newhop :: Functions (Neural Network Toolbox™)

newhop

Purpose

Create Hopfield recurrent network

Syntax

```
net = newhop(T)
```

Description

Hopfield networks are used for pattern recall.

newhop(T) takes one input argument,

T
R x Q matrix of Q target vectors (values must be +1 or -1)

`T`	`R` x `Q` matrix of `Q` target vectors (values must be `+1` or -`1`)

and returns a new Hopfield recurrent neural network with stable points at the vectors in T.

Properties

Hopfield networks consist of a single layer with the dotprod weight function, netsum net input function, and the satlins transfer function.

The layer has a recurrent weight from itself and a bias.

Examples

Here you create a Hopfield network with two three-element stable points T.

T = [-1 -1 1; 1 -1 1]';
net = newhop(T);

Check that the network is stable at these points by using them as initial layer delay conditions. If the network is stable, you would expect the outputs Y to be the same. (Because Hopfield networks have no inputs, the second argument to sim is Q = 2 when you use matrix notation).

Ai = T;
[Y,Pf,Af] = sim(net,2,[],Ai);
Y

To see if the network can correct a corrupted vector, run the following code, which simulates the Hopfield network for five time steps. (Because Hopfield networks have no inputs, the second argument to sim is {Q TS} = [1 5] when you use cell array notation.)

Ai = {[-0.9; -0.8; 0.7]};
[Y,Pf,Af] = sim(net,{1 5},{},Ai);
Y{1}

If you run the above code, Y{1} will equal T(:,1) if the network has managed to convert the corrupted vector Ai to the nearest target vector.

Algorithm

Hopfield networks are designed to have stable layer outputs as defined by user-supplied targets. The algorithm minimizes the number of unwanted stable points.

Reference

Li, J., A.N. Michel, and W. Porod, "Analysis and synthesis of a class of neural networks: linear systems operating on a closed hypercube," IEEE Transactions on Circuits and Systems, Vol. 36, No. 11, November 1989, pp. 1405-1422