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This behavior may indicate that the network contains too few hidden nodes. On the other hand, it may indicate that the number of hidden nodes in the network is actually the optimal number. We cannot know which of these situations is the case, however, until we try increasing the number of hidden nodes, and then retraining 38 Neural Network Data Analysis Using Simulnet the network. Suppose that we increase the number of hidden units by one unit, restart training, and find that the testing-error curve now does show a clear minimum, by falling initially and then rising again as training proceeds.
Again, this approach might require so many hidden nodes that training time could grow to become impracticably long. A more efficient alternative with such a data set would be to use two hidden layers. With two hidden layers, nodes in the first hidden level would act to some extent independently in abstracting the independent features of the discontinuous function. These features could then be combined by the nodes in the second hidden level. Training and Testing Matrices Network training and testing are carried out by presenting the network with examples of the relationship that the network is expected to acquire, the training exemplars.
2 .. ·.. ·· .. , .. ·· .... ·,·· .... · .. ,· .... ·.. ·1· .... 2 .... ·.... 1.. ·...... 1.... ·.... 1........ ·1 .... ·. ·· . I·· . ·. ·. :· . ·. ·j . ·· . ·. 4 ........ ·i ........ ·. i· ........ :.... 6 ........ ·I·. · ·.. B ......... j ......... j....... j ......... j..... -1 -5 ~ . 5. The logistic function o(x) is typical of the nonlinear transfer functions used for network hidden-level nodes. The function tends towards -1 for large negative values of x, and towards +1 for large positive values of x.