comparison toolboxes/FullBNT-1.0.7/netlab3.3/demgmm5.m @ 0:e9a9cd732c1e tip

first hg version after svn

+%DEMGMM5 Demonstrate density modelling with a PPCA mixture model.
+%
+%	Description
+%	 The problem consists of modelling data generated by a mixture of
+%	three Gaussians in 2 dimensions with a mixture model using full
+%	covariance matrices.  The priors are 0.3, 0.5 and 0.2; the centres
+%	are (2, 3.5), (0, 0) and (0,2); the variances are (0.16, 0.64) axis
+%	aligned, (0.25, 1) rotated by 30 degrees and the identity matrix. The
+%	first figure contains a scatter plot of the data.
+%
+%	A mixture model with three one-dimensional PPCA components is trained
+%	using EM.  The parameter vector is printed before training and after
+%	training.  The parameter vector consists of priors (the column), and
+%	centres (given as (x, y) pairs as the next two columns).
+%
+%	The second figure is a 3 dimensional view of the density function,
+%	while the third shows the axes of the 1-standard deviation ellipses
+%	for the three components of the mixture model together with the one
+%	standard deviation along the principal component of each mixture
+%	model component.
+%
+%	See also
+%	GMM, GMMINIT, GMMEM, GMMPROB, PPCA
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+
+ndata = 500;
+data = randn(ndata, 2);
+prior = [0.3 0.5 0.2];
+% Mixture model swaps clusters 1 and 3
+datap = [0.2 0.5 0.3];
+datac = [0 2; 0 0; 2 3.5];
+datacov = repmat(eye(2), [1 1 3]);
+data1 = data(1:prior(1)*ndata,:);
+data2 = data(prior(1)*ndata+1:(prior(2)+prior(1))*ndata, :);
+data3 = data((prior(1)+prior(2))*ndata +1:ndata, :);
+
+% First cluster has axis aligned variance and centre (2, 3.5)
+data1(:, 1) = data1(:, 1)*0.1 + 2.0;
+data1(:, 2) = data1(:, 2)*0.8 + 3.5;
+datacov(:, :, 3) = [0.1*0.1 0; 0 0.8*0.8];
+
+% Second cluster has variance axes rotated by 30 degrees and centre (0, 0)
+rotn = [cos(pi/6) -sin(pi/6); sin(pi/6) cos(pi/6)];
+data2(:,1) = data2(:, 1)*0.2;
+data2 = data2*rotn;
+datacov(:, :, 2) = rotn' * [0.04 0; 0 1] * rotn;
+
+% Third cluster is at (0,2)
+data3(:, 2) = data3(:, 2)*0.1;
+data3 = data3 + repmat([0 2], prior(3)*ndata, 1);
+
+% Put the dataset together again
+data = [data1; data2; data3];
+
+ndata = 100;			% Number of data points.
+noise = 0.2;			% Standard deviation of noise distribution.
+x = [0:1/(2*(ndata - 1)):0.5]';
+randn('state', 1);
+rand('state', 1);
+t = sin(2*pi*x) + noise*randn(ndata, 1);
+
+% Fit three one-dimensional PPCA models
+ncentres = 3;
+ppca_dim = 1;
+
+clc
+disp('This demonstration illustrates the use of a Gaussian mixture model')
+disp('with a probabilistic PCA covariance structure to approximate the')
+disp('unconditional probability density of data in a two-dimensional space.')
+disp('We begin by generating the data from a mixture of three Gaussians and')
+disp('plotting it.')
+disp(' ')
+disp('The first cluster has axis aligned variance and centre (0, 2).')
+disp('The variance parallel to the x-axis is significantly greater')
+disp('than that parallel to the y-axis.')
+disp('The second cluster has variance axes rotated by 30 degrees')
+disp('and centre (0, 0).  The third cluster has significant variance')
+disp('parallel to the y-axis and centre (2, 3.5).')
+disp(' ')
+disp('Press any key to continue.')
+pause
+
+fh1 = figure;
+plot(data(:, 1), data(:, 2), 'o')
+set(gca, 'Box', 'on')
+axis equal
+hold on
+
+mix = gmm(2, ncentres, 'ppca', ppca_dim);
+options = foptions;
+options(14) = 10;
+options(1) = -1;  % Switch off all warnings
+
+% Just use 10 iterations of k-means in initialisation
+% Initialise the model parameters from the data
+mix = gmminit(mix, data, options);
+disp('The mixture model has three components with 1-dimensional')
+disp('PPCA subspaces.  The model parameters after initialisation using')
+disp('the k-means algorithm are as follows')
+disp('    Priors        Centres')
+disp([mix.priors' mix.centres])
+disp(' ')
+disp('Press any key to continue')
+pause
+
+options(1)  = 1;		% Prints out error values.
+options(14) = 30;		% Number of iterations.
+
+disp('We now train the model using the EM algorithm for up to 30 iterations.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+
+[mix, options, errlog] = gmmem(mix, data, options);
+disp('The trained model has priors and centres:')
+disp('    Priors        Centres')
+disp([mix.priors' mix.centres])
+
+% Now plot the result
+for i = 1:ncentres
+  % Plot the PC vectors
+  v = mix.U(:,:,i);
+  start=mix.centres(i,:)-sqrt(mix.lambda(i))*(v');
+  endpt=mix.centres(i,:)+sqrt(mix.lambda(i))*(v');
+  linex = [start(1) endpt(1)];
+  liney = [start(2) endpt(2)];
+  line(linex, liney, 'Color', 'k', 'LineWidth', 3)
+  % Plot ellipses of one standard deviation
+  theta = 0:0.02:2*pi;
+  x = sqrt(mix.lambda(i))*cos(theta);
+  y = sqrt(mix.covars(i))*sin(theta);
+  % Rotate ellipse axes
+  rot_matrix = [v(1) -v(2); v(2) v(1)];
+  ellipse = (rot_matrix*([x; y]))';
+  % Adjust centre
+  ellipse = ellipse + ones(length(theta), 1)*mix.centres(i,:);
+  plot(ellipse(:,1), ellipse(:,2), 'r-')
+end
+
+disp(' ')
+disp('Press any key to exit')
+pause
+close (fh1);
+clear all;