comparison toolboxes/FullBNT-1.0.7/netlab3.3/demgmm2.m @ 0:e9a9cd732c1e tip

first hg version after svn

+%DEMGMM1 Demonstrate density modelling with a Gaussian mixture model.
+%
+%	Description
+%	The problem consists of modelling data generated by a mixture of
+%	three Gaussians in 2 dimensions.  The priors are 0.3, 0.5 and 0.2;
+%	the centres are (2, 3.5), (0, 0) and (0,2); the variances are 0.2,
+%	0.5 and 1.0. The first figure contains a  scatter plot of the data.
+%
+%	A Gaussian mixture model with three components is trained using EM.
+%	The parameter vector is printed before training and after training.
+%	The user should press any key to continue at these points.  The
+%	parameter vector consists of priors (the column), centres (given as
+%	(x, y) pairs as the next two columns), and variances (the last
+%	column).
+%
+%	The second figure is a 3 dimensional view of the density function,
+%	while the third shows the 1-standard deviation circles for the three
+%	components of the mixture model.
+%
+%	See also
+%	GMM, GMMINIT, GMMEM, GMMPROB, GMMUNPAK
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+% Generate the data
+% Fix seeds for reproducible results
+randn('state', 42);
+rand('state', 42);
+
+ndata = 500;
+[data, datac, datap, datasd] = dem2ddat(ndata);
+
+clc
+disp('This demonstration illustrates the use of a Gaussian mixture model')
+disp('to approximate the unconditional probability density of data in')
+disp('a two-dimensional space.  We begin by generating the data from')
+disp('a mixture of three Gaussians and plotting it.')
+disp(' ')
+disp('Press any key to continue')
+pause
+
+fh1 = figure;
+plot(data(:, 1), data(:, 2), 'o')
+set(gca, 'Box', 'on')
+% Set up mixture model
+ncentres = 3;
+input_dim = 2;
+mix = gmm(input_dim, ncentres, 'spherical');
+
+options = foptions;
+options(14) = 5;	% Just use 5 iterations of k-means in initialisation
+% Initialise the model parameters from the data
+mix = gmminit(mix, data, options);
+
+clc
+disp('The data is drawn from a mixture with parameters')
+disp('    Priors        Centres         Variances')
+disp([datap' datac (datasd.^2)'])
+disp(' ')
+disp('The mixture model has three components and spherical covariance')
+disp('matrices.  The model parameters after initialisation using the')
+disp('k-means algorithm are as follows')
+% Print out model
+disp('    Priors        Centres         Variances')
+disp([mix.priors' mix.centres mix.covars'])
+disp('Press any key to continue')
+pause
+
+% Set up vector of options for EM trainer
+options = zeros(1, 18);
+options(1)  = 1;		% Prints out error values.
+options(14) = 10;		% Max. Number of iterations.
+
+disp('We now train the model using the EM algorithm for 10 iterations')
+disp(' ')
+disp('Press any key to continue')
+pause
+[mix, options, errlog] = gmmem(mix, data, options);
+
+% Print out model
+disp(' ')
+disp('The trained model has parameters ')
+disp('    Priors        Centres         Variances')
+disp([mix.priors' mix.centres mix.covars'])
+disp('Note the close correspondence between these parameters and those')
+disp('of the distribution used to generate the data, which are repeated here.')
+disp('    Priors        Centres         Variances')
+disp([datap' datac (datasd.^2)'])
+disp(' ')
+disp('Press any key to continue')
+pause
+
+clc
+disp('We now plot the density given by the mixture model as a surface plot')
+disp(' ')
+disp('Press any key to continue')
+pause
+% Plot the result
+x = -4.0:0.2:5.0;
+y = -4.0:0.2:5.0;
+[X, Y] = meshgrid(x,y);
+X = X(:);
+Y = Y(:);
+grid = [X Y];
+Z = gmmprob(mix, grid);
+Z = reshape(Z, length(x), length(y));
+c = mesh(x, y, Z);
+hold on
+title('Surface plot of probability density')
+hold off
+
+clc
+disp('The final plot shows the centres and widths, given by one standard')
+disp('deviation, of the three components of the mixture model.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+% Try to calculate a sensible position for the second figure, below the first
+fig1_pos = get(fh1, 'Position');
+fig2_pos = fig1_pos;
+fig2_pos(2) = fig2_pos(2) - fig1_pos(4);
+fh2 = figure;
+set(fh2, 'Position', fig2_pos)
+
+hp1 = plot(data(:, 1), data(:, 2), 'bo');
+axis('equal');
+hold on
+hp2 = plot(mix.centres(:, 1), mix.centres(:,2), 'g+');
+set(hp2, 'MarkerSize', 10);
+set(hp2, 'LineWidth', 3);
+
+title('Plot of data and mixture centres')
+angles = 0:pi/30:2*pi;
+for i = 1 : mix.ncentres
+  x_circle = mix.centres(i,1)*ones(1, length(angles)) + ...
+    sqrt(mix.covars(i))*cos(angles);
+  y_circle = mix.centres(i,2)*ones(1, length(angles)) + ...
+    sqrt(mix.covars(i))*sin(angles);
+  plot(x_circle, y_circle, 'r')
+end
+hold off
+disp('Note how the data cluster positions and widths are captured by')
+disp('the mixture model.')
+disp(' ')
+disp('Press any key to end.')
+pause
+
+close(fh1);
+close(fh2);
+clear all; 
+