How can I change the 'radbas' transferFcn ?

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Nikos Vasileiadis
Nikos Vasileiadis 2016-12-22
评论： Nikos Vasileiadis 2016-12-23
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.

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John BG
John BG 2016-12-23
编辑：John BG 2016-12-23
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
<mailto:jgb2012@sky.com jgb2012@sky.com>
  1 个评论
Nikos Vasileiadis
Nikos Vasileiadis 2016-12-23
'further process before and after using radbas.m'
I think that's it. I was using wrong the neural network. Thanks

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更多回答（1 个）

John BG
John BG 2016-12-22
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
<mailto:jgb2012@sky.com jgb2012@sky.com>
  1 个评论
Nikos Vasileiadis
Nikos Vasileiadis 2016-12-22
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 ?

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