}
require(MASS)
-EMGrank = function(Pi, Rho, mini, maxi, X, Y, tau, rank){
+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
LLF = 0
#local variables
Phi = array(0, dim=c(p,m,k))
- deltaPhi = c(0)
- sumDeltaPhi = 0
+ deltaPhi = c()
+ sumDeltaPhi = 0.
deltaPhiBufferSize = 20
#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)
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$v
#Set m-rank(r) singular values to zero, and recompose
#best rank(r) approximation of the initial product
if(rank[r] < length(S))
S[(rank[r]+1):length(S)] = 0
- phi[,,r] = U %*% diag(S) %*% t(V) %*% Rho[,,r]
+ phi[,,r] = s$u %*% diag(S) %*% t(s$v) %*% Rho[,,r]
}
-
+
#Etape E et calcul de LLF
sumLogLLF2 = 0
- for(i in 1:n){
+ for(i in seq_len(n))
+ {
sumLLF1 = 0
maxLogGamIR = -Inf
- for(r in 1:k){
+ for (r in seq_len(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){
+ if(logGamIR > maxLogGamIR)
+ {
Z[i] = r
maxLogGamIR = logGamIR
}
- sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2)
+ 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){
- l_1 = c(2:length(deltaPhi))
- deltaPhi = deltaPhi[l_1]
- }
+ deltaPhi = c( deltaPhi, max( (abs(phi-Phi)) / (1+abs(phi)) ) ) #TODO: explain?
+ if (length(deltaPhi) > deltaPhiBufferSize)
+ deltaPhi = deltaPhi[2:length(deltaPhi)]
sumDeltaPhi = sum(abs(deltaPhi))
-
+
#update other local variables
Phi = phi
ite = ite+1
}
- return(list(phi=phi, LLF=LLF))
+ return(list("phi"=phi, "LLF"=LLF))
}