Biomedical Engineering Reference
In-Depth Information
Fig. 5.
The Perceptron
data can be accomplished with a perceptron, which is an MLP with no
hidden layers and only one output neuron
3
. In analyzing microarray data,
the pattern vector = (
1
; : : : ;
r
) represents the genetic expression of the
condition observed in the sample.
The backpropagation algorithm implies that after a large number of
training sessions, the weights are of the form
X
p
i
p
i
2
p
l
l
=
l
+
y
1y
fi j q
i
=1g
X
p
i
1y
2
p
i
p
l
y
fi j q
i
=0g
where
l
is a random initial oset that is very close to 0. It follows that
X
X
p
l
l
l
+
p
l
l
fi j q
i
=1g
fi j q
i
=1g
so that if
l
= 0; then we have
l
R
l
l
+
R
or equivalently,
l
l
: That is, input neurons (genes) not in the pattern
will on average correspond to weights
l
which are close to 0 (given that
l
is chosen to be close to 0 as well).
When combined with a simple genetic algorithm that eliminates the
input neurons corresponding to the
l
with the smallest magnitudes, the
result is a process for reducing the dimensionality of the classication data
p
i
; q
i
: A naive implementation of this process can be described as follows:
p
0
; q
0
(1) Let
; i = 1; : : : ; N denote the original training set.
(2) For k = 0; 1; 2; : : :
(a) Train the network with the data
p
i
k
; q
i
k
until the error E is su-
ciently close to 0.
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