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1 function g = rbfbkp(net, x, z, n2, deltas)
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2 %RBFBKP Backpropagate gradient of error function for RBF network.
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3 %
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4 % Description
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5 % G = RBFBKP(NET, X, Z, N2, DELTAS) takes a network data structure NET
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6 % together with a matrix X of input vectors, a matrix Z of hidden unit
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7 % activations, a matrix N2 of the squared distances between centres and
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8 % inputs, and a matrix DELTAS of the gradient of the error function
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9 % with respect to the values of the output units (i.e. the summed
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10 % inputs to the output units, before the activation function is
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11 % applied). The return value is the gradient G of the error function
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12 % with respect to the network weights. Each row of X corresponds to one
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13 % input vector.
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14 %
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15 % This function is provided so that the common backpropagation
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16 % algorithm can be used by RBF network models to compute gradients for
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17 % the output values (in RBFDERIV) as well as standard error functions.
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18 %
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19 % See also
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20 % RBF, RBFGRAD, RBFDERIV
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21 %
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22
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23 % Copyright (c) Ian T Nabney (1996-2001)
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24
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25 % Evaluate second-layer gradients.
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26 gw2 = z'*deltas;
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27 gb2 = sum(deltas);
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28
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29 % Evaluate hidden unit gradients
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30 delhid = deltas*net.w2';
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31
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32 gc = zeros(net.nhidden, net.nin);
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33 ndata = size(x, 1);
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34 t1 = ones(ndata, 1);
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35 t2 = ones(1, net.nin);
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36 % Switch on activation function type
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37 switch net.actfn
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38
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39 case 'gaussian' % Gaussian
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40 delhid = (delhid.*z);
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41 % A loop seems essential, so do it with the shortest index vector
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42 if (net.nin < net.nhidden)
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43 for i = 1:net.nin
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44 gc(:,i) = (sum(((x(:,i)*ones(1, net.nhidden)) - ...
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45 (ones(ndata, 1)*(net.c(:,i)'))).*delhid, 1)./net.wi)';
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46 end
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47 else
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48 for i = 1:net.nhidden
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49 gc(i,:) = sum((x - (t1*(net.c(i,:)))./net.wi(i)).*(delhid(:,i)*t2), 1);
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50 end
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51 end
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52 gwi = sum((n2.*delhid)./(2.*(ones(ndata, 1)*(net.wi.^2))), 1);
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53
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54 case 'tps' % Thin plate spline activation function
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55 delhid = delhid.*(1+log(n2+(n2==0)));
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56 for i = 1:net.nhidden
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57 gc(i,:) = sum(2.*((t1*(net.c(i,:)) - x)).*(delhid(:,i)*t2), 1);
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58 end
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59 % widths are not adjustable in this model
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60 gwi = [];
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61 case 'r4logr' % r^4 log r activation function
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62 delhid = delhid.*(n2.*(1+2.*log(n2+(n2==0))));
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63 for i = 1:net.nhidden
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64 gc(i,:) = sum(2.*((t1*(net.c(i,:)) - x)).*(delhid(:,i)*t2), 1);
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65 end
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66 % widths are not adjustable in this model
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67 gwi = [];
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68 otherwise
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69 error('Unknown activation function in rbfgrad')
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70 end
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71
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72 g = [gc(:)', gwi, gw2(:)', gb2];
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