Biomedical Engineering Reference
In-Depth Information
parabolic regression equation based on five values selected from output neuron
excitations according to the following rule. As a central point, we select the point
with the maximal value of excitation
E
max
(Fig.
11.10a
). In addition to this point,
two points to the left and two points to the right of
E
max
are selected. If point
E
max
is
located at the edge of the point sequence, additional points are obtained as a mirror
reflection (Fig.
11.10b
) of the points, which are situated on the other side of
E
max
.
After determining the functions
f
(
dx
) and
'
(
dy
), the parameters
dx
0
and
dy
0
, under
which the functions
f
(
dx
) and
(
dy
) have maximal values, are determined. These
parameters are recognized pin-hole displacements.
The interpolator training algorithm also differs from the classifier training
algorithm, and the resulting training rule is as follows. Weight modification is
carried out at every step according to the equation:
'
W
ij
ð
t
þ
1
Þ¼
W
ij
ð
t
Þþ
a
i
ðD
w
j
þ d
w
j
Þ;
(11.3)
where
W
ij
(
t
) is the weight of the connection between the
i
-neuron of the
A
-layer and
the
j
-neuron of the
R
-layer before reinforcement,
W
ij
(
t
+ 1) is the weight after
reinforcement, and
a
i
is the output signal (0 or 1) of the
i
-neuron of the
A
-layer.
Fig. 11.10a Parabolic
approximation
Fig. 11.10b Parabolic
approximation
