How does the routine newfftd work?

How does the routine newfftd work? (It's for time delay neural networks)

What does the vector ID represent?

net = newfftd(PR,ID,[S1 S2...SNl],{TF1 TF2...TFNl},BTF,BLF,PF)

PR-Rx2 matrix of min and max values for R input elements.

ID - Input delay vector.

In the example shown in the on-line help, the vector ID is [0 1]:

net = newfftd([0 1],[0 1],[5 1],{'tansig' 'purelin'});

Suppose that I have a time sequence P of N data, the instruction phase is

conducted on N/2 data assuming that the i-th data is predictable

considering the values at the time i-1,i-2,i-3 with one time delay.

My target vector is T and is generated from P by shifting back of three

position the vector P:

time*          1 2 3 4 5 6 7 8 9 10

data sequence  a b c d e f g h i j
|

(*)  numbers give the time sequence
(**) letters are real values between 0 and 1

In this case the input layer has 3 neurons while the output layer has only one.

My questions are:

1)How can I initialize the network assuming that all the data is normalized (i.e. min=0, max=1)?

2)How do I create vectors P and T for the training of the instruction net = train(net,P,T)?

Answer 1

[MathWorks Support Team]

In the NEWFFTD function, ID defines the vector of input delays. If you want the network to predict the target at time t given inputs at times t-1, t-2, and t-3 then ID would be [1 2 3].

If you want the target at time t to be predicted at times t, t-2, and t-4 then ID would be [0 2 4].

You can use PREMNMX, POSTMNMX, and TRAMNMX to normalize data to min and max of -1 and +1. They are described in their help comments and also on page 5-44 of the User's Guide.

Sequences are represented with row cell arrays. The following example may help you determine how to format your own prediction problem.

Let us say we have a sequence Z as defined below:

  t = 0, Z(:,t+1) = [0; 1];
t = 1, Z(:,t+1) = [-1; 0];
t = 2, Z(:,t+1) = [-1; 1];
t = 3, Z(:,t+1) = [0; 0];
t = 4, Z(:,t+1) = [1; -1];
t = 5, Z(:,t+1) = [0; -1];

We would like the network to predict Z(t) given Z(t-1), Z(t-2) and Z(t-3).

We can define this problem with three row cell arrays. They are:

Pi - the initial inputs for which the network will not have a target

P - the inputs for which the network will have a target

T - the targets

In this case two initial inputs must be presented before the network can predict anything:

Pi= {Z(0) Z(1)} = {[0;1] [-1;0]} = Pi = con2seq(Z(:,1:2));

The network will then be presented with Z(2) through Z(4)...

P = {Z(2) Z(3) Z(4)} = {[-1; 1] [0;0] [1;-1]} = con2seq(Z(:,3:5));

...and will be expected to respond with Z(3) through Z(5).

T = {Z(3) Z(4) Z(5)} = {[0;0] [1;-1] [0;-1]} = T = con2seq(Z(:,4:6));

Note that we would like the network to predict Z(t) given Z(t-1)..Z(t-3). This is equivalent to predicting T{i} given P{i}, P{i-1}, and P{i-2} so ID will equal [0 1 2].

Here a network is created that can do that. It has a two-element input whose values range from -1 to 1. It has input delays of 0, 1, and

2. It has 5 hidden neurons and 1 output.

net = newfftd(minmax(Z),[0 1 2],[5 2]);

It is then trained with P, Pi, and T as follows:

net.trainparam.epochs=500;

net = train(net,P,T,Pi);

The complete code follows:

Z = [ 0 -1 -1  0  1  0 ;
1  0  1  0 -1 -1 ];

Pi = con2seq(Z(:,1:2));
P = con2seq(Z(:,3:5));
T = con2seq(Z(:,4:6));

net = newfftd(minmax(Z),[0 1 2],[5 2]);
net.trainparam.epochs=500;
net = train(net,P,T,Pi);

Y=sim(net,P,Pi);
[Y{:}]-[T{:}]

For more neural network examples, visit the MATLAB Central File Exchange at https://www.mathworks.com/matlabcentral/