TESI DOCTORAL - La Salle

5.3. Multimodal consensus clustering results
Data set
IsoLetters
CAL500
InternetAds
Corel
Consensus function
CSPA EAC HGPA MCLA ALSAD KMSAD SLSAD
100 92.9 100 99.3 100 100 100
(96.4) (21.4) (2.9) (82.9) (100) (100) (96.4)
100 21.4 97.1 99.3 100 100 71.4
(100) (7.1) (15) (40) (100) (93.6) (32.1)
96.4 60.7 2.9 100 85.7 92.1 60.7
(75) (32.1) (0) (72.9) (75) (66.4) (17.9)
100 14.3 91.4 100 100 100 60.8
(100) (14.3) (10) (15.7) (89.3) (85) (17.9)
Table 5.12: Percentage of experiments in which the top quality (either non-refined or selfrefined)
consensus clustering solution is better than the median cluster ensemble component
(or MEC), across the four multimedia data collections and the seven consensus functions.
The percentages prior to self-refining are shown in brackets.
MEC), its quality is surpassed by the top quality consensus clustering in an average 83.8%
of the experiments conducted —see table 5.12 for a detailed vision of these results across
data sets and consensus functions. It can be observed that in a vast majority of cases, selfrefining
guarantees the obtention of partitions that are better than the median clustering
available in the cluster ensemble. Again, the percentage of experiments in which the nonrefined
intermodal consensus clustering attains a higher φ (NMI) than the MEC is presented
in brackets in each box of the table, yielding an average of 55.7% —that is, self-refining
increases the chances of obtaining a partition better than the median one in almost a 30%.
But better to what extent? So as to answer this question, table 5.13 presents the
relative φ (NMI) percentage differences between the top quality consensus clustering and
the MEC, considering only those experiments in which the former attains a higher φ (NMI)
value than the latter. In average, a relative percentage gain of 142.7% is achieved, which
again reinforces the notion that the proposed multimodal consensus self-refining process is,
by itself, capable of yielding good quality partitions upon a previously derived consensus
clustering solution. Moreover, each box in table 5.13 shows, in brackets, the relative φ (NMI)
percentage differences between the non-refined intermodal consensus clustering λc and the
MEC. Notice how the self-refining procedure, besides yielding consensus clusterings superior
to the MEC in a larger number of experiments, also increases the difference with respect
to it, rising it from an average 103.7% to the aforementioned 142.7%. In the experiments
in which the top quality fails to attain a higher φ (NMI) value than that of the MEC (i.e. a
16.2% of the total), their quality is a 32.1% lower, measured in average relative percentage
φ (NMI) terms.
However, it is to notice that, in tables 5.7 to 5.13, the performance of the self-refining
procedure has been evaluated taking the highest φ (NMI) self-refined consensus clustering
solution as a reference. But, as aforementioned, the self-refining process generates multiple
self-refined clusterings λ pi
c using distinct percentages pi of the original cluster ensemble
E. Therefore, the subsequent application of the average normalized mutual information
(φ (ANMI) ) based supraconsensus function is required so as to obtain the final partition of
the multimodal data set, λ final
c . As already described in chapter 4, the ability of the
supraconsensus function to select the top quality consensus clustering solution is a crucial
issue as regards the overall performance of the multimodal self-refining consensus clustering
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