Digital Signal Processing Reference
In-Depth Information
From that table, we can see that the update equations for
w
i
,
x
i
,and
Σ
−1
i
have different learning rates thus visualizing the different time-
scales. The presented procedure is different from the backpropagation of
the MLP.
Tabl e 6 . 1
Adaptation formulas for the linear weights and the position and widths of centers
for an RBF network [110].
1.
Linear weights of the output layer
∂E(n)
∂w
i
(n)
=
P
j=1
e
j
(
n
)
G
(
||
x
j
−
m
i
(
n
)
||
)
w
i
(
n
+1)=
w
i
(
n
)
∂E(n)
∂w
i
(n)
− η
1
,
i
=1
, ··· ,M
2.
Position of the centers of the hidden layer
=2
w
i
(
n
)
P
j=1
e
j
(
n
)
G
(
∂E(n)
∂
m
i
(n)
)
K
i
[
x
j
−
m
i
(
n
)]
||
x
j
−
m
i
(
n
)
||
∂E(n)
∂
m
i
(n)
m
i
(
n
+1)=
m
i
(
n
)
− η
2
,
i
=1
, ··· ,M
3.
Widths of the centers of the hidden layer
∂E(n)
∂
k
i
(n)
=
−w
i
(
n
)
P
j=1
e
j
(
n
)
G
(
||
x
j
−
m
i
(
n
)
||
)
Q
ji
(
n
)
Q
ji
(
n
)=[
x
j
−
m
i
(
n
)][
x
j
−
m
i
(
n
)]
T
K
i
(
n
+1)=
K
i
(
n
)
− η
3
∂E(n)
∂
K
i
(n)
6.5
Transformation Radial-Basis Networks (TRBNN)
The selection of appropriate features is an important precursor to most
statistical pattern recognition methods. A good feature selection mecha-
nism helps to facilitate classification by eliminating noisy or nonrepresen-
tative features that can impede recognition. Even features that provide
some useful information can reduce the accuracy of a classifier when the
amount of training data is limited. This
curse of dimensionality
,along
with the expense of measuring and including features, demonstrates the
utility of obtaining a minimum-sized set of features that allow a classi-
fier to discern pattern classes well. Well-known methods in the literature
that are applied to feature selection are floating search methods [214]
and genetic algorithms [232].
Radial-basis neural networks are excellent candidates for feature
selection. It is necessary to add an additional layer to the traditional
architecture to obtain a representation of relevant features. The new
paradigm is based on an explicit definition of the relevance of a feature
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