Commit | Line | Data |
---|---|---|
c3bc4705 | 1 | #helper to always have matrices as arg (TODO: put this elsewhere? improve?) |
f7244815 | 2 | # --> Yes, we should use by-columns storage everywhere... [later!] |
c3bc4705 BA |
3 | matricize <- function(X) |
4 | { | |
5 | if (!is.matrix(X)) | |
6 | return (t(as.matrix(X))) | |
7 | return (X) | |
8 | } | |
9 | ||
c3b2c1ab | 10 | require(MASS) |
f7244815 | 11 | EMGrank_R = function(Pi, Rho, mini, maxi, X, Y, tau, rank) |
ef67d338 | 12 | { |
c2028869 BG |
13 | #matrix dimensions |
14 | n = dim(X)[1] | |
15 | p = dim(X)[2] | |
16 | m = dim(Rho)[2] | |
17 | k = dim(Rho)[3] | |
18 | ||
19 | #init outputs | |
20 | phi = array(0, dim=c(p,m,k)) | |
21 | Z = rep(1, n) | |
c2028869 BG |
22 | LLF = 0 |
23 | ||
24 | #local variables | |
25 | Phi = array(0, dim=c(p,m,k)) | |
ef67d338 BA |
26 | deltaPhi = c() |
27 | sumDeltaPhi = 0. | |
c2028869 BG |
28 | deltaPhiBufferSize = 20 |
29 | ||
30 | #main loop | |
31 | ite = 1 | |
ef67d338 | 32 | while (ite<=mini || (ite<=maxi && sumDeltaPhi>tau)) |
c3bc4705 | 33 | { |
c2028869 | 34 | #M step: Mise à jour de Beta (et donc phi) |
c3bc4705 BA |
35 | for(r in 1:k) |
36 | { | |
37 | Z_indice = seq_len(n)[Z==r] #indices où Z == r | |
38 | if (length(Z_indice) == 0) | |
c2028869 | 39 | next |
c2028869 | 40 | #U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr |
c3bc4705 BA |
41 | s = svd( ginv(crossprod(matricize(X[Z_indice,]))) %*% |
42 | crossprod(matricize(X[Z_indice,]),matricize(Y[Z_indice,])) ) | |
43 | S = s$d | |
c2028869 BG |
44 | #Set m-rank(r) singular values to zero, and recompose |
45 | #best rank(r) approximation of the initial product | |
c3bc4705 BA |
46 | if(rank[r] < length(S)) |
47 | S[(rank[r]+1):length(S)] = 0 | |
ef67d338 | 48 | phi[,,r] = s$u %*% diag(S) %*% t(s$v) %*% Rho[,,r] |
c2028869 | 49 | } |
ef67d338 | 50 | |
c3bc4705 BA |
51 | #Etape E et calcul de LLF |
52 | sumLogLLF2 = 0 | |
ef67d338 BA |
53 | for(i in seq_len(n)) |
54 | { | |
c3bc4705 BA |
55 | sumLLF1 = 0 |
56 | maxLogGamIR = -Inf | |
ef67d338 BA |
57 | for (r in seq_len(k)) |
58 | { | |
c3bc4705 BA |
59 | dotProduct = tcrossprod(Y[i,]%*%Rho[,,r]-X[i,]%*%phi[,,r]) |
60 | logGamIR = log(Pi[r]) + log(det(Rho[,,r])) - 0.5*dotProduct | |
61 | #Z[i] = index of max (gam[i,]) | |
ef67d338 BA |
62 | if(logGamIR > maxLogGamIR) |
63 | { | |
c3bc4705 BA |
64 | Z[i] = r |
65 | maxLogGamIR = logGamIR | |
66 | } | |
ef67d338 | 67 | sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2) |
c3bc4705 BA |
68 | } |
69 | sumLogLLF2 = sumLogLLF2 + log(sumLLF1) | |
70 | } | |
c2028869 | 71 | |
c3bc4705 | 72 | LLF = -1/n * sumLogLLF2 |
ef67d338 | 73 | |
c3bc4705 | 74 | #update distance parameter to check algorithm convergence (delta(phi, Phi)) |
ef67d338 BA |
75 | deltaPhi = c( deltaPhi, max( (abs(phi-Phi)) / (1+abs(phi)) ) ) #TODO: explain? |
76 | if (length(deltaPhi) > deltaPhiBufferSize) | |
77 | deltaPhi = deltaPhi[2:length(deltaPhi)] | |
c3bc4705 | 78 | sumDeltaPhi = sum(abs(deltaPhi)) |
ef67d338 | 79 | |
c3bc4705 BA |
80 | #update other local variables |
81 | Phi = phi | |
82 | ite = ite+1 | |
c2028869 | 83 | } |
ef67d338 | 84 | return(list("phi"=phi, "LLF"=LLF)) |
9ade3f1b | 85 | } |