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Appendix F. Experiments on soft consensus clustering
involved in the Condorcet voting method. However, executing CC takes approximately as
long as running CSPA, and much less time than doing so with EAC, which is, by far, the
least efficient consensus function.
When the quality of the consensus clustering solutions delivered by these consensus
functions is compared, we can see that PC, BC and CC obtain the highest φ (NMI) scores
–with no significant differences among them–, closely followed by VMA, SC and CSPA.
φ (NMI)
1
0.8
0.6
0.4
0.2
0
10 0
MFEAT
CPU time (sec.)
10 2
CSPA
EAC
HGPA
MCLA
VMA
BC
CC
PC
SC
Figure F.7: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus
functions on the MFeat data collection.
CSPA EAC HGPA MCLA VMA BC CC PC SC
CSPA ——— 0.0001 0.0001 0.0001 0.0001 0.0001 0.0022 0.0001 0.0001
EAC 0.0001 ——— 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
HGPA 0.0001 0.0001 ——— 0.0013 0.0001 0.0015 0.0001 0.0266 0.026
MCLA 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 × ×
VMA × 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 0.0001
BC 0.0007 0.0001 0.0001 0.0001 0.0034 ——— 0.0001 0.0001 0.0001
CC 0.0008 0.0001 0.0001 0.0001 0.0043 × ——— 0.0001 0.0001
PC 0.0382 0.0001 0.0001 0.0001 × × × ——— ×
SC × 0.0001 0.0001 0.0001 × 0.0024 0.003 × ———
Table F.7: Significance levels p corresponding to the pairwise comparison of soft consensus
functions using a t-paired test on the MFeat 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.8 miniNG data set
In this section we present the results of the soft consensus clustering experiments conducted
on the miniNG data collection. The φ (NMI) vs CPU time diagram of figure F.8 reveals that
three of the proposed voting based consensus functions (BC, PC and SC) constitute a good
trade-off between consensus quality and time complexity.
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