clusters
depending on whether their average distance is below a predefined threshold, stopping when
further cluster merging does not reduce the number of disagreements of the consensus solution
with respect to the cluster ensemble. Secondly, the FURTHEST consensus function can
be regarded as the converse of AGGLOMERATIVE , as it consists of a top-down procedure that
iteratively separates maximally distant graph vertices into consensus clusters, assigning
the remaining objects to the cluster that minimizes the overall number of disagreements.
This process is stopped when no disagreement reduction is achieved from additional cluster
splitting. And fifthly, the LOCALSEARCH algorithm is derived from the application of a local
search correlation clustering heuristic, which is based on a greedy procedure that, starting
with a specific (possibly random) partition of the graph, tries to minimize the number of
disagreements resulting from moving objects to different clusters or creating new singleton
clusters, stopping when no move can decrease the disagreements rate. Interestingly, the authors
point out that, despite its high computational cost, the LOCALSEARCH algorithm can be
employed as a post-processing step for refining a previously obtained consensus clustering
solution.
2.2.10 Consensus functions based on search techniques
In (Goder and Filkov, 2008), two consensus functions based on search techniques were
introduced. Their rationale consists of building the consensus clustering solution by means
of a greedy search process aiming to minimize the cost function —the authors implement
such search processes either by means of Simulated Annealing (SA), as in (Filkov and Skiena,
2004), and on successive single object movements that guarantee the largest decrease of the
cost function (Best One Element Moves or BOEM).
2.2.11 Consensus functions based on cluster ensemble component selection
Recall that the aim of any consensus clustering process is to obtain a single partition
from a collection of l clustering solutions. As an alternative means for achieving that
goal, cluster ensemble component selection techniques are based on obtaining the consensus
clustering solution by selection, not by combination. For instance, the BESTCLUSTERING
algorithm (Gionis, Mannila, and Tsaparas, 2007) is not a consensus function proper, as it
identifies as the consensus clustering the individual partition that minimizes the number of
disagreements with respect to the remaining clusterings in the cluster ensemble.
Following a very similar approach, the Best of K (BOK) consensus function is based on
selecting that individual clustering from the cluster ensemble that minimizes the number
of pairwise co-clustering disagreements between the individual partitions in the cluster
ensemble (Goder and Filkov, 2008).
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