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1 %DEMKMEAN Demonstrate simple clustering model trained with K-means.
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2 %
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3 % Description
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4 % The problem consists of data in a two-dimensional space. The data is
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5 % drawn from three spherical Gaussian distributions with priors 0.3,
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6 % 0.5 and 0.2; centres (2, 3.5), (0, 0) and (0,2); and standard
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7 % deviations 0.2, 0.5 and 1.0. The first figure contains a scatter plot
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8 % of the data. The data is the same as in DEMGMM1.
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9 %
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10 % A cluster model with three components is trained using the batch K-
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11 % means algorithm. The matrix of centres is printed after training. The
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12 % second figure shows the data labelled with a colour derived from the
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13 % corresponding cluster
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14 %
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15 % See also
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16 % DEM2DDAT, DEMGMM1, KNN1, KMEANS
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17 %
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18
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19 % Copyright (c) Ian T Nabney (1996-2001)
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20
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21 % Generate the data, fixing seeds for reproducible results
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22 ndata = 250;
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23 randn('state', 42);
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24 rand('state', 42);
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25 data = dem2ddat(ndata);
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26
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27 % Randomise data order
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28 data = data(randperm(ndata),:);
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29
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30 clc
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31 disp('This demonstration illustrates the use of a cluster model to')
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32 disp('find centres that reflect the distribution of data points.')
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33 disp('We begin by generating the data from a mixture of three Gaussians')
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34 disp('in two-dimensional space and plotting it.')
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35 disp(' ')
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36 disp('Press any key to continue.')
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37 pause
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38
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39 fh1 = figure;
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40 plot(data(:, 1), data(:, 2), 'o')
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41 set(gca, 'Box', 'on')
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42 title('Data')
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43
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44 % Set up cluster model
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45 ncentres = 3;
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46 centres = zeros(ncentres, 2);
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47
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48 % Set up vector of options for kmeans trainer
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49 options = foptions;
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50 options(1) = 1; % Prints out error values.
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51 options(5) = 1;
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52 options(14) = 10; % Number of iterations.
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53
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54 clc
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55 disp('The model is chosen to have three centres, which are initialised')
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56 disp('at randomly selected data points. We now train the model using')
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57 disp('the batch K-means algorithm with a maximum of 10 iterations and')
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58 disp('stopping tolerance of 1e-4.')
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59 disp(' ')
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60 disp('Press any key to continue.')
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61 pause
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62
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63 % Train the centres from the data
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64 [centres, options, post] = kmeans(centres, data, options);
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65
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66 % Print out model
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67 disp(' ')
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68 disp('Note that training has terminated before 10 iterations as there')
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69 disp('has been no change in the centres or error function.')
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70 disp(' ')
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71 disp('The trained model has centres:')
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72 disp(centres);
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73 disp('Press any key to continue.')
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74 pause
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75
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76 clc
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77 disp('We now plot each data point coloured according to its classification')
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78 disp('given by the nearest cluster centre. The cluster centres are denoted')
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79 disp('by black crosses.')
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80
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81 % Plot the result
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82 fh2 = figure;
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83
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84 hold on
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85 colours = ['b.'; 'r.'; 'g.'];
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86
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87 [tempi, tempj] = find(post);
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88 hold on
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89 for i = 1:3
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90 % Select data points closest to ith centre
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91 thisX = data(tempi(tempj == i), 1);
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92 thisY = data(tempi(tempj == i), 2);
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93 hp(i) = plot(thisX, thisY, colours(i,:));
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94 set(hp(i), 'MarkerSize', 12);
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95 end
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96 set(gca, 'Box', 'on')
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97 legend('Class 1', 'Class 2', 'Class 3', 2)
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98 hold on
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99 plot(centres(:, 1), centres(:,2), 'k+', 'LineWidth', 2, ...
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100 'MarkerSize', 8)
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101 title('Centres and data labels')
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102 hold off
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103
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104 disp(' ')
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105 disp('Press any key to end.')
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106 pause
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107
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108 close(fh1);
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109 close(fh2);
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110 clear all;
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111
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