TESI DOCTORAL - La Salle

3.4. Flat vs. hierarchical consensus
and allegedly correct cluster structure (or ground truth), measuring their degree
of resemblance in terms of normalized mutual information, φ (NMI) —recall that
φ (NMI) ∈ [0, 1] and the higher its value, the better the quality of the consensus
clustering solution. We measure the percentage of experiments and the relative
φ (NMI) differences between the consensus clusterings and the cluster ensemble
components of maximum and median φ (NMI) score.
ii) We compare the φ (NMI) scores of the consensus clusterings obtained by the three
consensus architectures subject to evaluation.
– How are the experiments designed? The experimental methodology followed is
the same as when the computational efficiency of consensus architectures was analyzed
in the previous sections. That is, the consensus quality comparison has been
conducted on the four diversity scenarios described in appendix A.4. In each diversity
scenario, ten independent experiments have been conducted using the seven consensus
functions for hard cluster ensembles employed in this work (CSPA, EAC, HGPA,
MCLA, ALSAD, KMSAD and SLSAD). From a formal viewpoint, the φ (NMI) values
of the consensus clustering solutions obtained in the 10 experiments corresponding to
each consensus function and diversity scenario are presented.
– How are results presented? In formal terms, the measured φ (NMI) values are
presented by means of boxplot charts. By doing so, we can see the quality scatter
of each consensus function and architecture. Again, non-overlapping boxes notches
indicate that the medians of the compared φ (NMI) differ at the 5% significance level.
– Which data sets are employed? In this section, we present in detail the results
obtained on the Zoo data collection —for the sake of brevity, the results obtained in
the remaining eleven unimodal data sets are deferred to appendix C.4. However, at
the end of this section, the φ (NMI) scores of the three compared consensus architectures
measured across the experiments conducted on the twelve unimodal data collections
employed in this work are compiled and compared. The goal of such comparison is
to analyze whether any of the consensus architecture tends to yield better consensus
clustering solutions than the rest.
One last before proceeding: notice that the only differences between serial and parallel
hierarchical consensus architectures refer to their time complexity, not the quality of the
consensus clustering solutions they yield. For this reason, the distinction between serial and
parallel architectures is not found in this section.
Diversity scenario |df A| =1
Firstly, the φ (NMI) values of the estimated optimal serial and parallel DHCA and RHCA
implementations and flat consensus architectures in the lowest diversity scenario are presented
in figure 3.21. Each chart presents four boxes that, from left to right, represent the
φ (NMI) values of the components of the cluster ensemble E, and of the consensus clustering
solutions output by the RHCA, DHCA and flat consensus architectures, respectively. It
can observed that the three consensus architectures, yield, in general, pretty similar quality
consensus solutions (in fact, the differences between them are statistically non significant
at the 5% level for the CSPA, MCLA, ALSAD and KMSAD consensus functions). The
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