AI - a Guide to Intelligent Systems.pdf - Member of EEPIS

180
ARTIFICIAL NEURAL NETWORKS
(b) Calculate the actual outputs of the neurons in the output layer:
2
3
y k ðpÞ ¼sigmoid4
Xm
x jk ðpÞw jk ðpÞ 5;
j¼1
where m is the number of inputs of neuron k in the output layer.
k
Step 3:
Weight training
Update the weights in the back-propagation network propagating
backward the errors associated with output neurons.
(a)
Calculate the error gradient for the neurons in the output layer:
k ðpÞ ¼y k ðpÞ½1 y k ðpÞŠ e k ðpÞ
where
e k ðpÞ ¼y d;k ðpÞ
y k ðpÞ
Calculate the weight corrections:
w jk ðpÞ ¼ y j ðpÞ k ðpÞ
Update the weights at the output neurons:
w jk ðp þ 1Þ ¼w jk ðpÞþw jk ðpÞ
(b) Calculate the error gradient for the neurons in the hidden layer:
j ðpÞ ¼y j ðpÞ½1
y j ðpÞŠ Xl
k¼1
k ðpÞw jk ðpÞ
Calculate the weight corrections:
w ij ðpÞ ¼ x i ðpÞ j ðpÞ
Update the weights at the hidden neurons:
w ij ðp þ 1Þ ¼w ij ðpÞþw ij ðpÞ
Step 4:
Iteration
Increase iteration p by one, go back to Step 2 and repeat the process
until the selected error criterion is satisfied.
As an example, we may consider the three-layer back-propagation network
shown in Figure 6.10. Suppose that the network is required to perform logical
operation Exclusive-OR. Recall that a single-layer perceptron could not do
this operation. Now we will apply the three-layer net.
Neurons 1 and 2 in the input layer accept inputs x 1 and x 2 , respectively, and
redistribute these inputs to the neurons in the hidden layer without any
processing:
x 13 ¼ x 14 ¼ x 1 and x 23 ¼ x 24 ¼ x 2 .