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I'm trying to approximate various signals using radial basis networks. In particular, I make use of MATLAB's newrb.

My problem is that this function seems to behave incorrectly if I follow the description of newrb. As I understand it, it makes sense to transpose all arguments despite the documentation.

The following example hopefully illustrates my problem.

I create one period of a sine wave with 100 samples. I would like to approximate this sine wave by means of a radial basis network with maximally two hidden neurons. I have one input vector (t) and one target vector (s). Hence, according to the documentation, I should call newrb with two column vectors. However, the approximation is too good. In fact, the mean squared error is 0 which can't be true using only two neurons. Additionally, the visualization with view(net) shows not only one but 100 inputs if I use column vectors.

In the example, the vectors corresponding to the "correct" (according to the documentation) function call are indicated by _doc, the ones corresponding to the "incorrect" call by _not_doc.

Can anybody explain this behavior?

% one period sine signal with
% carrier frequency = 1, sampling frequency = 100
Ts  = 1 / 100;
t   = 2 * pi * (0:Ts:1-Ts); % size(t) = 1 100
s   = sin(t);               % size(s) = 1 100

% design radial basis network
MSE_goal    = 0.0;  % mean squared error goal, default value
spread      = 1.0;  % spread of readial basis functions, default value
max_neurons = 2;    % maximum number of neurons, custom value
DF          = 25;   % number of neurons to add between displays, default value

net_not_doc     = newrb( t , s , MSE_goal, spread, max_neurons, DF );   % row vectors
net_doc         = newrb( t', s', MSE_goal, spread, max_neurons, DF );   % column vectors

% simulate network
approx_not_doc   = sim( net_not_doc, t );
approx_doc       = sim( net_doc, t' );

% plot
figure;
plot( t, s, 'DisplayName', 'Sine' );
hold on;
plot( t, approx_not_doc, 'r:', 'DisplayName', 'Approximation_{not doc}');
hold on;
plot( t, approx_doc', 'g:', 'DisplayName', 'Approximation_{doc}');
grid on;
legend show;

% view neural networks
view(net_not_doc);
view(net_doc);
Maryks
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1 Answers1

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Because I had the same problem myself, I'll try to give an answer for anyone who will stumble upon the same post.

As I figured the problem is not the transpose vectors. You can use your data as it is, without transposing anything. The fact that you train your RBF network with vector t and then simulate with the same vector that you trained your network, is the reason why you have so perfect approximation. You test your network with the same values that you taught it.

If you realy want to test your network you must choose a different vector for testing. In your example I used this:

    % simulate network
    t_test = 2 * pi * ((1-Ts)/2:Ts:3-Ts);
    approx_not_doc   = sim( net_not_doc, t_test );

And now when you plot your results, you can observe that the points that have the same value as in your train vector are almost flawless. The rest have an unknown target because of the small number of neurons (as you expected). Plot of t_test with approx_not_doc.

Now If you add more neurons (in this example I used 100), you can see that now the new network can predict, with the same test vector t_test, an unknown part of your function. Plot t_test with approx_not_doc for 100 neurons. Of course, if you try with different number of neurons and spread your results will vary.

Hope this will help anyone with the same problem.

VassilisCN
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