projects / valse.git / blame
| Commit | Line | Data |
|---|---|---|
| c3bc4705 BA |
1 | #helper to always have matrices as arg (TODO: put this elsewhere? improve?) |
| 2 | matricize <- function(X) | |
| 3 | { | |
| 4 | if (!is.matrix(X)) | |
| 5 | return (t(as.matrix(X))) | |
| 6 | return (X) | |
| 7 | } | |
| 8 | ||
| c3b2c1ab | 9 | require(MASS) |
| ef67d338 BA |
10 | EMGrank = function(Pi, Rho, mini, maxi, X, Y, tau, rank) |
| 11 | { | |
| c2028869 BG |
12 | #matrix dimensions |
| 13 | n = dim(X)[1] | |
| 14 | p = dim(X)[2] | |
| 15 | m = dim(Rho)[2] | |
| 16 | k = dim(Rho)[3] | |
| 17 | ||
| 18 | #init outputs | |
| 19 | phi = array(0, dim=c(p,m,k)) | |
| 20 | Z = rep(1, n) | |
| c2028869 BG |
21 | LLF = 0 |
| 22 | ||
| 23 | #local variables | |
| 24 | Phi = array(0, dim=c(p,m,k)) | |
| ef67d338 BA |
25 | deltaPhi = c() |
| 26 | sumDeltaPhi = 0. | |
| c2028869 BG |
27 | deltaPhiBufferSize = 20 |
| 28 | ||
| 29 | #main loop | |
| 30 | ite = 1 | |
| ef67d338 | 31 | while (ite<=mini || (ite<=maxi && sumDeltaPhi>tau)) |
| c3bc4705 | 32 | { |
| c2028869 | 33 | #M step: Mise à jour de Beta (et donc phi) |
| c3bc4705 BA |
34 | for(r in 1:k) |
| 35 | { | |
| 36 | Z_indice = seq_len(n)[Z==r] #indices où Z == r | |
| 37 | if (length(Z_indice) == 0) | |
| c2028869 | 38 | next |
| c2028869 | 39 | #U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr |
| c3bc4705 BA |
40 | s = svd( ginv(crossprod(matricize(X[Z_indice,]))) %*% |
| 41 | crossprod(matricize(X[Z_indice,]),matricize(Y[Z_indice,])) ) | |
| 42 | S = s$d | |
| c2028869 BG |
43 | #Set m-rank(r) singular values to zero, and recompose |
| 44 | #best rank(r) approximation of the initial product | |
| c3bc4705 BA |
45 | if(rank[r] < length(S)) |
| 46 | S[(rank[r]+1):length(S)] = 0 | |
| ef67d338 | 47 | phi[,,r] = s$u %*% diag(S) %*% t(s$v) %*% Rho[,,r] |
| c2028869 | 48 | } |
| ef67d338 | 49 | |
| c3bc4705 BA |
50 | #Etape E et calcul de LLF |
| 51 | sumLogLLF2 = 0 | |
| ef67d338 BA |
52 | for(i in seq_len(n)) |
| 53 | { | |
| c3bc4705 BA |
54 | sumLLF1 = 0 |
| 55 | maxLogGamIR = -Inf | |
| ef67d338 BA |
56 | for (r in seq_len(k)) |
| 57 | { | |
| c3bc4705 BA |
58 | dotProduct = tcrossprod(Y[i,]%*%Rho[,,r]-X[i,]%*%phi[,,r]) |
| 59 | logGamIR = log(Pi[r]) + log(det(Rho[,,r])) - 0.5*dotProduct | |
| 60 | #Z[i] = index of max (gam[i,]) | |
| ef67d338 BA |
61 | if(logGamIR > maxLogGamIR) |
| 62 | { | |
| c3bc4705 BA |
63 | Z[i] = r |
| 64 | maxLogGamIR = logGamIR | |
| 65 | } | |
| ef67d338 | 66 | sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2) |
| c3bc4705 BA |
67 | } |
| 68 | sumLogLLF2 = sumLogLLF2 + log(sumLLF1) | |
| 69 | } | |
| c2028869 | 70 | |
| c3bc4705 | 71 | LLF = -1/n * sumLogLLF2 |
| ef67d338 | 72 | |
| c3bc4705 | 73 | #update distance parameter to check algorithm convergence (delta(phi, Phi)) |
| ef67d338 BA |
74 | deltaPhi = c( deltaPhi, max( (abs(phi-Phi)) / (1+abs(phi)) ) ) #TODO: explain? |
| 75 | if (length(deltaPhi) > deltaPhiBufferSize) | |
| 76 | deltaPhi = deltaPhi[2:length(deltaPhi)] | |
| c3bc4705 | 77 | sumDeltaPhi = sum(abs(deltaPhi)) |
| ef67d338 | 78 | |
| c3bc4705 BA |
79 | #update other local variables |
| 80 | Phi = phi | |
| 81 | ite = ite+1 | |
| c2028869 | 82 | } |
| ef67d338 | 83 | return(list("phi"=phi, "LLF"=LLF)) |
| 9ade3f1b | 84 | } |