Mercurial > hg > camir-aes2014

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

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
parents
children
rev   line source
wolffd@0 1 %DEMRBF1 Demonstrate simple regression using a radial basis function network.
wolffd@0 2 %
wolffd@0 3 % Description
wolffd@0 4 % The problem consists of one input variable X and one target variable
wolffd@0 5 % T with data generated by sampling X at equal intervals and then
wolffd@0 6 % generating target data by computing SIN(2*PI*X) and adding Gaussian
wolffd@0 7 % noise. This data is the same as that used in demmlp1.
wolffd@0 8 %
wolffd@0 9 % Three different RBF networks (with different activation functions)
wolffd@0 10 % are trained in two stages. First, a Gaussian mixture model is trained
wolffd@0 11 % using the EM algorithm, and the centres of this model are used to set
wolffd@0 12 % the centres of the RBF. Second, the output weights (and biases) are
wolffd@0 13 % determined using the pseudo-inverse of the design matrix.
wolffd@0 14 %
wolffd@0 15 % See also
wolffd@0 16 % DEMMLP1, RBF, RBFFWD, GMM, GMMEM
wolffd@0 17 %
wolffd@0 18
wolffd@0 19 % Copyright (c) Ian T Nabney (1996-2001)
wolffd@0 20
wolffd@0 21
wolffd@0 22 % Generate the matrix of inputs x and targets t.
wolffd@0 23 randn('state', 42);
wolffd@0 24 rand('state', 42);
wolffd@0 25 ndata = 20; % Number of data points.
wolffd@0 26 noise = 0.2; % Standard deviation of noise distribution.
wolffd@0 27 x = (linspace(0, 1, ndata))';
wolffd@0 28 t = sin(2*pi*x) + noise*randn(ndata, 1);
wolffd@0 29 mu = mean(x);
wolffd@0 30 sigma = std(x);
wolffd@0 31 tr_in = (x - mu)./(sigma);
wolffd@0 32
wolffd@0 33 clc
wolffd@0 34 disp('This demonstration illustrates the use of a Radial Basis Function')
wolffd@0 35 disp('network for regression problems. The data is generated from a noisy')
wolffd@0 36 disp('sine function.')
wolffd@0 37 disp(' ')
wolffd@0 38 disp('Press any key to continue.')
wolffd@0 39 pause
wolffd@0 40 % Set up network parameters.
wolffd@0 41 nin = 1; % Number of inputs.
wolffd@0 42 nhidden = 7; % Number of hidden units.
wolffd@0 43 nout = 1; % Number of outputs.
wolffd@0 44
wolffd@0 45 clc
wolffd@0 46 disp('We assess the effect of three different activation functions.')
wolffd@0 47 disp('First we create a network with Gaussian activations.')
wolffd@0 48 disp(' ')
wolffd@0 49 disp('Press any key to continue.')
wolffd@0 50 pause
wolffd@0 51 % Create and initialize network weight and parameter vectors.
wolffd@0 52 net = rbf(nin, nhidden, nout, 'gaussian');
wolffd@0 53
wolffd@0 54 disp('A two-stage training algorithm is used: it uses a small number of')
wolffd@0 55 disp('iterations of EM to position the centres, and then the pseudo-inverse')
wolffd@0 56 disp('of the design matrix to find the second layer weights.')
wolffd@0 57 disp(' ')
wolffd@0 58 disp('Press any key to continue.')
wolffd@0 59 pause
wolffd@0 60 disp('Error values from EM training.')
wolffd@0 61 % Use fast training method
wolffd@0 62 options = foptions;
wolffd@0 63 options(1) = 1; % Display EM training
wolffd@0 64 options(14) = 10; % number of iterations of EM
wolffd@0 65 net = rbftrain(net, options, tr_in, t);
wolffd@0 66
wolffd@0 67 disp(' ')
wolffd@0 68 disp('Press any key to continue.')
wolffd@0 69 pause
wolffd@0 70 clc
wolffd@0 71 disp('The second RBF network has thin plate spline activations.')
wolffd@0 72 disp('The same centres are used again, so we just need to calculate')
wolffd@0 73 disp('the second layer weights.')
wolffd@0 74 disp(' ')
wolffd@0 75 disp('Press any key to continue.')
wolffd@0 76 pause
wolffd@0 77 % Create a second RBF with thin plate spline functions
wolffd@0 78 net2 = rbf(nin, nhidden, nout, 'tps');
wolffd@0 79
wolffd@0 80 % Re-use previous centres rather than calling rbftrain again
wolffd@0 81 net2.c = net.c;
wolffd@0 82 [y, act2] = rbffwd(net2, tr_in);
wolffd@0 83
wolffd@0 84 % Solve for new output weights and biases from RBF activations
wolffd@0 85 temp = pinv([act2 ones(ndata, 1)]) * t;
wolffd@0 86 net2.w2 = temp(1:nhidden, :);
wolffd@0 87 net2.b2 = temp(nhidden+1, :);
wolffd@0 88
wolffd@0 89 disp('The third RBF network has r^4 log r activations.')
wolffd@0 90 disp(' ')
wolffd@0 91 disp('Press any key to continue.')
wolffd@0 92 pause
wolffd@0 93 % Create a third RBF with r^4 log r functions
wolffd@0 94 net3 = rbf(nin, nhidden, nout, 'r4logr');
wolffd@0 95
wolffd@0 96 % Overwrite weight vector with parameters from first RBF
wolffd@0 97 net3.c = net.c;
wolffd@0 98 [y, act3] = rbffwd(net3, tr_in);
wolffd@0 99 temp = pinv([act3 ones(ndata, 1)]) * t;
wolffd@0 100 net3.w2 = temp(1:nhidden, :);
wolffd@0 101 net3.b2 = temp(nhidden+1, :);
wolffd@0 102
wolffd@0 103 disp('Now we plot the data, underlying function, and network outputs')
wolffd@0 104 disp('on a single graph to compare the results.')
wolffd@0 105 disp(' ')
wolffd@0 106 disp('Press any key to continue.')
wolffd@0 107 pause
wolffd@0 108 % Plot the data, the original function, and the trained network functions.
wolffd@0 109 plotvals = [x(1):0.01:x(end)]';
wolffd@0 110 inputvals = (plotvals-mu)./sigma;
wolffd@0 111 y = rbffwd(net, inputvals);
wolffd@0 112 y2 = rbffwd(net2, inputvals);
wolffd@0 113 y3 = rbffwd(net3, inputvals);
wolffd@0 114 fh1 = figure;
wolffd@0 115
wolffd@0 116 plot(x, t, 'ob')
wolffd@0 117 hold on
wolffd@0 118 xlabel('Input')
wolffd@0 119 ylabel('Target')
wolffd@0 120 axis([x(1) x(end) -1.5 1.5])
wolffd@0 121 [fx, fy] = fplot('sin(2*pi*x)', [x(1) x(end)]);
wolffd@0 122 plot(fx, fy, '-r', 'LineWidth', 2)
wolffd@0 123 plot(plotvals, y, '--g', 'LineWidth', 2)
wolffd@0 124 plot(plotvals, y2, 'k--', 'LineWidth', 2)
wolffd@0 125 plot(plotvals, y3, '-.c', 'LineWidth', 2)
wolffd@0 126 legend('data', 'function', 'Gaussian RBF', 'Thin plate spline RBF', ...
wolffd@0 127 'r^4 log r RBF');
wolffd@0 128 hold off
wolffd@0 129
wolffd@0 130 disp('RBF training errors are');
wolffd@0 131 disp(['Gaussian ', num2str(rbferr(net, tr_in, t)), ' TPS ', ...
wolffd@0 132 num2str(rbferr(net2, tr_in, t)), ' R4logr ', num2str(rbferr(net3, tr_in, t))]);
wolffd@0 133
wolffd@0 134 disp(' ')
wolffd@0 135 disp('Press any key to end.')
wolffd@0 136 pause
wolffd@0 137 close(fh1);
wolffd@0 138 clear all;