-EMGLLF = function(Pi, Rho, mini, maxi, X, Y, tau, rank){
+#helper to always have matrices as arg (TODO: put this elsewhere? improve?)
+matricize <- function(X)
+{
+ if (!is.matrix(X))
+ return (t(as.matrix(X)))
+ return (X)
+}
+
+require(MASS)
+EMGrank = function(Pi, Rho, mini, maxi, X, Y, tau, rank){
#matrix dimensions
n = dim(X)[1]
p = dim(X)[2]
#init outputs
phi = array(0, dim=c(p,m,k))
Z = rep(1, n)
- Pi = piInit
+# Pi = piInit
LLF = 0
#local variables
#main loop
ite = 1
- while(ite<=mini || (ite<=maxi && sumDeltaPhi>tau)){
+ while(ite<=mini || (ite<=maxi && sumDeltaPhi>tau))
+ {
#M step: Mise à jour de Beta (et donc phi)
- for(r in 1:k){
- Z_bin = vec_bin(Z,r)
- Z_vec = Z_bin$vec #vecteur 0 et 1 aux endroits o? Z==r
- Z_indice = Z_bin$indice
- if(sum(Z_indice) == 0){
+ for(r in 1:k)
+ {
+ Z_indice = seq_len(n)[Z==r] #indices où Z == r
+ if (length(Z_indice) == 0)
next
- }
#U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
- [U,S,V] = svd(ginv(crossprod(X[Z_indice,]))%*% (X[Z_indice,])%*%Y[Z_indice,] )
+ s = svd( ginv(crossprod(matricize(X[Z_indice,]))) %*%
+ crossprod(matricize(X[Z_indice,]),matricize(Y[Z_indice,])) )
+ S = s$d
+ U = s$u
+ V = s$v
#Set m-rank(r) singular values to zero, and recompose
#best rank(r) approximation of the initial product
- S[rank(r)+1:end,] = 0
- phi[,,r] = U %*%S%*%t(V)%*%Rho[,,r]
+ if(rank[r] < length(S))
+ S[(rank[r]+1):length(S)] = 0
+ phi[,,r] = U %*% diag(S) %*% t(V) %*% Rho[,,r]
}
- #Etape E et calcul de LLF
- sumLogLLF2 = 0
- for(i in 1:n){
- sumLLF1 = 0
- maxLogGamIR = -Inf
- for(r in 1:k){
- dotProduct = tcrossprod(Y[i,]%*%Rho[,,r]-X[i,]%*%phi[,,r])
- logGamIR = log(Pi[r]) + log(det(Rho[,,r])) - 0.5*dotProduct
- #Z[i] = index of max (gam[i,])
- if(logGamIR > maxLogGamIR){
- Z[i] = r
- maxLogGamIR = logGamIR
- }
- sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2)
- }
- sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
- }
+ #Etape E et calcul de LLF
+ sumLogLLF2 = 0
+ for(i in 1:n){
+ sumLLF1 = 0
+ maxLogGamIR = -Inf
+ for(r in 1:k){
+ dotProduct = tcrossprod(Y[i,]%*%Rho[,,r]-X[i,]%*%phi[,,r])
+ logGamIR = log(Pi[r]) + log(det(Rho[,,r])) - 0.5*dotProduct
+ #Z[i] = index of max (gam[i,])
+ if(logGamIR > maxLogGamIR){
+ Z[i] = r
+ maxLogGamIR = logGamIR
+ }
+ sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2)
+ }
+ sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
+ }
- LLF = -1/n * sumLogLLF2
-
- #update distance parameter to check algorithm convergence (delta(phi, Phi))
- deltaPhi = c(deltaPhi, max(max(max((abs(phi-Phi))/(1+abs(phi))))) )
- if(length(deltaPhi) > deltaPhiBufferSize){
- deltaPhi = deltaPhi[2:length(deltaPhi)]
- }
- sumDeltaPhi = sum(abs(deltaPhi))
+ LLF = -1/n * sumLogLLF2
- #update other local variables
- Phi = phi
- ite = ite+1
+ #update distance parameter to check algorithm convergence (delta(phi, Phi))
+ deltaPhi = c(deltaPhi, max(max(max((abs(phi-Phi))/(1+abs(phi))))) )
+ if(length(deltaPhi) > deltaPhiBufferSize){
+ l_1 = c(2:length(deltaPhi))
+ deltaPhi = deltaPhi[l_1]
+ }
+ sumDeltaPhi = sum(abs(deltaPhi))
+ #update other local variables
+ Phi = phi
+ ite = ite+1
}
return(list(phi=phi, LLF=LLF))
-}
\ No newline at end of file
+}