R/initSmallEM.R

   1 #' initialization of the EM algorithm
   2 #'
   3 #' @param k number of components
   4 #' @param X matrix of covariates (of size n*p)
   5 #' @param Y matrix of responses (of size n*m)
   6 #' @param tau threshold to stop EM algorithm
   7 #'
   8 #' @return a list with phiInit, rhoInit, piInit, gamInit
   9 #' @export
  10 initSmallEM = function(k,X,Y,tau)
  11 {
  12     n = nrow(Y)
  13     m = ncol(Y)
  14     p = ncol(X)
  15
  16     Zinit1 = array(0, dim=c(n,20))
  17     betaInit1 = array(0, dim=c(p,m,k,20))
  18     sigmaInit1 = array(0, dim = c(m,m,k,20))
  19     phiInit1 = array(0, dim = c(p,m,k,20))
  20     rhoInit1 = array(0, dim = c(m,m,k,20))
  21     Gam = matrix(0, n, k)
  22     piInit1 = matrix(0,20,k)
  23     gamInit1 = array(0, dim=c(n,k,20))
  24     LLFinit1 = list()
  25
  26     require(MASS) #Moore-Penrose generalized inverse of matrix
  27     for(repet in 1:20)
  28     {
  29       distance_clus = dist(X)
  30       tree_hier = hclust(distance_clus)
  31       Zinit1[,repet] = cutree(tree_hier, k)
  32
  33         for(r in 1:k)
  34         {
  35             Z = Zinit1[,repet]
  36             Z_indice = seq_len(n)[Z == r] #renvoit les indices où Z==r
  37
  38             betaInit1[,,r,repet] = ginv(crossprod(X[Z_indice,])) %*%
  39                 crossprod(X[Z_indice,], Y[Z_indice,])
  40             sigmaInit1[,,r,repet] = diag(m)
  41             phiInit1[,,r,repet] = betaInit1[,,r,repet] #/ sigmaInit1[,,r,repet]
  42             rhoInit1[,,r,repet] = solve(sigmaInit1[,,r,repet])
  43             piInit1[repet,r] = mean(Z == r)
  44         }
  45
  46         for(i in 1:n)
  47         {
  48             for(r in 1:k)
  49             {
  50                 dotProduct = tcrossprod(Y[i,]%*%rhoInit1[,,r,repet]-X[i,]%*%phiInit1[,,r,repet])
  51                 Gam[i,r] = piInit1[repet,r]*det(rhoInit1[,,r,repet])*exp(-0.5*dotProduct)
  52             }
  53             sumGamI = sum(Gam[i,])
  54             gamInit1[i,,repet]= Gam[i,] / sumGamI
  55         }
  56
  57         miniInit = 10
  58         maxiInit = 11
  59
  60         new_EMG = .Call("EMGLLF_core",phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],
  61             gamInit1[,,repet],miniInit,maxiInit,1,0,X,Y,tau)
  62         LLFEessai = new_EMG$LLF
  63         LLFinit1[repet] = LLFEessai[length(LLFEessai)]
  64     }
  65
  66     b = which.max(LLFinit1)
  67     phiInit = phiInit1[,,,b]
  68     rhoInit = rhoInit1[,,,b]
  69     piInit = piInit1[b,]
  70     gamInit = gamInit1[,,b]
  71
  72     return (list(phiInit=phiInit, rhoInit=rhoInit, piInit=piInit, gamInit=gamInit))
  73 }