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4.3. Selection-based self-refining
4.3 Selection-based self-refining
The consensus self-refining procedure proposed in section 4.1 is based on using a consensus
clustering solution as a reference for computing the φ (NMI) of the cluster ensemble components,
which, at the same time, constitutes the guiding principle of the creation of the select
cluster ensemble Ep, upon which the self-refining process is conducted.
In this section, we propose an alternative procedure for obtaining a self-refined consensus
clustering solution. The only difference between this proposal and the one put forward in
section 4.1 lies in the fact that the computation of the φ (NMI) of the cluster ensemble
components –a step prior to the creation of the select cluster ensemble Ep– is not referred
to a previously obtained consensus labeling λc, but to one of the components of the cluster
ensemble E.
By doing so, we aim to devise an alternative means for obtaining a high quality clustering
from a large cluster ensemble that does not require the execution of any consensus process
for obtaining the reference clustering with respect to which the cluster ensemble components
are compared in terms of normalized mutual information, with the obvious computational
savings it conveys.
Due to the fact that this proposed method is based on selecting one of the cluster
ensemble components for initiating the consensus self-refining process, we have called it
selection-based self-refining, and its constituting steps are presented in table 4.11.
In the next paragraphs, we will analyze the performance of this second self-refining
proposal, following the same experimental scheme employed in section 4.2. That is, we firstly
review the results obtained on the Zoo data collection at a qualitative level (the analysis
corresponding to the remaining data collections is presented in appendix D.2), followed by
a quantitative study of the quality of the self-refined consensus clustering solutions across
all the experiments conducted.
With the objective of making the results of selection-based consensus self-refining comparable
to those presented in the previous section, we have followed the same experimental
procedure, that is: i) the experiments have been replicated for a set of self-refining percentage
values in the range p ∈ [2, 90], ii) the experiments have been executed on the cluster
ensembles corresponding to the highest diversity scenario.
For starters, figure 4.3 depicts the boxplot charts of the φ (NMI) values corresponding to
the selection-based consensus self-refining process. Each chart depicts –from left to right–
the φ (NMI) values of: i) the components of the cluster ensemble E, ii) the cluster ensemble
component with maximum φ (ANMI) with respect to the whole ensemble, i.e. λref, andiii)
the self-refined consensus clusterings λcpi obtained upon select cluster ensembles created
using percentages pi = {2, 5, 10, 15, 20, 30, 40, 50, 60, 75, 90}.
Firstly, we can notice the high quality of the selected cluster ensemble component λref,
the φ (NMI) of which is pretty close to the highest quality component of the cluster ensemble
E. Thus, it seems that the proposed selection procedure constitutes, by itself, a fairly good
approach for obtaining clustering solutions that are robust to the inherent indeterminacies
of the clustering problem. When the self-refining procedure is applied on the select cluster
ensemble created upon λref, distinct performances are observed. Whereas in some cases
none of the self-refined clustering solutions λcpi attains higher φ (NMI) values than λref (see,
for instance, figure 4.3(a)), the opposite is observed when self-refining based on the EAC and
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