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1 function a = gmmactiv(mix, x)
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2 %GMMACTIV Computes the activations of a Gaussian mixture model.
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3 %
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4 % Description
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5 % This function computes the activations A (i.e. the probability
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6 % P(X|J) of the data conditioned on each component density) for a
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7 % Gaussian mixture model. For the PPCA model, each activation is the
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8 % conditional probability of X given that it is generated by the
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9 % component subspace. The data structure MIX defines the mixture model,
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10 % while the matrix X contains the data vectors. Each row of X
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11 % represents a single vector.
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12 %
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13 % See also
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14 % GMM, GMMPOST, GMMPROB
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15 %
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16
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17 % Copyright (c) Ian T Nabney (1996-2001)
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18
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19 % Check that inputs are consistent
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20 errstring = consist(mix, 'gmm', x);
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21 if ~isempty(errstring)
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22 error(errstring);
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23 end
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24
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25 ndata = size(x, 1);
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26 a = zeros(ndata, mix.ncentres); % Preallocate matrix
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27
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28 switch mix.covar_type
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29
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30 case 'spherical'
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31 % Calculate squared norm matrix, of dimension (ndata, ncentres)
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32 n2 = dist2(x, mix.centres);
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33
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34 % Calculate width factors
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35 wi2 = ones(ndata, 1) * (2 .* mix.covars);
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36 normal = (pi .* wi2) .^ (mix.nin/2);
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37
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38 % Now compute the activations
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39 a = exp(-(n2./wi2))./ normal;
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40
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41 case 'diag'
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42 normal = (2*pi)^(mix.nin/2);
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43 s = prod(sqrt(mix.covars), 2);
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44 for j = 1:mix.ncentres
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45 diffs = x - (ones(ndata, 1) * mix.centres(j, :));
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46 a(:, j) = exp(-0.5*sum((diffs.*diffs)./(ones(ndata, 1) * ...
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47 mix.covars(j, :)), 2)) ./ (normal*s(j));
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48 end
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49
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50 case 'full'
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51 normal = (2*pi)^(mix.nin/2);
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52 for j = 1:mix.ncentres
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53 diffs = x - (ones(ndata, 1) * mix.centres(j, :));
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54 % Use Cholesky decomposition of covariance matrix to speed computation
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55 c = chol(mix.covars(:, :, j));
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56 temp = diffs/c;
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57 a(:, j) = exp(-0.5*sum(temp.*temp, 2))./(normal*prod(diag(c)));
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58 end
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59 case 'ppca'
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60 log_normal = mix.nin*log(2*pi);
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61 d2 = zeros(ndata, mix.ncentres);
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62 logZ = zeros(1, mix.ncentres);
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63 for i = 1:mix.ncentres
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64 k = 1 - mix.covars(i)./mix.lambda(i, :);
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65 logZ(i) = log_normal + mix.nin*log(mix.covars(i)) - ...
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66 sum(log(1 - k));
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67 diffs = x - ones(ndata, 1)*mix.centres(i, :);
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68 proj = diffs*mix.U(:, :, i);
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69 d2(:,i) = (sum(diffs.*diffs, 2) - ...
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70 sum((proj.*(ones(ndata, 1)*k)).*proj, 2)) / ...
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71 mix.covars(i);
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72 end
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73 a = exp(-0.5*(d2 + ones(ndata, 1)*logZ));
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74 otherwise
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75 error(['Unknown covariance type ', mix.covar_type]);
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76 end
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77
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