TESI DOCTORAL - La Salle

5.3. Multimodal consensus clustering results
5.3.2 Self-refined consensus clustering across modalities
In this section, we analyze the results of subjecting the intermodal consensus clustering
solution λc to a self-refining procedure based on a cluster ensemble E, the components of
which correspond to both unimodal and multimodal partitions.
As described in chapter 4, the self-refining process is based on the creation of a select
cluster ensemble Epi –containing a percentatge pi of the clusterings in E– followed by
the application of a (either flat or hierarchical) consensus process on it, which yields a
self-refined consensus clustering λ pi
c . In this work, the refining consensus processes are
conducted by means of a flat consensus architecture, and the set of percentages pi employed
is pi = {2, 5, 10, 15, 20, 30, 40, 50, 75}.
For this reason, the obtention of the final consensus clustering solution λ final
c
relies on the
application of a supraconsensus selection function onto the set of self-refined clusterings λ pi
c
—see section 4.1 for a description of the φ (ANMI) -based supraconsensus function employed
in this work. In the following paragraphs, the performances of these two processes (i.e. the
self-refining procedure and the supraconsensus function) are evaluated separately.
As in the previous section, the results of the execution of these processes on the IsoLetters
data collection are described in detail next. Again, for brevity reasons, the presentation of
the results corresponding to the CAL500, InternetAds and Corel data sets is deferred to
appendix E.
Evaluation of the multimodal self-refining process
For starters, figure 5.7 depicts the results of the self-refining process using the multimodal
cluster ensemble resulting from gathering the partitions output by the agglo-cos-upgma
clustering algorithm of the CLUTO package. Each one of the seven boxplots presented (one
per consensus function) shows, from left to right, the φ (NMI) values of the multimodal cluster
ensemble E components, of the intermodal consensus clustering λc, and of the self-refined
consensus clustering solutions λ pi
c . The consensus clustering selected by the supraconsensus
, is highlighted by a vertical green dashed line.
Notice that, regardless of the consensus function employed, there always exists at least
one self-refined consensus clustering solution that attains a φ (NMI) value that is statistically
significantly higher than the one achieved by the non-refined version λc. In some cases, as
when consensus is based on CSPA (figure 5.7(a)), relatively small φ (NMI) gains are obtained,
specially if they are compared with the dramatic φ (NMI) increases brought about by selfrefining
when, for instance, the EAC, HGPA or SLSAD consensus functions are employed
(see figures 5.7(b), 5.7(c) and 5.7(g)).
As regards the ability of the supraconsensus function to select the highest quality (either
refined or non-refined) consensus clustering as the final partition of the data, it is to
notice that it apparently performs reasonably well, as it mostly succeeds in picking up the
clustering solution of maximum φ (NMI) as λfinal c . A deeper analysis of the supraconsensus
function performance will be presented in the next section.
Notice that the proposed intermodal consensus self-refining procedure shows a very similar
behaviour in the experiments conducted on the multimodal cluster ensembles created
upon the partitions output by the direct-cos-i2, thegraph-cos-i2 and the rb-cos-i2 clustering
algorithms from the CLUTO toolbox —see figures 5.8, 5.9 and 5.10, respectively.
function, λ final
c
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