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1 %DEMGLM2 Demonstrate simple classification using a generalized linear model.
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2 %
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3 % Description
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4 % The problem consists of a two dimensional input matrix DATA and a
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5 % vector of classifications T. The data is generated from three
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6 % Gaussian clusters, and a generalized linear model with softmax output
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7 % is trained using iterative reweighted least squares. A plot of the
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8 % data together with regions shaded by the classification given by the
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9 % network is generated.
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10 %
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11 % See also
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12 % DEMGLM1, GLM, GLMTRAIN
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13 %
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14
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15 % Copyright (c) Ian T Nabney (1996-2001)
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16
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17
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18 % Generate data from three classes in 2d
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19 input_dim = 2;
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20
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21 % Fix seeds for reproducible results
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22 randn('state', 42);
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23 rand('state', 42);
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24
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25 ndata = 100;
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26 % Generate mixture of three Gaussians in two dimensional space
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27 mix = gmm(2, 3, 'spherical');
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28 mix.priors = [0.4 0.3 0.3]; % Cluster priors
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29 mix.centres = [2, 2; 0.0, 0.0; 1, -1]; % Cluster centres
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30 mix.covars = [0.5 1.0 0.6];
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31
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32 [data, label] = gmmsamp(mix, ndata);
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33 id = eye(3);
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34 targets = id(label,:);
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35
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36 % Plot the result
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37
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38 clc
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39 disp('This demonstration illustrates the use of a generalized linear model')
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40 disp('to classify data from three classes in a two-dimensional space. We')
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41 disp('begin by generating and plotting the data.')
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42 disp(' ')
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43 disp('Press any key to continue.')
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44 pause
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45
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46 fh1 = figure;
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47 plot(data(label==1,1), data(label==1,2), 'bo');
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48 hold on
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49 axis([-4 5 -4 5]);
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50 set(gca, 'Box', 'on')
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51 plot(data(label==2,1), data(label==2,2), 'rx')
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52 plot(data(label==3, 1), data(label==3, 2), 'go')
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53 title('Data')
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54
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55 clc
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56 disp('Now we fit a model consisting of a softmax function of')
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57 disp('a linear combination of the input variables.')
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58 disp(' ')
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59 disp('The model is trained using the IRLS algorithm for up to 10 iterations')
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60 disp(' ')
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61 disp('Press any key to continue.')
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62 pause
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63
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64 net = glm(input_dim, size(targets, 2), 'softmax');
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65 options = foptions;
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66 options(1) = 1;
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67 options(14) = 10;
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68 net = glmtrain(net, options, data, targets);
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69
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70 disp(' ')
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71 disp('We now plot the decision regions given by this model.')
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72 disp(' ')
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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 x = -4.0:0.2:5.0;
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77 y = -4.0:0.2:5.0;
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78 [X, Y] = meshgrid(x,y);
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79 X = X(:);
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80 Y = Y(:);
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81 grid = [X Y];
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82 Z = glmfwd(net, grid);
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83 [foo , class] = max(Z');
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84 class = class';
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85 colors = ['b.'; 'r.'; 'g.'];
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86 for i = 1:3
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87 thisX = X(class == i);
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88 thisY = Y(class == i);
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89 h = plot(thisX, thisY, colors(i,:));
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90 set(h, 'MarkerSize', 8);
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91 end
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92 title('Plot of Decision regions')
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93
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94 hold off
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95
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96 clc
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97 disp('Note that the boundaries of decision regions are straight lines.')
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98 disp(' ')
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99 disp('Press any key to end.')
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100 pause
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101 close(fh1);
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102 clear all;
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103
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