How can I change the 'radbas' transferFcn ?

I want to do a 2D interpolation with a feedforward neural net in Matlab and I choose to use a radial bade transfer function on the neurons of the hidden layer. The problem is that the radbas function gives a hyperplane like figure 1 and I want a hyperplane more like figure 2. out=exp(-(x-x0)^2/2 + (y-y0)^2/2);

What should I do?

In other words I want each neuron creates and shift a bell shaped (hyper)plane along my 2D input space.

[Star Strider]

Neural network transfer functions are only defined in 2D.

Answer 1

[John BG]

ok

the reason why radbas.m is called radial function is not because when plotting the outcome on a plane it should look like a 'hat', but because the function output is input phase independent:

.

https://en.wikipedia.org/wiki/Radial_basis_function

you are right that inside radbas.m there is no mesh capability by this meaning that it's a 1D function and we have to either modify readbas.m, build another function, or further process before and after using radbas.m

Inside radbas.m

function a = radbas(n,b) 
%RADBAS Radial basis transfer function. 
%   
%  RADBAS(N) 
%    N - SxQ matrix of distance vectors. 
%  Returns values of N passed through radial basis function. 
%   
%  EXAMPLE: n = -4:0.1:4; 
%           a = radbas(n); 
%           plot(n,a) 
%   
%  RADBAS(Z,B) ...used when batching. 
%    Z - SxQ matrix of unbiased distance vectors. 
%    B - Sx1 bias vector. 
%  Obtains N by multiplying elements in each column of Z by 
%    the elements in B, then returns RADBAS(N). 

% Mark Beale, 12-15-93 
% Copyright (c) 1992-94 by The MathWorks, Inc. 
% $Revision: 1.1 $  $Date: 1994/01/11 16:28:18 $ 

if nargin < 1, error('Not enough arguments.'); end 

if nargin==2 
  [nr,nc] = size(n); 
  n = n .* (b*ones(1,nc)); 
end 

a = exp(-(n.*n));

although Srouceforge has a download for radbas.m that is slightly different:

https://sourceforge.net/p/octave/nnet/ci/default/tree/inst/radbas.m

function retval = radbas (n)
  if (nargin != 1)
    print_usage ();
  else
    retval = exp (-n^2);
  endif
endfunction

I suggest you start with something like the following:

    b=0  % keep it 0 for now
    dn=0.1  % step
    nr=5   % range limit

    range= -nr:dn:nr;

    x0=1;y0=1  % center

    xc=1;yc=1;

    nx=range+xc;ny=range+yc

    [X,Y]=meshgrid(nx,ny)  % required to hve surf generating 3D points

    Z=exp(-(X.^2+Y.^2))
    surf(X,Y,Z)

and to colour according to 'altitude' proportional to heat, the higher the hotter, I am afraid you may have to define your own colormap. Some time ago I looked for the common heat color maps that have white yellow red blue black going from hottest to coldest, but MATLAB only has the following standard colormaps

the closest to white hottest black coldest seems to be 'jet'

colormap(jet)
colorbar

you can also delete the fine 'net' so it looks closer to the image you are after.

at this point, would you please accept my answer?

Thanks for time and attention, awaiting answer

John BG

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[Nikos Vasileiadis]

'further process before and after using radbas.m'

I think that's it. I was using wrong the neural network. Thanks

Answer 2

[John BG]

you probably missed using the coordinates out of meshgrid rather than the ranges x and y.

Try adding

[X,Y]=meshgrid(-3:.01:3)

then have your function working on X and Y rather than x and y:

Z=exp(-(X-x0)^2/2 + (Y-y0)^2/2);

and check

C=gradient(Z)
figure;
mesh(X,Y,Z,C)

if you find my answer useful would you please mark it as Accepted Answer by clicking on the ACCEPT ANSWER button?

thanks in advance for time and attention

John BG

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[Nikos Vasileiadis]

Firstly thank you Jonh, but I think the problem is inside the radbas function. Could you do that -you tell me above- using this function instead https://www.mathworks.com/help/nnet/ref/radbas.html ?