projects / valse.git / blame
| Commit | Line | Data |
|---|---|---|
| 0f51ccae BA |
1 | function[phi,LLF] = EMGrank(Pi,Rho,mini,maxi,X,Y,tau,rank)\r |
| 2 | \r | |
| 3 | % get matrix sizes\r | |
| 4 | [~,m,k] = size(Rho);\r | |
| 5 | [n,p] = size(X);\r | |
| 6 | \r | |
| 7 | % allocate output matrices\r | |
| 8 | phi = zeros(p,m,k);\r | |
| 9 | Z = ones(n,1,'int64');\r | |
| 10 | LLF = 0.0;\r | |
| 11 | \r | |
| 12 | % local variables\r | |
| 13 | Phi = zeros(p,m,k);\r | |
| 14 | deltaPhi = 0.0;\r | |
| 15 | deltaPhi = [];\r | |
| 16 | sumDeltaPhi = 0.0;\r | |
| 17 | deltaPhiBufferSize = 20;\r | |
| 18 | \r | |
| 19 | %main loop (at least mini iterations)\r | |
| 20 | ite = int64(1);\r | |
| 21 | while ite<=mini || (ite<=maxi && sumDeltaPhi>tau)\r | |
| 22 | \r | |
| 23 | %M step: Mise à jour de Beta (et donc phi)\r | |
| 24 | for r=1:k\r | |
| 25 | if (sum(Z==r) == 0)\r | |
| 26 | continue;\r | |
| 27 | end\r | |
| 28 | %U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr\r | |
| 29 | [U,S,V] = svd(pinv(transpose(X(Z==r,:))*X(Z==r,:))*transpose(X(Z==r,:))*Y(Z==r,:));\r | |
| 30 | %Set m-rank(r) singular values to zero, and recompose\r | |
| 31 | %best rank(r) approximation of the initial product\r | |
| 32 | S(rank(r)+1:end,:) = 0;\r | |
| 33 | phi(:,:,r) = U * S * transpose(V) * Rho(:,:,r);\r | |
| 34 | end\r | |
| 35 | \r | |
| 36 | %Etape E et calcul de LLF\r | |
| 37 | sumLogLLF2 = 0.0;\r | |
| 38 | for i=1:n\r | |
| 39 | sumLLF1 = 0.0;\r | |
| 40 | maxLogGamIR = -Inf;\r | |
| 41 | for r=1:k\r | |
| 42 | dotProduct = (Y(i,:)*Rho(:,:,r)-X(i,:)*phi(:,:,r)) * transpose(Y(i,:)*Rho(:,:,r)-X(i,:)*phi(:,:,r));\r | |
| 43 | logGamIR = log(Pi(r)) + log(det(Rho(:,:,r))) - 0.5*dotProduct;\r | |
| 44 | %Z(i) = index of max (gam(i,:))\r | |
| 45 | if logGamIR > maxLogGamIR\r | |
| 46 | Z(i) = r;\r | |
| 47 | maxLogGamIR = logGamIR;\r | |
| 48 | end\r | |
| 49 | sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2);\r | |
| 50 | end\r | |
| 51 | sumLogLLF2 = sumLogLLF2 + log(sumLLF1);\r | |
| 52 | end\r | |
| 53 | \r | |
| 54 | LLF = -1/n * sumLogLLF2;\r | |
| 55 | \r | |
| 56 | % update distance parameter to check algorithm convergence (delta(phi, Phi))\r | |
| 57 | deltaPhi = [ deltaPhi, max(max(max((abs(phi-Phi))./(1+abs(phi))))) ];\r | |
| 58 | if length(deltaPhi) > deltaPhiBufferSize\r | |
| 59 | deltaPhi = deltaPhi(2:length(deltaPhi));\r | |
| 60 | end\r | |
| 61 | sumDeltaPhi = sum(abs(deltaPhi));\r | |
| 62 | \r | |
| 63 | % update other local variables\r | |
| 64 | Phi = phi;\r | |
| 65 | ite = ite+1;\r | |
| 66 | \r | |
| 67 | end\r | |
| 68 | \r | |
| 69 | end\r |