Daniel@0: %DEMKMEAN Demonstrate simple clustering model trained with K-means.
Daniel@0: %
Daniel@0: %	Description
Daniel@0: %	The problem consists of data in a two-dimensional space.  The data is
Daniel@0: %	drawn from three spherical Gaussian distributions with priors 0.3,
Daniel@0: %	0.5 and 0.2; centres (2, 3.5), (0, 0) and (0,2); and standard
Daniel@0: %	deviations 0.2, 0.5 and 1.0. The first figure contains a scatter plot
Daniel@0: %	of the data.  The data is the same as in DEMGMM1.
Daniel@0: %
Daniel@0: %	A cluster model with three components is trained using the batch K-
Daniel@0: %	means algorithm. The matrix of centres is printed after training. The
Daniel@0: %	second figure shows the data labelled with a colour derived from the
Daniel@0: %	corresponding  cluster
Daniel@0: %
Daniel@0: %	See also
Daniel@0: %	DEM2DDAT, DEMGMM1, KNN1, KMEANS
Daniel@0: %
Daniel@0: 
Daniel@0: %	Copyright (c) Ian T Nabney (1996-2001)
Daniel@0: 
Daniel@0: % Generate the data, fixing seeds for reproducible results
Daniel@0: ndata = 250;
Daniel@0: randn('state', 42);
Daniel@0: rand('state', 42);
Daniel@0: data = dem2ddat(ndata);
Daniel@0: 
Daniel@0: % Randomise data order
Daniel@0: data = data(randperm(ndata),:);
Daniel@0: 
Daniel@0: clc 
Daniel@0: disp('This demonstration illustrates the use of a cluster model to')
Daniel@0: disp('find centres that reflect the distribution of data points.')
Daniel@0: disp('We begin by generating the data from a mixture of three Gaussians')
Daniel@0: disp('in two-dimensional space and plotting it.')
Daniel@0: disp(' ')
Daniel@0: disp('Press any key to continue.')
Daniel@0: pause
Daniel@0: 
Daniel@0: fh1 = figure;
Daniel@0: plot(data(:, 1), data(:, 2), 'o')
Daniel@0: set(gca, 'Box', 'on')
Daniel@0: title('Data')
Daniel@0: 
Daniel@0: % Set up cluster model
Daniel@0: ncentres = 3;
Daniel@0: centres = zeros(ncentres, 2);
Daniel@0: 
Daniel@0: % Set up vector of options for kmeans trainer
Daniel@0: options = foptions;
Daniel@0: options(1)  = 1;		% Prints out error values.
Daniel@0: options(5) = 1;
Daniel@0: options(14) = 10;		% Number of iterations.
Daniel@0: 
Daniel@0: clc
Daniel@0: disp('The model is chosen to have three centres, which are initialised')
Daniel@0: disp('at randomly selected data points.  We now train the model using')
Daniel@0: disp('the batch K-means algorithm with a maximum of 10 iterations and')
Daniel@0: disp('stopping tolerance of 1e-4.')
Daniel@0: disp(' ')
Daniel@0: disp('Press any key to continue.')
Daniel@0: pause
Daniel@0: 
Daniel@0: % Train the centres from the data
Daniel@0: [centres, options, post] = kmeans(centres, data, options);
Daniel@0: 
Daniel@0: % Print out model
Daniel@0: disp(' ')
Daniel@0: disp('Note that training has terminated before 10 iterations as there')
Daniel@0: disp('has been no change in the centres or error function.')
Daniel@0: disp(' ')
Daniel@0: disp('The trained model has centres:')
Daniel@0: disp(centres);
Daniel@0: disp('Press any key to continue.')
Daniel@0: pause
Daniel@0: 
Daniel@0: clc
Daniel@0: disp('We now plot each data point coloured according to its classification')
Daniel@0: disp('given by the nearest cluster centre.  The cluster centres are denoted')
Daniel@0: disp('by black crosses.')
Daniel@0: 
Daniel@0: % 					Plot the result
Daniel@0: fh2 = figure;
Daniel@0: 
Daniel@0: hold on
Daniel@0: colours = ['b.'; 'r.'; 'g.'];
Daniel@0: 
Daniel@0: [tempi, tempj] = find(post);
Daniel@0: hold on
Daniel@0: for i = 1:3
Daniel@0:   % Select data points closest to ith centre
Daniel@0:   thisX = data(tempi(tempj == i), 1);
Daniel@0:   thisY = data(tempi(tempj == i), 2);
Daniel@0:   hp(i) = plot(thisX, thisY, colours(i,:));
Daniel@0:   set(hp(i), 'MarkerSize', 12);
Daniel@0: end
Daniel@0: set(gca, 'Box', 'on')
Daniel@0: legend('Class 1', 'Class 2', 'Class 3', 2)
Daniel@0: hold on
Daniel@0: plot(centres(:, 1), centres(:,2), 'k+', 'LineWidth', 2, ...
Daniel@0:   'MarkerSize', 8)
Daniel@0: title('Centres and data labels')
Daniel@0: hold off
Daniel@0: 
Daniel@0: disp(' ')
Daniel@0: disp('Press any key to end.')
Daniel@0: pause
Daniel@0: 
Daniel@0: close(fh1);
Daniel@0: close(fh2);
Daniel@0: clear all;
Daniel@0: