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1 function mix = netlabgmminit(mix, x, options)
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2 %GMMINIT Initialises Gaussian mixture model from data
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3 %(Renamed NETLABGMMINIT in MIRtoolbox to avoid conflict with statistics
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4 %toolbox)
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5 % Description
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6 % MIX = GMMINIT(MIX, X, OPTIONS) uses a dataset X to initialise the
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7 % parameters of a Gaussian mixture model defined by the data structure
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8 % MIX. The k-means algorithm is used to determine the centres. The
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9 % priors are computed from the proportion of examples belonging to each
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10 % cluster. The covariance matrices are calculated as the sample
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11 % covariance of the points associated with (i.e. closest to) the
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12 % corresponding centres. For a mixture of PPCA model, the PPCA
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13 % decomposition is calculated for the points closest to a given centre.
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14 % This initialisation can be used as the starting point for training
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15 % the model using the EM algorithm.
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16 %
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17 % See also
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18 % GMM
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19 %
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20
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21 % Copyright (c) Ian T Nabney (1996-2001)
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22
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23 [ndata, xdim] = size(x);
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24
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25 % Check that inputs are consistent
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26 errstring = consist(mix, 'gmm', x);
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27 if ~isempty(errstring)
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28 error(errstring);
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29 end
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30
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31 % Arbitrary width used if variance collapses to zero: make it 'large' so
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32 % that centre is responsible for a reasonable number of points.
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33 GMM_WIDTH = 1.0;
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34
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35 % Use kmeans algorithm to set centres
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36 options(5) = 1;
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37 [mix.centres, options, post] = netlabkmeans(mix.centres, x, options);
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38
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39 % Set priors depending on number of points in each cluster
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40 cluster_sizes = max(sum(post, 1), 1); % Make sure that no prior is zero
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41 mix.priors = cluster_sizes/sum(cluster_sizes); % Normalise priors
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42
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43 switch mix.covar_type
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44 case 'spherical'
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45 if mix.ncentres > 1
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46 % Determine widths as distance to nearest centre
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47 % (or a constant if this is zero)
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48 cdist = dist2(mix.centres, mix.centres);
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49 cdist = cdist + diag(ones(mix.ncentres, 1)*realmax);
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50 mix.covars = min(cdist);
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51 mix.covars = mix.covars + GMM_WIDTH*(mix.covars < eps);
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52 else
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53 % Just use variance of all data points averaged over all
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54 % dimensions
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55 mix.covars = mean(diag(cov(x)));
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56 end
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57 case 'diag'
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58 for j = 1:mix.ncentres
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59 % Pick out data points belonging to this centre
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60 c = x(find(post(:, j)),:);
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61 diffs = c - (ones(size(c, 1), 1) * mix.centres(j, :));
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62 mix.covars(j, :) = sum((diffs.*diffs), 1)/size(c, 1);
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63 % Replace small entries by GMM_WIDTH value
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64 mix.covars(j, :) = mix.covars(j, :) + GMM_WIDTH.*(mix.covars(j, :)<eps);
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65 end
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66 case 'full'
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67 for j = 1:mix.ncentres
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68 % Pick out data points belonging to this centre
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69 c = x(find(post(:, j)),:);
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70 diffs = c - (ones(size(c, 1), 1) * mix.centres(j, :));
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71 mix.covars(:,:,j) = (diffs'*diffs)/(size(c, 1));
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72 % Add GMM_WIDTH*Identity to rank-deficient covariance matrices
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73 if rank(mix.covars(:,:,j)) < mix.nin
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74 mix.covars(:,:,j) = mix.covars(:,:,j) + GMM_WIDTH.*eye(mix.nin);
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75 end
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76 end
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77 case 'ppca'
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78 for j = 1:mix.ncentres
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79 % Pick out data points belonging to this centre
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80 c = x(find(post(:,j)),:);
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81 diffs = c - (ones(size(c, 1), 1) * mix.centres(j, :));
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82 [tempcovars, tempU, templambda] = ...
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83 ppca((diffs'*diffs)/size(c, 1), mix.ppca_dim);
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84 if length(templambda) ~= mix.ppca_dim
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85 error('Unable to extract enough components');
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86 else
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87 mix.covars(j) = tempcovars;
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88 mix.U(:, :, j) = tempU;
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89 mix.lambda(j, :) = templambda;
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90 end
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91 end
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92 otherwise
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93 error(['Unknown covariance type ', mix.covar_type]);
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94 end
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95
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