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 #'
   7 #' @return a list with phiInit, rhoInit, piInit, gamInit
   8 #' @export
   9 #' @importFrom methods new
  10 #' @importFrom stats cutree dist hclust runif
  11 initSmallEM = function(k,X,Y)
  12 {
  13     n = nrow(Y)
  14     m = ncol(Y)
  15     p = ncol(X)
  16
  17     Zinit1 = array(0, dim=c(n,20))
  18     betaInit1 = array(0, dim=c(p,m,k,20))
  19     sigmaInit1 = array(0, dim = c(m,m,k,20))
  20     phiInit1 = array(0, dim = c(p,m,k,20))
  21     rhoInit1 = array(0, dim = c(m,m,k,20))
  22     Gam = matrix(0, n, k)
  23     piInit1 = matrix(0,20,k)
  24     gamInit1 = array(0, dim=c(n,k,20))
  25     LLFinit1 = list()
  26
  27     require(MASS) #Moore-Penrose generalized inverse of matrix
  28     for(repet in 1:20)
  29     {
  30       distance_clus = dist(X)
  31       tree_hier = hclust(distance_clus)
  32       Zinit1[,repet] = cutree(tree_hier, k)
  33
  34         for(r in 1:k)
  35         {
  36             Z = Zinit1[,repet]
  37             Z_indice = seq_len(n)[Z == r] #renvoit les indices où Z==r
  38             if (length(Z_indice) == 1) {
  39               betaInit1[,,r,repet] = ginv(crossprod(t(X[Z_indice,]))) %*%
  40                 crossprod(t(X[Z_indice,]), Y[Z_indice,])
  41             } else {
  42             betaInit1[,,r,repet] = ginv(crossprod(X[Z_indice,])) %*%
  43                 crossprod(X[Z_indice,], Y[Z_indice,])
  44             }
  45             sigmaInit1[,,r,repet] = diag(m)
  46             phiInit1[,,r,repet] = betaInit1[,,r,repet] #/ sigmaInit1[,,r,repet]
  47             rhoInit1[,,r,repet] = solve(sigmaInit1[,,r,repet])
  48             piInit1[repet,r] = mean(Z == r)
  49         }
  50
  51         for(i in 1:n)
  52         {
  53             for(r in 1:k)
  54             {
  55                 dotProduct = tcrossprod(Y[i,]%*%rhoInit1[,,r,repet]-X[i,]%*%phiInit1[,,r,repet])
  56                 Gam[i,r] = piInit1[repet,r]*det(rhoInit1[,,r,repet])*exp(-0.5*dotProduct)
  57             }
  58             sumGamI = sum(Gam[i,])
  59             gamInit1[i,,repet]= Gam[i,] / sumGamI
  60         }
  61
  62         miniInit = 10
  63         maxiInit = 11
  64
  65         new_EMG = .Call("EMGLLF_core",phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],
  66             gamInit1[,,repet],miniInit,maxiInit,1,0,X,Y,1e-4)
  67         LLFEessai = new_EMG$LLF
  68         LLFinit1[repet] = LLFEessai[length(LLFEessai)]
  69     }
  70
  71     b = which.max(LLFinit1)
  72     phiInit = phiInit1[,,,b]
  73     rhoInit = rhoInit1[,,,b]
  74     piInit = piInit1[b,]
  75     gamInit = gamInit1[,,b]
  76
  77     return (list(phiInit=phiInit, rhoInit=rhoInit, piInit=piInit, gamInit=gamInit))
  78 }