Daniel@0: %DEMMLP1 Demonstrate simple regression using a multi-layer perceptron
Daniel@0: %
Daniel@0: %	Description
Daniel@0: %	The problem consists of one input variable X and one target variable
Daniel@0: %	T with data generated by sampling X at equal intervals and then
Daniel@0: %	generating target data by computing SIN(2*PI*X) and adding Gaussian
Daniel@0: %	noise. A 2-layer network with linear outputs is trained by minimizing
Daniel@0: %	a  sum-of-squares error function using the scaled conjugate gradient
Daniel@0: %	optimizer.
Daniel@0: %
Daniel@0: %	See also
Daniel@0: %	MLP, MLPERR, MLPGRAD, SCG
Daniel@0: %
Daniel@0: 
Daniel@0: %	Copyright (c) Ian T Nabney (1996-2001)
Daniel@0: 
Daniel@0: 
Daniel@0: % Generate the matrix of inputs x and targets t.
Daniel@0: 
Daniel@0: ndata = 20;			% Number of data points.
Daniel@0: noise = 0.2;			% Standard deviation of noise distribution.
Daniel@0: x = [0:1/(ndata - 1):1]';
Daniel@0: randn('state', 1);
Daniel@0: t = sin(2*pi*x) + noise*randn(ndata, 1);
Daniel@0: 
Daniel@0: clc
Daniel@0: disp('This demonstration illustrates the use of a Multi-Layer Perceptron')
Daniel@0: disp('network for regression problems.  The data is generated from a noisy')
Daniel@0: disp('sine function.')
Daniel@0: disp(' ')
Daniel@0: disp('Press any key to continue.')
Daniel@0: pause
Daniel@0: 
Daniel@0: % Set up network parameters.
Daniel@0: nin = 1;			% Number of inputs.
Daniel@0: nhidden = 3;			% Number of hidden units.
Daniel@0: nout = 1;			% Number of outputs.
Daniel@0: alpha = 0.01;			% Coefficient of weight-decay prior. 
Daniel@0: 
Daniel@0: % Create and initialize network weight vector.
Daniel@0: 
Daniel@0: net = mlp(nin, nhidden, nout, 'linear', alpha);
Daniel@0: 
Daniel@0: % Set up vector of options for the optimiser.
Daniel@0: 
Daniel@0: options = zeros(1,18);
Daniel@0: options(1) = 1;			% This provides display of error values.
Daniel@0: options(14) = 100;		% Number of training cycles. 
Daniel@0: 
Daniel@0: clc
Daniel@0: disp(['The network has ', num2str(nhidden), ' hidden units and a weight decay'])
Daniel@0: disp(['coefficient of ', num2str(alpha), '.'])
Daniel@0: disp(' ')
Daniel@0: disp('After initializing the network, we train it use the scaled conjugate')
Daniel@0: disp('gradients algorithm for 100 cycles.')
Daniel@0: disp(' ')
Daniel@0: disp('Press any key to continue')
Daniel@0: pause
Daniel@0: 
Daniel@0: % Train using scaled conjugate gradients.
Daniel@0: [net, options] = netopt(net, options, x, t, 'scg');
Daniel@0: 
Daniel@0: disp(' ')
Daniel@0: disp('Now we plot the data, underlying function, and network outputs')
Daniel@0: disp('on a single graph to compare the results.')
Daniel@0: disp(' ')
Daniel@0: disp('Press any key to continue.')
Daniel@0: pause
Daniel@0: 
Daniel@0: % Plot the data, the original function, and the trained network function.
Daniel@0: plotvals = [0:0.01:1]';
Daniel@0: y = mlpfwd(net, plotvals);
Daniel@0: fh1 = figure;
Daniel@0: plot(x, t, 'ob')
Daniel@0: hold on
Daniel@0: xlabel('Input')
Daniel@0: ylabel('Target')
Daniel@0: axis([0 1 -1.5 1.5])
Daniel@0: [fx, fy] = fplot('sin(2*pi*x)', [0 1]);
Daniel@0: plot(fx, fy, '-r', 'LineWidth', 2)
Daniel@0: plot(plotvals, y, '-k', 'LineWidth', 2)
Daniel@0: legend('data', 'function', 'network');
Daniel@0: 
Daniel@0: disp(' ')
Daniel@0: disp('Press any key to end.')
Daniel@0: pause
Daniel@0: close(fh1);
Daniel@0: clear all;