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06 Nov 2002 (Updated )

Pattern analysis toolbox.

rbfbkp(net, x, z, n2, deltas)
function g = rbfbkp(net, x, z, n2, deltas)
%RBFBKP	Backpropagate gradient of error function for RBF network.
%
%	Description
%	G = RBFBKP(NET, X, Z, N2, DELTAS) takes a network data structure NET
%	together with a matrix X of input vectors, a matrix  Z of hidden unit
%	activations, a matrix N2 of the squared distances between centres and
%	inputs, and a matrix DELTAS of the  gradient of the error function
%	with respect to the values of the output units (i.e. the summed
%	inputs to the output units, before the activation function is
%	applied). The return value is the gradient G of the error function
%	with respect to the network weights. Each row of X corresponds to one
%	input vector.
%
%	This function is provided so that the common backpropagation
%	algorithm can be used by RBF network models to compute gradients for
%	the output values (in RBFDERIV) as well as standard error functions.
%
%	See also
%	RBF, RBFGRAD, RBFDERIV
%

%	Copyright (c) Ian T Nabney (1996-2001)

% Evaluate second-layer gradients.
gw2 = z'*deltas;
gb2 = sum(deltas);

% Evaluate hidden unit gradients
delhid = deltas*net.w2';

gc = zeros(net.nhidden, net.nin);
ndata = size(x, 1);
t1 = ones(ndata, 1);
t2 = ones(1, net.nin);
% Switch on activation function type
switch net.actfn
      
case 'gaussian' % Gaussian
   delhid = (delhid.*z);
   % A loop seems essential, so do it with the shortest index vector
   if (net.nin < net.nhidden)
      for i = 1:net.nin
         gc(:,i) = (sum(((x(:,i)*ones(1, net.nhidden)) - ...
            (ones(ndata, 1)*(net.c(:,i)'))).*delhid, 1)./net.wi)';
      end
   else
      for i = 1:net.nhidden
         gc(i,:) = sum((x - (t1*(net.c(i,:)))./net.wi(i)).*(delhid(:,i)*t2), 1);
      end
   end
   gwi = sum((n2.*delhid)./(2.*(ones(ndata, 1)*(net.wi.^2))), 1);
   
case 'tps'	% Thin plate spline activation function
   delhid = delhid.*(1+log(n2+(n2==0)));
   for i = 1:net.nhidden
      gc(i,:) = sum(2.*((t1*(net.c(i,:)) - x)).*(delhid(:,i)*t2), 1);
   end
   % widths are not adjustable in this model
   gwi = [];
case 'r4logr' % r^4 log r activation function
   delhid = delhid.*(n2.*(1+2.*log(n2+(n2==0))));
   for i = 1:net.nhidden
      gc(i,:) = sum(2.*((t1*(net.c(i,:)) - x)).*(delhid(:,i)*t2), 1);
   end
   % widths are not adjustable in this model
   gwi = [];
otherwise
   error('Unknown activation function in rbfgrad')
end
   
g = [gc(:)', gwi, gw2(:)', gb2];

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