Argentum Solutions, Inc.
Sterling guidance on corrosion and materials degradation
| Potential-pH Diagrams |
 |
|
| Intelligent Tools |
 |
|
 |
|
 |
|
| Corrosion Calculator |
 |
|
| Corrosion Economics Estimator |
 |
|
|
David C. Silverman |
|
Example of Back-propagation Artificial Neural Network The following simple example of the back-propagation neural network is provided to illustrate the points outlined in the sections on the computing element , back-propagation network structure , and back-propagation network training of this tutorial. This same example is used elsewhere in this tutorial when discussing other types of neural or belief networks so that differences and similarities among networks can be seen.
TRAINING Five hundred training sets were created by using two random number generators. The values were about evenly divided between those when squared rounded to 1 and those when squared rounded to 0. Three networks that had 1, 2, or 3 hidden nodes were created and trained. All had one hidden layer. The network with two hidden nodes is shown in this figure ) .
as an example.
Note the additional node on the left is a constant.
This node is like a threshold or offset and has a constant value of 1. Its weight
is determined during training. It is comparable to the constant in a polynomial
fit whose value is determined during non-linear regression.
Each of the three networks was trained for between 500 and 1000 epochs where an epoch is one complete pass through the complete set of training data. The sum of the squares of differences between calculated and expected (0 or 1) values was used to track the error. There was virtually no change in error between training for 500 epochs and 1000 epochs. Since the number of data sets was no less than about 50 times the number of connections, the expectation would be that each of the networks would generalize on the information, not memorize it. RESULTS A different set of 100 randomly generated input-output combinations were used to test the trained networks. They were about evenly distributed between the two classes. The calculated output values were between about -.1 and +1.1. The strategy used to assess error was to assume that if the value predicted by the network was less than 0.5, the interpreted prediction would have been zero and if the value was greater than or equal to 0.5, the interpreted prediction would have been 1. These values were compared to the expected rounding outputs to assess error. No attempt was made to compare actual values because non-linear regression was not the goal of the exercise. This figure ) .
shows correct and incorrect responses for the neural network
with one hidden node. This figure ) .
shows the correct and incorrect responses for the neural network with two hidden
nodes. This figure ) .
shows the correct
and incorrect responses for the neural network with three hidden nodes.
CONCLUSIONS
|
|
Previous Page: Training the Back-Propagation Neural Network |
|
David C. Silverman, Ph.D. - Primary Consultant |