TESI DOCTORAL - La Salle

5.3. Multimodal consensus clustering results
cluster ensemble components that attain φ (NMI) scores higher than that of the
evaluated consensus clusterings, and the percentage of experiments and relative
percentage φ (NMI) differences between them and the cluster ensemble components
of maximum and median quality.
ii) The quality of the self-refined consensus clusterings is measured in terms of their
φ (NMI) with respect to the ground truth of the data set. We also compute the percentage
of experiments in which the top quality self-refined consensus clustering
attains a higher φ (NMI) score than its non-refined counterpart, besides the relative
percentage φ (NMI) differences between them and the maximum and median
cluster ensemble components. On the other hand, the ability of the supraconsensus
function is evaluated by the computation of the percentage of experiments in
which it succeeds in selecting the highest quality consensus clustering available
as the final partition of the data, besides the relative percentage φ (NMI) losses
suffered when it does not.
– How are the experiments designed? Just like in all the experimental sections
of this thesis, consensus clusterings have been derived by means of the seven consensus
functions described in appendix A.5, namely CSPA, EAC, HGPA, MCLA,
ALSAD, KMSAD and SLSAD. By doing so, it is possible to compare their performances
across all the consensus clustering problems conducted. It is important to
note that, in this chapter, we are solely interested in analyzing the quality of the consensus
clustering solutions obtained, as the main purpose of the proposed multimodal
consensus clustering approach is achieving robustness to clustering indeterminacies,
which, as aforementioned, are increased due to multimodality. For brevity reasons,
only the results corresponding to cluster ensembles based on four distinct clustering
algorithms are graphically displayed. These four clustering algorithms –namely
agglo-cos-upgma, direct-cos-i2, graph-cos-i2 and rb-cos-i2 – cover all the clustering
approaches encompassed in the CLUTO clustering package (see appendix A.1 for a
description). However, when global analyses are presented, the results obtained on
the |dfA| = 28 multimodal cluster ensembles are considered.
– How are results presented?
i) The quality of the unimodal, multimodal and intermodal consensus clusterings
obtained is presented by means of φ (NMI) score boxplots. Recall that nonoverlapping
boxes notches indicate that the medians of the compared running
times differ at the 5% significance level, which allows a quick inference of the statistical
significance of the results. Quantitative performance evaluation measures
are presented in the shape of numeric tables showing the average values of the
magnitudes analyzed (mainly, percentage of experiments and relative percentage
φ (NMI) differences).
ii) 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
–fromlefttoright–theφ (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 λcpi obtained upon select
cluster ensembles created using percentages pi = {2, 5, 10, 15, 20, 30, 40, 50, 75}.
140