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1 function [var, U, lambda] = ppca(x, ppca_dim)
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2 %PPCA Probabilistic Principal Components Analysis
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3 %
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4 % Description
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5 % [VAR, U, LAMBDA] = PPCA(X, PPCA_DIM) computes the principal
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6 % component subspace U of dimension PPCA_DIM using a centred covariance
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7 % matrix X. The variable VAR contains the off-subspace variance (which
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8 % is assumed to be spherical), while the vector LAMBDA contains the
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9 % variances of each of the principal components. This is computed
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10 % using the eigenvalue and eigenvector decomposition of X.
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11 %
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12 % See also
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13 % EIGDEC, PCA
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14 %
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15
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16 % Copyright (c) Ian T Nabney (1996-2001)
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17
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18
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19 if ppca_dim ~= round(ppca_dim) | ppca_dim < 1 | ppca_dim > size(x, 2)
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20 error('Number of PCs must be integer, >0, < dim');
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21 end
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22
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23 [ndata, data_dim] = size(x);
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24 % Assumes that x is centred and responsibility weighted
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25 % covariance matrix
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26 [l Utemp] = eigdec(x, data_dim);
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27 % Zero any negative eigenvalues (caused by rounding)
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28 l(l<0) = 0;
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29 % Now compute the sigma squared values for all possible values
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30 % of q
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31 s2_temp = cumsum(l(end:-1:1))./[1:data_dim]';
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32 % If necessary, reduce the value of q so that var is at least
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33 % eps * largest eigenvalue
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34 q_temp = min([ppca_dim; data_dim-min(find(s2_temp/l(1) > eps))]);
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35 if q_temp ~= ppca_dim
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36 wstringpart = 'Covariance matrix ill-conditioned: extracted';
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37 wstring = sprintf('%s %d/%d PCs', ...
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38 wstringpart, q_temp, ppca_dim);
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39 warning(wstring);
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40 end
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41 if q_temp == 0
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42 % All the latent dimensions have disappeared, so we are
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43 % just left with the noise model
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44 var = l(1)/data_dim;
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45 lambda = var*ones(1, ppca_dim);
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46 else
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47 var = mean(l(q_temp+1:end));
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48 end
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49 U = Utemp(:, 1:q_temp);
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50 lambda(1:q_temp) = l(1:q_temp);
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51
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52
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