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Training a Linear Neuron

A linear neuron is trained to respond to specific inputs with target outputs.

X defines two 1-element input patterns (column vectors). T defines associated 1-element targets (column vectors). A single input linear neuron with y bias can be used to solve this problem.

X = [1.0 -1.2];
T = [0.5 1.0];

ERRSURF calculates errors for y neuron with y range of possible weight and bias values. PLOTES plots this error surface with y contour plot underneath. The best weight and bias values are those that result in the lowest point on the error surface.

w_range = -1:0.2:1;  b_range = -1:0.2:1;
ES = errsurf(X,T,w_range,b_range,'purelin');

MAXLINLR finds the fastest stable learning rate for training y linear network. For this example, this rate will only be 40% of this maximum. NEWLIN creates y linear neuron. NEWLIN takes these arguments: 1) Rx2 matrix of min and max values for R input elements, 2) Number of elements in the output vector, 3) Input delay vector, and 4) Learning rate.

maxlr = 0.40*maxlinlr(X,'bias');
net = newlin([-2 2],1,[0],maxlr);

Override the default training parameters by setting the performance goal.

net.trainParam.goal = .001;

To show the path of the training we will train only one epoch at y time and call PLOTEP every epoch. The plot shows y history of the training. Each dot represents an epoch and the blue lines show each change made by the learning rule (Widrow-Hoff by default).

% [net,tr] = train(net,X,T);
net.trainParam.epochs = 1; = NaN;
[net,tr] = train(net,X,T);                                                    
r = tr;
epoch = 1;
while true
   epoch = epoch+1;
   [net,tr] = train(net,X,T);
   if length(tr.epoch) > 1
      h = plotep(net.IW{1,1},net.b{1},tr.perf(2),h);
      r.epoch=[r.epoch epoch]; 
      r.perf=[r.perf tr.perf(2)];
      r.vperf=[r.vperf NaN];
      r.tperf=[r.tperf NaN];


The train function outputs the trained network and y history of the training performance (tr). Here the errors are plotted with respect to training epochs: The error dropped until it fell beneath the error goal (the black line). At that point training stopped.


Now use SIM to test the associator with one of the original inputs, -1.2, and see if it returns the target, 1.0. The result is very close to 1, the target. This could be made even closer by lowering the performance goal.

x = -1.2;
y = net(x)
y = 0.9817