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1 %DEMGLM1 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 two
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6 % Gaussian clusters, and a generalized linear model with logistic
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7 % output is trained using iterative reweighted least squares. A plot of
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8 % the data together with the 0.1, 0.5 and 0.9 contour lines of the
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9 % conditional probability is generated.
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10 %
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11 % See also
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12 % DEMGLM2, 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 two 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 two Gaussians in two dimensional space
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27 mix = gmm(2, 2, 'spherical');
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28 mix.priors = [0.4 0.6]; % Cluster priors
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29 mix.centres = [2.0, 2.0; 0.0, 0.0]; % Cluster centres
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30 mix.covars = [0.5, 1.0];
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31
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32 [data, label] = gmmsamp(mix, ndata);
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33 targets = label - ones(ndata, 1);
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34
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35 % Plot the result
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36
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37 clc
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38 disp('This demonstration illustrates the use of a generalized linear model')
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39 disp('to classify data from two classes in a two-dimensional space. We')
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40 disp('begin by generating and plotting the data.')
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41 disp(' ')
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42 disp('Press any key to continue.')
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43 pause
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44
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45 fh1 = figure;
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46 plot(data(label==1,1), data(label==1,2), 'bo');
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47 hold on
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48 axis([-4 5 -4 5])
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49 set(gca, 'box', 'on')
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50 plot(data(label==2,1), data(label==2,2), 'rx')
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51 title('Data')
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52
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53 clc
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54 disp('Now we fit a model consisting of a logistic sigmoid function of')
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55 disp('a linear combination of the input variables.')
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56 disp(' ')
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57 disp('The model is trained using the IRLS algorithm for 5 iterations')
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58 disp(' ')
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59 disp('Press any key to continue.')
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60 pause
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61
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62 net = glm(input_dim, 1, 'logistic');
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63 options = foptions;
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64 options(1) = 1;
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65 options(14) = 5;
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66 net = glmtrain(net, options, data, targets);
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67
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68 disp(' ')
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69 disp('We now plot some density contours given by this model.')
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70 disp('The contour labelled 0.5 is the decision boundary.')
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71 disp(' ')
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72 disp('Press any key to continue.')
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73 pause
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74 x = -4.0:0.2:5.0;
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75 y = -4.0:0.2:5.0;
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76 [X, Y] = meshgrid(x,y);
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77 X = X(:);
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78 Y = Y(:);
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79 grid = [X Y];
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80 Z = glmfwd(net, grid);
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81 Z = reshape(Z, length(x), length(y));
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82 v = [0.1 0.5 0.9];
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83 [c, h] = contour(x, y, Z, v);
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84 title('Generalized Linear Model')
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85 set(h, 'linewidth', 3)
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86 clabel(c, h);
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87
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88 clc
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89 disp('Note that the contours of constant density are straight lines.')
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90 disp(' ')
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91 disp('Press any key to end.')
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92 pause
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93 close(fh1);
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94 clear all;
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95
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