comparison toolboxes/FullBNT-1.0.7/netlab3.3/demrbf1.m @ 0:e9a9cd732c1e tip

first hg version after svn

+%DEMRBF1 Demonstrate simple regression using a radial basis function network.
+%
+%	Description
+%	The problem consists of one input variable X and one target variable
+%	T with data generated by sampling X at equal intervals and then
+%	generating target data by computing SIN(2*PI*X) and adding Gaussian
+%	noise. This data is the same as that used in demmlp1.
+%
+%	Three different RBF networks (with different activation functions)
+%	are trained in two stages. First, a Gaussian mixture model is trained
+%	using the EM algorithm, and the centres of this model are used to set
+%	the centres of the RBF.  Second, the output weights (and biases) are
+%	determined using the pseudo-inverse of the design matrix.
+%
+%	See also
+%	DEMMLP1, RBF, RBFFWD, GMM, GMMEM
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+
+% Generate the matrix of inputs x and targets t.
+randn('state', 42);
+rand('state', 42);
+ndata = 20;			% Number of data points.
+noise = 0.2;			% Standard deviation of noise distribution.
+x = (linspace(0, 1, ndata))';
+t = sin(2*pi*x) + noise*randn(ndata, 1);
+mu = mean(x);
+sigma = std(x);
+tr_in = (x - mu)./(sigma);
+
+clc
+disp('This demonstration illustrates the use of a Radial Basis Function')
+disp('network for regression problems.  The data is generated from a noisy')
+disp('sine function.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+% Set up network parameters.
+nin = 1;			% Number of inputs.
+nhidden = 7;			% Number of hidden units.
+nout = 1;			% Number of outputs.
+
+clc
+disp('We assess the effect of three different activation functions.')
+disp('First we create a network with Gaussian activations.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+% Create and initialize network weight and parameter vectors.
+net = rbf(nin, nhidden, nout, 'gaussian');
+
+disp('A two-stage training algorithm is used: it uses a small number of')
+disp('iterations of EM to position the centres, and then the pseudo-inverse')
+disp('of the design matrix to find the second layer weights.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+disp('Error values from EM training.')
+% Use fast training method
+options = foptions;
+options(1) = 1;		% Display EM training
+options(14) = 10;	% number of iterations of EM
+net = rbftrain(net, options, tr_in, t);
+
+disp(' ')
+disp('Press any key to continue.')
+pause
+clc
+disp('The second RBF network has thin plate spline activations.')
+disp('The same centres are used again, so we just need to calculate')
+disp('the second layer weights.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+% Create a second RBF with thin plate spline functions
+net2 = rbf(nin, nhidden, nout, 'tps');
+
+% Re-use previous centres rather than calling rbftrain again
+net2.c = net.c;
+[y, act2] = rbffwd(net2, tr_in);
+
+% Solve for new output weights and biases from RBF activations
+temp = pinv([act2 ones(ndata, 1)]) * t;
+net2.w2 = temp(1:nhidden, :);
+net2.b2 = temp(nhidden+1, :);
+
+disp('The third RBF network has r^4 log r activations.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+% Create a third RBF with r^4 log r functions
+net3 = rbf(nin, nhidden, nout, 'r4logr');
+
+% Overwrite weight vector with parameters from first RBF
+net3.c = net.c;
+[y, act3] = rbffwd(net3, tr_in);
+temp = pinv([act3 ones(ndata, 1)]) * t;
+net3.w2 = temp(1:nhidden, :);
+net3.b2 = temp(nhidden+1, :);
+
+disp('Now we plot the data, underlying function, and network outputs')
+disp('on a single graph to compare the results.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+% Plot the data, the original function, and the trained network functions.
+plotvals = [x(1):0.01:x(end)]';
+inputvals = (plotvals-mu)./sigma;
+y = rbffwd(net, inputvals);
+y2 = rbffwd(net2, inputvals);
+y3 = rbffwd(net3, inputvals);
+fh1 = figure;
+
+plot(x, t, 'ob')
+hold on
+xlabel('Input')
+ylabel('Target')
+axis([x(1) x(end) -1.5 1.5])
+[fx, fy] = fplot('sin(2*pi*x)', [x(1) x(end)]);
+plot(fx, fy, '-r', 'LineWidth', 2)
+plot(plotvals, y, '--g', 'LineWidth', 2)
+plot(plotvals, y2, 'k--', 'LineWidth', 2)
+plot(plotvals, y3, '-.c', 'LineWidth', 2)
+legend('data', 'function', 'Gaussian RBF', 'Thin plate spline RBF', ...
+  'r^4 log r RBF');
+hold off
+
+disp('RBF training errors are');
+disp(['Gaussian ', num2str(rbferr(net, tr_in, t)), ' TPS ',  ...
+num2str(rbferr(net2, tr_in, t)), ' R4logr ', num2str(rbferr(net3, tr_in, t))]);
+
+disp(' ')
+disp('Press any key to end.')
+pause
+close(fh1);
+clear all;