TESI DOCTORAL - La Salle

6.4. Experiments
CSPA
EAC
HGPA
MCLA
VMA
φ (NMI) BC CC PC SC
better than ... 27.3% 27.3% 9.1% 9.1%
equivalent to ... 9.1% 9.1% 45.4% 45.4%
worse than ... 63.6% 63.6% 45.4% 45.4%
better than ... 0% 0% 0% 0%
equivalent to ... 0% 0% 0% 0%
worse than ... 100% 100% 100% 100%
better than ... 0% 0% 0% 0%
equivalent to ... 0% 0% 0% 0%
worse than ... 100% 100% 100% 100%
better than ... 0% 0% 0% 0%
equivalent to ... 16.7% 16.7% 16.7% 16.7%
worse than ... 83.3% 83.3% 83.3% 83.3%
better than ... 25% 25% 0% 0%
equivalent to ... 33.3% 33.3% 100% 91.7%
worse than ... 41.7% 41.7% 0% 8.3%
Table 6.3: Percentage of experiments in which the state-of-the-art consensus functions
(CSPA, EAC, HGPA, MCLA and VMA) yield (statistically significant) better/equivalent/worse
consensus clustering solutions than the four proposed consensus functions
(BC, CC, PC and SC).
differences between the distinct voting strategies is somehow lost.
In either case, the φ (NMI) scores obtained by the four proposed voting based consensus
functions is statistically significantly lower than that of CSPA and VMA in only a 15.3% of
the experiments conducted, which clearly indicates that, from a consensus quality perspective,
our proposals constitute an attractive alternative for conducting consensus clustering
on soft cluster ensembles.
And secondly, the results of the previously described comparison, but referred to execution
CPU time, are presented in table 6.4. In general terms, the state-of-the-art consensus
functions (except for EAC) are faster than the proposed consensus functions based on positional
voting methods (BC and CC). This is due to the candidates ranking step that
precedes the voting process itself (see algorithms 6.3 and 6.4). Moreover, the execution of
CC takes longer than BC, due to the exhaustive pairwise candidate comparison involved in
the Condorcet voting method. In contrast, the confidence voting based consensus functions
(PC and SC) are more computationally efficient, being as fast or faster than CSPA, EAC,
HGPA and MCLA in an average 80.7% of the experiments. However, they are unable to
match the computational efficiency of VMA, which, as mentioned earlier, is caused by its
simultaneous and iterative cluster disambiguation and voting procedure.
As a conclusion, it can be stated that the four voting based consensus functions proposed
in this chapter are indeed worthy of being considered as an alternative when it comes to
creating consensus clustering solutions on soft cluster ensembles, as they are capable of
delivering high quality consensus clustering solutions at an acceptable computational cost
—this is specially true for those consensus functions based on confidence voting methods
(i.e. PC and SC). The higher computational complexity of positional voting based consensus
functions (BC and CC) suggests limiting their application to those cases in which the
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