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1 function [g, gdata, gprior] = rbfgrad(net, x, t)
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2 %RBFGRAD Evaluate gradient of error function for RBF network.
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3 %
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4 % Description
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5 % G = RBFGRAD(NET, X, T) takes a network data structure NET together
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6 % with a matrix X of input vectors and a matrix T of target vectors,
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7 % and evaluates the gradient G of the error function with respect to
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8 % the network weights (i.e. including the hidden unit parameters). The
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9 % error function is sum of squares. Each row of X corresponds to one
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10 % input vector and each row of T contains the corresponding target
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11 % vector. If the output function is 'NEUROSCALE' then the gradient is
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12 % only computed for the output layer weights and biases.
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13 %
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14 % [G, GDATA, GPRIOR] = RBFGRAD(NET, X, T) also returns separately the
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15 % data and prior contributions to the gradient. In the case of multiple
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16 % groups in the prior, GPRIOR is a matrix with a row for each group and
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17 % a column for each weight parameter.
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18 %
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19 % See also
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20 % RBF, RBFFWD, RBFERR, RBFPAK, RBFUNPAK, RBFBKP
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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 % Check arguments for consistency
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26 switch net.outfn
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27 case 'linear'
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28 errstring = consist(net, 'rbf', x, t);
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29 case 'neuroscale'
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30 errstring = consist(net, 'rbf', x);
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31 otherwise
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32 error(['Unknown output function ', net.outfn]);
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33 end
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34 if ~isempty(errstring);
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35 error(errstring);
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36 end
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37
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38 ndata = size(x, 1);
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39
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40 [y, z, n2] = rbffwd(net, x);
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41
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42 switch net.outfn
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43 case 'linear'
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44
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45 % Sum squared error at output units
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46 delout = y - t;
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47
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48 gdata = rbfbkp(net, x, z, n2, delout);
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49 [g, gdata, gprior] = gbayes(net, gdata);
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50
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51 case 'neuroscale'
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52 % Compute the error gradient with respect to outputs
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53 y_dist = sqrt(dist2(y, y));
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54 D = (t - y_dist)./(y_dist+diag(ones(ndata, 1)));
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55 temp = y';
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56 gradient = 2.*sum(kron(D, ones(1, net.nout)) .* ...
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57 (repmat(y, 1, ndata) - repmat((temp(:))', ndata, 1)), 1);
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58 gradient = (reshape(gradient, net.nout, ndata))';
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59 % Compute the error gradient
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60 gdata = rbfbkp(net, x, z, n2, gradient);
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61 [g, gdata, gprior] = gbayes(net, gdata);
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62 otherwise
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63 error(['Unknown output function ', net.outfn]);
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64 end
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65
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