TESI DOCTORAL - La Salle

4.2. Flat vs. hierarchical self-refining
in all the experimental sections of this thesis, consensus processes have been replicated
using the set of seven consensus functions described in appendix A.5, namely: CSPA,
EAC, HGPA, MCLA, ALSAD, KMSAD and SLSAD. Results are averaged across ten
independent experiments consisting of ten consensus function runs each. With the
objective of analyzing the expectable dependence between the degree of refinement of
the consensus clustering solution and the percentage p of cluster ensemble components
included in the select cluster ensemble Ep, the experiments have been replicated for a
set of percentage values in the range p ∈ [2, 90]. Subsequently, the final consensus label
vector λ final
c is selected among all the available (i.e. non-refined and refined) consensus
clustering solutions through the application of the supraconsensus function presented
in equation (4.3). Last, it is important to state that, although it is possible (and, in
fact, recommendable) to apply either flat or hierarchical consensus on the select cluster
ensemble depending on which is the most computationally efficient option, all selfrefining
consensus processes in our experiments have been conducted, for simplicity,
using a flat consensus architecture.
– How are results presented? Results are presented by means of boxplot charts of
the φ (NMI) values corresponding to the consensus self-refining process. In particular,
each subfigure depicts –from left to right– the φ (NMI) values of: i) the components of
the cluster ensemble E, ii) the non-refined consensus clustering solution (i.e. the one
resulting from the application of either a hierarchical or a flat consensus architecture,
denoted as λc), and iii) the self-refined consensus labelings λc p i obtained upon select
cluster ensembles created using percentages pi = {2, 5, 10, 15, 20, 30, 40, 50, 60, 75, 90}.
Moreover, the consensus clustering solution deemed as the optimal one (across a
majority of experiment runs) by the supraconsensus function is identified by means
of a vertical green dashed line. Moreover, the quality comparisons between the selfrefined
consensus clusterings, the non-refined consensus clusterings and the cluster
ensemble components are presented by means of tables showing the average values of
the measured magnitudes.
– Which data sets are employed? These experiments span the twelve unimodal data
collections employed in this work. For brevity reasons, and following the presentation
scheme of the previous chapter, this section only describes in detail the results of
the self-refining procedure obtained on the Zoo data set, deferring the portrayal of
the results obtained on the remaining data collections to appendix D.1. However,
the global evaluation of the self-refining and the supraconsensus processes entails the
results obtained on the twelve unimodal collections employed in this work.
Figure 4.1 presents the boxplot charts of the φ (NMI) values corresponding to the consensus
self-refining process applied on the Zoo data set. Notice that figure 4.1 is organized into
three columns of subfigures, each one of which corresponds to one of the three consensus
architectures, i.e. flat, RHCA and DHCA.
Pretty varied results can be observed in figure 4.1, as regards both the performance of
the self-refining process in itself and of the supraconsensus selection function. For instance,
when the consensus clustering solution output by the flat consensus architecture using the
CSPA consensus function is subject to self-refining (see the leftmost boxplot on the top
row of figure 4.1), we can observe that two of the refined solutions yield clearly higher
φ (NMI) values than their non-refined counterpart —in particular, the ones obtained using
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