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Linear Prediction Design

This example illustrates how to design a linear neuron to predict the next value in a time series given the last five values.

Defining a Wave Form

Here time is defined from 0 to 5 seconds in steps of 1/40 of a second.

time = 0:0.025:5;

We can define a signal with respect to time.

signal = sin(time*4*pi);
title('Signal to be Predicted');

Figure contains an axes object. The axes object with title Signal to be Predicted, xlabel Time, ylabel Signal contains an object of type line.

Setting up the Problem for a Neural Network

The signal convert is then converted to a cell array. Neural Networks represent timesteps as columns of a cell array, do distinguish them from different samples at a given time, which are represented with columns of matrices.

signal = con2seq(signal);

To set up the problem we will use the first four values of the signal as initial input delay states, and the rest except for the last step as inputs.

Xi = signal(1:4);
X = signal(5:(end-1));
timex = time(5:(end-1));

The targets are now defined to match the inputs, but shifted earlier by one timestep.

T = signal(6:end);

Designing the Linear Layer

The function newlind will now design a linear layer with a single neuron which predicts the next timestep of the signal given the current and four past values.

net = newlind(X,T,Xi);

Testing the Linear Layer

The network can now be called like a function on the inputs and delayed states to get its time response.

Y = net(X,Xi);

The output signal is plotted with the targets.

ylabel('Output -  Target +');
title('Output and Target Signals');

Figure contains an axes object. The axes object with title Output and Target Signals, xlabel Time, ylabel Output - Target + contains 2 objects of type line. One or more of the lines displays its values using only markers

The error can also be plotted.

E = cell2mat(T)-cell2mat(Y);
hold off
title('Error Signal');

Figure contains an axes object. The axes object with title Error Signal, xlabel Time, ylabel Error contains an object of type line.

Notice how small the error is!

This example illustrated how to design a dynamic linear network which can predict a signal's next value from current and past values.