%DEMKMEAN Demonstrate simple clustering model trained with K-means.%%	Description%	The problem consists of data in a two-dimensional space.  The data is%	drawn from three spherical Gaussian distributions with priors 0.3,%	0.5 and 0.2; centres (2, 3.5), (0, 0) and (0,2); and standard%	deviations 0.2, 0.5 and 1.0. The first figure contains a scatter plot%	of the data.  The data is the same as in DEMGMM1.%%	A cluster model with three components is trained using the batch K-%	means algorithm. The matrix of centres is printed after training. The%	second figure shows the data labelled with a colour derived from the%	corresponding  cluster%%	See also%	DEM2DDAT, DEMGMM1, KNN1, KMEANS%%	Copyright (c) Ian T Nabney (1996-2001)% Generate the data, fixing seeds for reproducible resultsndata = 250;randn('state', 42);rand('state', 42);data = dem2ddat(ndata);% Randomise data orderdata = data(randperm(ndata),:);clc disp('This demonstration illustrates the use of a cluster model to')disp('find centres that reflect the distribution of data points.')disp('We begin by generating the data from a mixture of three Gaussians')disp('in two-dimensional space and plotting it.')disp(' ')disp('Press any key to continue.')pausefh1 = figure;plot(data(:, 1), data(:, 2), 'o')set(gca, 'Box', 'on')title('Data')% Set up cluster modelncentres = 3;centres = zeros(ncentres, 2);% Set up vector of options for kmeans traineroptions = foptions;options(1)  = 1;		% Prints out error values.options(5) = 1;options(14) = 10;		% Number of iterations.clcdisp('The model is chosen to have three centres, which are initialised')disp('at randomly selected data points.  We now train the model using')disp('the batch K-means algorithm with a maximum of 10 iterations and')disp('stopping tolerance of 1e-4.')disp(' ')disp('Press any key to continue.')pause% Train the centres from the data[centres, options, post] = kmeans(centres, data, options);% Print out modeldisp(' ')disp('Note that training has terminated before 10 iterations as there')disp('has been no change in the centres or error function.')disp(' ')disp('The trained model has centres:')disp(centres);disp('Press any key to continue.')pauseclcdisp('We now plot each data point coloured according to its classification')disp('given by the nearest cluster centre.  The cluster centres are denoted')disp('by black crosses.')% 					Plot the resultfh2 = figure;hold oncolours = ['b.'; 'r.'; 'g.'];[tempi, tempj] = find(post);hold onfor i = 1:3  % Select data points closest to ith centre  thisX = data(tempi(tempj == i), 1);  thisY = data(tempi(tempj == i), 2);  hp(i) = plot(thisX, thisY, colours(i,:));  set(hp(i), 'MarkerSize', 12);endset(gca, 'Box', 'on')legend('Class 1', 'Class 2', 'Class 3', 2)hold onplot(centres(:, 1), centres(:,2), 'k+', 'LineWidth', 2, ...  'MarkerSize', 8)title('Centres and data labels')hold offdisp(' ')disp('Press any key to end.')pauseclose(fh1);close(fh2);clear all;