test/generate_test_data/EMGrank.R

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