TESI DOCTORAL - La Salle

F.3. Glass data set
CSPA EAC HGPA MCLA VMA BC CC PC SC
CSPA ——— 0.001 0.0001 × 0.0001 0.0249 0.0005 0.0001 0.0001
EAC 0.0001 ——— 0.0001 × 0.0001 × 0.0105 0.0001 0.0001
HGPA 0.0001 0.0001 ——— 0.0004 0.0001 0.0001 0.0001 × ×
MCLA × 0.0001 0.0001 ——— 0.0001 × 0.0199 0.0013 0.0014
VMA 0.0001 0.0001 0.0001 0.0001 ——— 0.0001 0.0001 0.0002 0.0002
BC 0.0001 0.0001 0.0001 0.0001 0.0006 ——— × 0.0001 0.0001
CC 0.0001 0.0001 0.0001 0.0001 0.0006 × ——— 0.0001 0.0001
PC 0.0001 0.0001 0.0001 0.0001 × 0.001 0.001 ——— ×
SC 0.0001 0.0001 0.0001 0.0001 × 0.0129 0.0129 × ———
Table F.2: Significance levels p corresponding to the pairwise comparison of soft consensus
functions using a t-paired test on the Wine 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 ×.
φ (NMI)
1
0.8
0.6
0.4
0.2
GLASS
0
0 0.5 1 1.5 2 2.5
CPU time (sec.)
CSPA
EAC
HGPA
MCLA
VMA
BC
CC
PC
SC
Figure F.3: φ (NMI) vs CPU time mean ± 2-standard deviation regions of the soft consensus
functions on the Glass data collection.
As figure F.3 suggests, VMA is again the least time consuming consensus function. As
mentioned earlier, this is due to the simultaneity of the cluster disambiguation and voting
processes in this consensus function. In contast, the proposed CC consensus function is by
far the slowest, probably due to the exhaustive pairwise cluster confrontation implicit in
the Condorcet voting method.
In terms of quality, there is an apparent equality between the VMA, PC and SC consensus
functions, attaining the highest φ (NMI) scores. The CSPA, BC, CC and MCLA
consensus functions apparently yield lower quality consensus clustering solutions.
When the statistical significance of these results is analyzed –see table F.3–, we see that
the apparent time complexity superiority of VMA is statistically significant. As regards the
quality of the consensus clustering solutions, it can be observed that the performances of
VMA, SC and PC are statistically equivalent, whereas the differences between these and
BC and CC are indeed significant.
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