-#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]
- m = dim(Rho)[2]
- k = dim(Rho)[3]
-
- #init outputs
- phi = array(0, dim=c(p,m,k))
- Z = rep(1, n)
- LLF = 0
-
- #local variables
- Phi = array(0, dim=c(p,m,k))
- deltaPhi = c()
- sumDeltaPhi = 0.
- deltaPhiBufferSize = 20
-
- #main loop
- ite = 1
- while (ite<=mini || (ite<=maxi && sumDeltaPhi>tau))
- {
- #M step: Mise à jour de Beta (et donc phi)
- 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
- s = svd( ginv(crossprod(matricize(X[Z_indice,]))) %*%
- crossprod(matricize(X[Z_indice,]),matricize(Y[Z_indice,])) )
- S = s$d
- #Set m-rank(r) singular values to zero, and recompose
- #best rank(r) approximation of the initial product
- if(rank[r] < length(S))
- S[(rank[r]+1):length(S)] = 0
- phi[,,r] = s$u %*% diag(S) %*% t(s$v) %*% Rho[,,r]
- }
-
- #Etape E et calcul de LLF
- sumLogLLF2 = 0
- for(i in seq_len(n))
- {
- sumLLF1 = 0
- maxLogGamIR = -Inf
- 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)
- {
- 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( (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))
-}