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RBF kernel [227] (best value for parameter
g
varying from 2.2 to 0.8 in steps
of 0.2, for
C
=10and
C
= 100),
k
-NN [59] (best value for
k
=1, 3, 5 and 7)
and the C4.5 decision tree [177]. For the MEE version three results for each
value of the learning rate were obtained for kernel bandwidths of 1.0, 1.2 and
1.4. Only the best results are reported in Table 6.13. Also the results shown
for the CVNNs were the best obtained when training ran for 4 000 epochs,
evaluated at 20 epochs intervals on the test set.
The results for the Checkerboard problem are impressive: the CVNN is
able to attain almost perfect classification with the second best method, SVM
with RBF, lagging behind. The different performance is statistically highly
significant: e.g.,
t
-test
p
0 for the last row MEE average error rate of 0.23.
For this dataset, the MEE algorithm is also the best one for the tested values
of the parameters, when compared with the other two CVNN versions; even
when one takes the
η
=0
.
07 case, where the difference between the MEE
and the MMSE algorithms is the smallest, the superiorness of the MEE is
statistically significant (
t
-test
p
=0
.
006).
For the Brest Cancer problem, the SVM with RBF was the best classifier.
The CVNN algorithms came in second place. However the difference between
the SVM performance and the best MEE performance (33.00) has no statis-
tical significance (
t
-test
p
=0
.
148). The same can be said of the difference
between the MEE CVNN and the other CVNNs.
≈
Tabl e 6 . 13 Average error in percentage, with standard deviation for 30 repetitions
of a two fold-cross validation for both datasets. CVNN B-MMSE is the batch MMSE
algorithm.
Checkerboard
Breast cancer
Classifier
Parameters
Error (std)
Parameters
Error (std)
SVM RBF
g=1.8, C=10
2.92 (0.60)
g=1.0, C=10
31.83 (3.23)
k
-NN
k
=1
4.48 (0.98)
k
=5
34.42 (2.99)
C4.5
None
25.22 (0.29)
None
35.28 (5.28)
CVNN MMSE
η
=0
.
09
0.51 (0.38)
η
=0
.
09
32.11 (5.68)
CVNN B-MMSE
η
=0
.
09
0.60 (0.43)
η
=0
.
09
33.25 (6.05)
CVNN MEE
η
=0
.
09
,h
=1
.
0
0.30 (0.22)
η
=0
.
09
,h
=1
.
0
33.14 (5.55)
CVNN MMSE
η
=0
.
07
0.43 (0.26)
η
=0
.
07
32.69 (5.30)
CVNN B-MMSE
η
=0
.
07
0.48 (0.39)
η
=0
.
07
33.25 (6.05)
CVNN MEE
η
=0
.
07
,h
=1
.
4
0.32 (0.31)
η
=0
.
07
,h
=1
.
4
33.47 (6.19)
CVNN MMSE
η
=0
.
05
0.57 (0.50)
η
=0
.
05
33.64 (5.07)
η
=0
.
05
η
=0
.
05
CVNN B-MMSE
0.45 (0.30)
33.03 (5.26)
η
=0
.
05
,h
=1
.
4
η
=0
.
05
,h
=1
.
0
33.00 (4.94)
CVNN MEE
0.33 (0.24)
CVNN MMSE
η
=0
.
03
0.72 (0.55)
η
=0
.
03
33.17 (6.18)
CVNN B-MMSE
η
=0
.
03
0.58 (0.36)
η
=0
.
03
32.94 (5.74)
CVNN MEE
η
=0
.
03
,h
=1
.
4
0.37 (0.22)
η
=0
.
03
,h
=1
.
0
33.50 (4.43)
CVNN MMSE
η
=0
.
01
0.68 (0.32)
η
=0
.
01
33.28 (5.66)
CVNN B-MMSE
η
=0
.
01
0.68 (0.54)
η
=0
.
01
33.61 (5.29)
CVNN MEE
η
=0
.
01
,h
=1
.
0
0.23 (0.31)
η
=0
.
01
,h
=1
.
0
34.58 (3.84)
