Information Technology Reference
In-Depth Information
∂V
R
2
∂θ
k
The update equations for the thresholds can be obtained by finding
and
∂V
R
2
∂θ
k
. These equations are
K
e
i
− e
u
h
((
s
(
z
i
)
n
n
∂V
R
2
∂θ
k
2
h
s
(
z
i
))
s
(
z
i
)
=
−
−
u
=1
i
=1
(
s
(
z
u
)
s
(
z
u
))
s
(
z
u
))
−
−
(6.47)
and
K
e
i
− e
u
h
((
s
(
z
i
)
n
n
∂V
R
2
∂θ
k
2
h
s
(
z
i
))
s
(
z
i
)
=
−
−
u
=1
i
=1
(
s
(
z
u
)
s
(
z
u
))
s
(
z
u
))
.
−
−
(6.48)
6.3.5 Experiments
In the following we describe experiments presented in [3] where the original
single layer CVNN is compared against other classifiers, including the MEE-
based (R
2
EE) version of the single layer CVNN.
6.3.5.1
Datasets
An artificially generated dataset (Checkerboard) as in Fig. 6.10, was used
in [3] which consisted of a 2 by 2 grid of domains with alternate classes in
the domains. The dataset had 400 instances (100 per grid position and 200
per class). In this case it is considered that the value of the
X
coordinate of
a point is the real part of a complex measurement and the
Y
coordinate is
the imaginary part. The second dataset is the breast cancer dataset studied
in [211]. It consists of electrical impedance measurements that were performed
on 120 samples of freshly excised breast tissue. The dataset has 6 classes, 120
instances and 24 features (real and imaginary parts of 12 measurements of
impedance at different frequencies). The data was normalized with zero mean
and unit standard deviation for all algorithms with the exception of the SVM
where a normalization in the interval [
−
1
,
1] was done for each feature.
6.3.5.2
Results
The results are in Table 6.13 showing average errors and standard deviations
of 30 repetitions of two-fold cross-validation. Besides the results obtained with
MMSE and MEE, Table 6.13 also shows the results obtained using SVM with
