TESI DOCTORAL - La Salle

φ (NMI)
1
0.8
0.6
0.4
0.2
0
10 0
Appendix F. Experiments on soft consensus clustering
SEGMENTATION
CPU time (sec.)
10 2
CSPA
EAC
HGPA
MCLA
VMA
BC
CC
PC
SC
Figure F.9: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus
functions on the Segmentation data collection.
HPGA, are the immediate followers. Between the two proposed consensus functions based
on positional voting, BC is once more the most efficient (being comparable to CSPA in
terms of execution CPU time), as Borda voting is less computationally demanding than
Condorcet voting.
CSPA EAC HGPA MCLA VMA BC CC PC SC
CSPA ——— 0.0001 0.0001 0.0001 0.0001 × 0.0001 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 ——— × 0.0001 0.0002 0.0001 × ×
MCLA 0.0001 0.0001 0.0001 ——— 0.0001 0.006 0.0001 × ×
VMA × 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0001 0.0001
BC 0.0006 0.0001 0.0001 0.0001 0.0069 ——— 0.0001 0.0007 0.0007
CC 0.0006 0.0001 0.0001 0.0001 0.0069 × ——— 0.0001 0.0001
PC × 0.0001 0.0001 0.0001 × 0.02 0.02 ——— ×
SC × 0.0001 0.0001 0.0001 × 0.0307 0.0307 × ———
Table F.9: Significance levels p corresponding to the pairwise comparison of soft consensus
functions using a t-paired test on the Segmentation 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
×.
However, these two consensus functions (BC and CC) are the ones to obtain the highest
quality consensus clustering solutions, and the difference between their φ (NMI) scores and
those of the remaining clustering combiners is statistically significant, as the figures shown
in table F.9 reveal. The quality of the consensus clusterings output by the other two voting
based consensus functions (PC and SC) is, from a statistical standpoint, equivalent to that
of the VMA and CSPA consensus functions.
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