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9.1.4 NetPlot

A Hopfield network can be evaluated directly on a data vector by applying the evaluation rule as shown earlier. The command NetPlot can also be used, and it gives some more information about the evaluation. It works in the following way.

Illustrate Hopfield networks.

NetPlot takes the following option when it is applied to a Hopfield network.

Option of NetPlot.

NetPlot simulates the Hopfield network, as described in Section 2.7, Hopfield Network, using the supplied disturbed data vector x as an initial state. By giving different values to the option DataFormat you can obtain the result, which may be presented in different ways.

The default DataFormat->Trajectories gives a plot of the components of the state vector as a function of time. In addition to DataFormat, NetPlot also passes on any other options to its plot commands so that you can modify the plots.

Possible values for DataFormat include the following.

Possible values of DataFormat.

As described in Section 2.7, Hopfield Network, the convergence points of a Hopfield network are always local energy minima. That is why the energy is strictly decreasing.

For a continuous-time two-dimensional Hopfield network, you can also get the energy surface together with the state trajectories by choosing the option Surface.

