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%of
experiments
relative %
φ (NMI) loss
Chapter 4. Self-refining consensus architectures
Consensus function
CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
37.5 61.2 84.6 30.6 12.5 23 60
24.6 10.4 16.8 12.2 10.9 12.7 11.9
Table 4.16: Percentage of experiments in which the supraconsensus function selects the top
quality clustering solution, and relative percentage φ (NMI) losses between the top quality
clustering solution and the one selected by supraconsensus, averaged across the twelve data
collections.
sensus function). The results of these two experiments are presented in table 4.16, averaged
across all the data collections and for each consensus function.
The average accuracy with which the supraconsensus function selects the top quality
self-refined consensus selection is 44.2%, i.e. it manages to select the best solution in less
than a half of the experiments conducted. Moreover, this apparent lack of precision entails
an average relative φ (NMI) reduction of 14.2%.
These results reinforce the idea that the supraconsensus function proposed in (Strehl
and Ghosh, 2002) is still far from constituting the most appropriate means for selecting, in
a completely unsupervised manner, the best consensus clustering solution among a bunch
of them, specially if they have pretty similar qualities. This is the reason why the average
level of selection accuracy attained by the supraconsensus function in the selection-based
self-refining scenario is higher than in the consensus-based context (44.2% vs. 29%), as
the φ (NMI) differences between the top quality clustering solution and the remaining ones
is notably higher in the former case than in the latter —in selection-based self-refining,
the selected cluster ensemble component λref is often of notably higher quality than the
self-refined consensus clustering solutions λcpi , see appendix D.2.
In contrast, similar results are obtained in both the selection-based and consensusbased
self-refining scenarios when the efficiency of the supraconsensus function is measured
in terms of the φ (NMI) loss caused from erroneous selections (i.e. when a clustering solution
other than the highest quality one is selected by the supraconsensus function). In
selection-based self-refining, this relative percentage φ (NMI) loss is 14.2%, being 14.9% in
the consensus-based self-refining context.
4.4 Discussion
In this chapter, we have put forward a couple of proposals oriented to obtain a high quality
clustering solution given a cluster ensemble and a similarity measure between partitions,
using consensus clustering and following a fully unsupervised procedure. Together with the
computationally efficient consensus architectures presented in chapter 3, these proposals
constitute the basis for constructing robust consensus clustering systems.
Our proposals are based on applying consensus clustering on a set of clusterings –
compiled in a select cluster ensemble– which are chosen from the cluster ensemble according
to their similarity with respect to an initially available clustering solution. By doing so, we
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