TESI DOCTORAL - La Salle

Appendix F. Experiments on soft consensus clustering
CSPA EAC HGPA MCLA VMA BC CC PC SC
CSPA ——— 0.0002 0.0001 0.0345 0.0001 × 0.0001 0.0016 0.0017
EAC 0.0001 ——— 0.0001 × 0.0001 × 0.0001 0.0001 0.0001
HGPA 0.0001 0.0001 ——— 0.0002 0.0001 0.0001 0.0001 × ×
MCLA × 0.0001 0.0001 ——— 0.0001 × 0.0001 0.002 0.002
VMA 0.0001 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 0.0001
BC 0.0233 0.0001 0.0001 0.0001 0.0025 ——— 0.0001 0.0037 0.0038
CC 0.0247 0.0001 0.0001 0.0001 0.0022 × ——— 0.0001 0.0001
PC 0.0001 0.0001 0.0001 0.0001 × 0.0092 0.0084 ——— ×
SC 0.0001 0.0001 0.0001 0.0001 × 0.0064 0.0058 × ———
Table F.3: Significance levels p corresponding to the pairwise comparison of soft consensus
functions using a t-paired test on the Glass data set. The upper and lower triangular sections
of the table correspond to the comparison in terms of CPU time and φ (NMI) , respectively.
Statistically non-significant differences (p >0.05) are denoted by the symbol ×.
F.4 Ionosphere data set
In the following paragraphs, the results of the soft consensus clustering experiments conducted
on the Ionosphere data collection are described.
For starters, figure F.4 displays the φ (NMI) vs CPU time mean ± 2-standard deviation
regions corresponding to the nine consensus functions compared in this experiment. It can
be observed that pretty low quality consensus clustering solutions (φ (NMI) < 0.1) are yielded
by all clustering combiners. The highest φ (NMI) scores are obtained by CSPA, BC and CC,
whose performance is statistically significantly better than that of the other six consensus
functions —see table F.4 for the results of the statistical significance analysis of the results
of this experiment.
As regards time complexity, it can be observed that VMA is the most computationally
efficient option, closely followed by HGPA. The proposed PC and SC consensus functions
are comparable to CSPA and MCLA in computational terms, while the positional voting
based BC and CC consensus functions are, together with EAC, the most time consuming
alternatives. The differences between these three groups are statistically significant, as it
can be inferred from the data measurements presented in table F.4.
F.5 WDBC data set
This section describes the results of the soft consensus clustering experiments conducted on
the WDBC data set.
The φ (NMI) vs CPU time mean ± 2-standard deviation regions of the consensus functions
are depicted in figure F.5. Once again, VMA is the most computationally efficient
consensus function (which, as mentioned earlier, is due to the simultaneity of the cluster
disambiguation and voting processes), closely followed by HGPA. However, the confidence
voting based consensus functions (PC and SC) are pretty close to VMA in CPU time terms,
being slightly faster than CSPA and MCLA. As already noticed in the previous experiments,
positional voting makes the BC and CC consensus functions more computationally costly
(in this case, CC is slightly faster than BC, due to the fact that the low number of clusters
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