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significant difference among the five risk functionals at the usual 5% signifi-
cance level (
p
=0
.
1 for the Friedman test). The area under the Receiver Oper-
ating Characteristic curve didn't alter these conclusions for the checkerboard
datasets. The counts of wins suggest a superior performance of CE and EXP; the
number of datasets is, however, too small to afford more definite conclusions.
P
bct
and
P
ct
with 'wins'
Tabl e 6 . 6
Percent mean (standard deviation) values of
(bold).
P
bct
CB2
×
2(50)
CB2
×
2(25)
CB2
×
2(10)
CB4
×
4(50)
CB4
×
4(25)
CB4
×
4(10)
MSE
92.87 (2.48) 92.47 (4.73) 76.97 (6.51) 77.94 (4.39) 76.56 (3.96) 70.77 (3.63)
CE
91.25 (2.50) 92.87 (2.35) 83.40 (3.69) 79.40 (3.20) 82.98 (1.78) 80.49 (1.98)
EXP
92.94 (4.30) 93.29 (3.61) 94.14 (5.16) 78.54 (3.57) 80.21 (3.05) 81.47 (3.64)
SEE
86.96 (3.17) 94.36 (1.80) 90.22 (5.66) 73.58 (4.96) 70.93 (4.03) 67.98 (3.95)
R
2
EE
92.48 (3.17) 90.70 (5.45) 91.80 (4.87) 75.59 (5.45) 71.20 (3.69) 73.04 (3.71)
P
ct
Clev. H. D.
Diabetes
Ionosphere
Liver
Sonar
Wdbc
MSE
82.42 (1.08) 76.58 (0.88) 87.81 (1.21) 68.52 (1.97) 78.82 (2.51) 97.39 (0.67)
CE
83.33 (1.07) 76.82 (0.77) 88.04 (1.46) 69.04 (2.01) 78.70 (2.60) 97.44 (0.55)
EXP
81.72 (1.29) 76.76 (0.79) 88.37 (1.88) 69.80 (1.27) 78.82 (2.92) 97.21 (0.68)
SEE
82.72 (1.11) 76.66 (0.85) 87.71 (1.37) 69.08 (1.96) 79.18 (2.50) 97.36 (0.66)
R
2
EE
81.77 (1.81) 75.84 (0.78) 88.50 (1.33) 70.32 (1.54) 77.43 (3.01) 96.89 (0.42)
Further experiments with the datasets of Table 6.5 (not described in [215])
were performed aimed at the comparison of activation functions tanh (used by
default in all experiments described in this chapter), atan, and logistic sigmoid
(see Sect. 3.3). The risk functional used was R
2
EE and the experiments were run
following the same protocol as in [215]. Table 6.7 shows the respective results
("sig" means "logistic sigmoid"). The logistic sigmoid was the activation func-
tion that led to poorer performances in these twelve datasets. The differences
between the tanh and atan activation functions seem more moderate.
P
bct
and
P
ct
with 'wins'
Tabl e 6 . 7
Percent mean (standard deviation) values of
(bold).
P
bct
a.f. CB2x2(50) CB2x2(25) CB2x2(10) CB4x4(50) CB4x4(25) CB4x4(10)
tanh 92.48 (3.17) 90.70 (5.45) 91.80 (4.87) 75.59 (5.45) 71.20 (3.69) 73.04 (3.71)
sig 86.16 (4.78) 85.03 (10.93) 68.08 (6.58) 72.21 (4.83) 70.87 (6.76) 68.79 (6.86)
atan 86.40 (6.81) 90.25 (4.02) 83.71 (8.25) 70.85 (6.54) 72.89 (6.79) 60.63 (6.08)
P
ct
a.f. Clev. H. D. Diabetes Ionosphere Liver Sonar20 Wdbc
tanh 81.77 (1.81) 75.84 (0.78) 88.50 (1.33) 70.32 (1.54) 77.43 (3.01) 96.89 (0.42)
sig 82.25 (1.33) 73.74 (1.43) 86.06 (1.53) 67.19 (3.41) 77.60 (2.76) 96.79 (0.82)
atan 82.87 (0.94) 75.72 (1.09) 87.70 (1.14) 68.66 (1.91) 78.52 (3.04) 96.86 (0.61)
