test/generate_test_data/EMGrank.R

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