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156 5 Neural Networks

points. This solution can be obtained either by solving the normal equations or by
using the gradient descent method.

Figure 5.8. Parabolic discriminant for a two-class one-dimensional situation: (a)
Design set; (b) Network with parabolic activation function; (c) Energy surface with
two global minima.

Figure 5.9. Parabolic discriminants for a two-class one-dimensional situation: (a)
Discriminants corresponding to the global minima (solid curve) and local minima
(dotted curve); (b) Energy surface showing one global and one local minima.

Let us now displace point 1 to the 0.5 position as shown in Figure 5.9a. The
energy function has radically changed as shown in Figure 5.9b, where only the part