TESI DOCTORAL - La Salle

5.3. Multimodal consensus clustering results
The second analysis consists of comparing the unimodal and multimodal consensus
clusterings with the cluster ensemble components of maximum and median φ (NMI) (which
we call best and median ensemble components, or BEC and MEC for short). Taking these
two cluster ensemble components as a reference, we have computed i) the percentage of
experiments in which the evaluated consensus clustering attains a higher φ (NMI) ,andii) the
relative percentage φ (NMI) differences between them and the evaluated consensus clustering.
The results of this analysis are presented, per data collection and consensus function, in
tables 5.3 and 5.4, where evaluation is referred to BEC and the MEC, respectively.
It can be observed that, as already noticed in previous experiments, the EAC and
HGPA consensus functions perform notably worse than the remaining ones. In average,
unimodal consensus clusterings are better than their corresponding BEC in a 6.5% of the
experiments, whereas the multimodal consensus clustering solutions attain a higher φ (NMI)
than the BEC in a 8.7% of the occasions (see table 5.3). If this comparison is made in
terms of the relative percentage φ (NMI) differences, we see that, in average, the unimodal
consensus clusterings are a 33.5% worse than the BEC, while this percentage reduces to
28.2% when the multimodal consensus clusterings are considered.
If the median ensemble component is taken as a reference –see table 5.4–, we observe
that unimodal consensus clusterings are better than the MEC in a 54% of the experiments
conducted. In contrast, when the multimodal consensus clustering solution is considered,
superiority with respect to the MEC is obtained in a 62.3% of the cases. If the MEC and
the consensus clusterings are compared in terms of relative percentage φ (NMI) differences,
we see that the unimodal consensus yields clusterings which are a 21.1% better than the
MEC, while this percentage rises to 39.6% in the case of multimodal consensus.
Thus, a conclusion we can draw at this point is that, in view of the results just reported,
the execution of consensus processes on multimodal cluster ensembles yields better quality
consensus clusterings than those obtained upon cluster ensembles based on a single modality,
which somehow constitutes a claim in favour of early fusion techniques. However, this
statement must be made with caution, as it is not supported by evidence in all the data
collections (for instance, the CAL500 collection constitutes an exception to this rule).
Multimodal vs unimodal consensus clustering
Secondly, we have compared the quality of the multimodal consensus clusterings (that is,
mod 1+mod 2
mod 1 mod 2
λ ) with the quality of their unimodal counterparts (λ and λ ). Again,
c
c
c
this comparison has been made in terms of the percentage of experiments in which the
former attains a higher φ (NMI) than the latter, and the relative percentage φ (NMI) differences
between them, taking the unimodal consensus clusterings as a reference. The results are
presented in table 5.5.
mod 1+mod 2
In average terms, the multimodal consensus clustering λc is better than its
two unimodal counterparts in a 53.3% of the experiments conducted, and worse than both
of them in only a 13% of the occasions. If the φ (NMI) differences between these consensus
clusterings are measured, we observe that multimodal consensus yields partitions that, in
average relative percentage φ (NMI) terms, are a 4802.4% better. Although this large figure is
mainly caused by two outliers (on the InternetAds data set using the ALSAD and KMSAD
consensus functions), the results presented in table 5.5 show an overwhelming majority of
positive Δφ (NMI) values, which reinforces the notion that multimodal consensus processes,
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