comparison toolboxes/FullBNT-1.0.7/netlab3.3/demolgd1.m @ 0:e9a9cd732c1e tip

first hg version after svn

+%DEMOLGD1 Demonstrate simple MLP optimisation with on-line gradient descent
+%
+%	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. A 2-layer network with linear outputs is trained by minimizing
+%	a  sum-of-squares error function using on-line gradient descent.
+%
+%	See also
+%	DEMMLP1, OLGD
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+
+% Generate the matrix of inputs x and targets t.
+
+ndata = 20;			% Number of data points.
+noise = 0.2;			% Standard deviation of noise distribution.
+x = [0:1/(ndata - 1):1]';
+randn('state', 42);
+rand('state', 42);
+t = sin(2*pi*x) + noise*randn(ndata, 1);
+
+clc
+disp('This demonstration illustrates the use of the on-line gradient')
+disp('descent algorithm to train a Multi-Layer Perceptron network for')
+disp('regression problems.  It is intended to illustrate the drawbacks')
+disp('of this algorithm compared to more powerful non-linear optimisation')
+disp('algorithms, such as conjugate gradients.')
+disp(' ')
+disp('First we generate the data from a noisy sine function and construct')
+disp('the network.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+% Set up network parameters.
+nin = 1;			% Number of inputs.
+nhidden = 3;			% Number of hidden units.
+nout = 1;			% Number of outputs.
+alpha = 0.01;			% Coefficient of weight-decay prior. 
+
+% Create and initialize network weight vector.
+net = mlp(nin, nhidden, nout, 'linear');
+% Initialise weights reasonably close to 0
+net = mlpinit(net, 10);
+
+% Set up vector of options for the optimiser.
+options = foptions;
+options(1) = 1;			% This provides display of error values.
+options(14) = 20;		% Number of training cycles. 
+options(18) = 0.1;		% Learning rate
+%options(17) = 0.4;		% Momentum
+options(17) = 0.4;		% Momentum
+options(5) = 1; 		% Do randomise pattern order
+clc
+disp('Then we set the options for the training algorithm.')
+disp(['In the first phase of training, which lasts for ',...
+    num2str(options(14)), ' cycles,'])
+disp(['the learning rate is ', num2str(options(18)), ...
+    ' and the momentum is ', num2str(options(17)), '.'])
+disp('The error values are displayed at the end of each pass through the')
+disp('entire pattern set.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+
+% Train using online gradient descent
+[net, options] = olgd(net, options, x, t);
+
+% Now allow learning rate to decay and remove momentum
+options(2) = 0;
+options(3) = 0;
+options(17) = 0.4;	% Turn off momentum
+options(5) = 1;		% Randomise pattern order
+options(6) = 1;		% Set learning rate decay on
+options(14) = 200;
+options(18) = 0.1;	% Initial learning rate
+
+disp(['In the second phase of training, which lasts for up to ',...
+    num2str(options(14)), ' cycles,'])
+disp(['the learning rate starts at ', num2str(options(18)), ...
+    ', decaying at 1/t and the momentum is ', num2str(options(17)), '.'])
+disp(' ')
+disp('Press any key to continue.')
+pause
+[net, options] = olgd(net, options, x, t);
+
+clc
+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 function.
+plotvals = [0:0.01:1]';
+y = mlpfwd(net, plotvals);
+fh1 = figure;
+plot(x, t, 'ob')
+hold on
+axis([0 1 -1.5 1.5])
+fplot('sin(2*pi*x)', [0 1], '--g')
+plot(plotvals, y, '-r')
+legend('data', 'function', 'network');
+hold off
+
+disp('Note the very poor fit to the data: this should be compared with')
+disp('the results obtained in demmlp1.')
+disp(' ')
+disp('Press any key to exit.')
+pause
+close(fh1);
+clear all;