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   betaInit1 = array(0, dim=c(p,m,k,20))
  17   sigmaInit1 = array(0, dim = c(m,m,k,20))
  18   phiInit1 = array(0, dim = c(p,m,k,20))
  19   rhoInit1 = array(0, dim = c(m,m,k,20))
  20   piInit1 = matrix(0,20,k)
  21   gamInit1 = array(0, dim=c(n,k,20))
  22   LLFinit1 = list()
  23
  24   require(MASS) #Moore-Penrose generalized inverse of matrix
  25   for(repet in 1:20)
  26   {
  27     clusters = hclust(dist(y)) #default distance : euclidean
  28     #cutree retourne les indices (? quel cluster indiv_i appartient) d'un clustering hierarchique
  29     clusterCut = cutree(clusters,k)
  30     Zinit1[,repet] = clusterCut
  31
  32     for(r in 1:k)
  33     {
  34       Z = Zinit1[,repet]
  35       Z_bin = vec_bin(Z,r)
  36       Z_vec = Z_bin$Z #vecteur 0 et 1 aux endroits o? Z==r
  37       Z_indice = Z_bin$indice #renvoit les indices o? Z==r
  38
  39       betaInit1[,,r,repet] =
  40         ginv(t(x[Z_indice,])%*%x[Z_indice,])%*%t(x[Z_indice,])%*%y[Z_indice,]
  41       sigmaInit1[,,r,repet] = diag(m)
  42       phiInit1[,,r,repet] = betaInit1[,,r,repet]/sigmaInit1[,,r,repet]
  43       rhoInit1[,,r,repet] = solve(sigmaInit1[,,r,repet])
  44       piInit1[repet,r] = sum(Z_vec)/n
  45     }
  46
  47     for(i in 1:n)
  48     {
  49       for(r in 1:k)
  50       {
  51         dotProduct = (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet]) %*%
  52           (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet])
  53         Gam[i,r] = piInit1[repet,r]*det(rhoInit1[,,r,repet])*exp(-0.5*dotProduct)
  54       }
  55       sumGamI = sum(gam[i,])
  56       gamInit1[i,,repet]= Gam[i,] / sumGamI
  57     }
  58
  59     miniInit = 10
  60     maxiInit = 11
  61
  62     new_EMG = .Call("EMGLLF",phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],
  63                     gamInit1[,,repet],miniInit,maxiInit,1,0,x,y,tau)
  64     LLFEessai = new_EMG$LLF
  65     LLFinit1[repet] = LLFEessai[length(LLFEessai)]
  66   }
  67
  68   b = which.max(LLFinit1)
  69   phiInit = phiInit1[,,,b]
  70   rhoInit = rhoInit1[,,,b]
  71   piInit = piInit1[b,]
  72   gamInit = gamInit1[,,b]
  73
  74   return (list(phiInit=phiInit, rhoInit=rhoInit, piInit=piInit, gamInit=gamInit))
  75 }