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   require(mclust) # K-means with selection of K
  26   for(repet in 1:20)
  27   {
  28     clusters = Mclust(matrix(c(X,Y),nrow=n),k) #default distance : euclidean
  29     Zinit1[,repet] = clusters$classification
  30
  31     for(r in 1:k)
  32     {
  33       Z = Zinit1[,repet]
  34       Z_bin = vec_bin(Z,r)
  35       Z_vec = Z_bin$Z #vecteur 0 et 1 aux endroits o? Z==r
  36       Z_indice = Z_bin$indice #renvoit les indices o? Z==r
  37
  38       betaInit1[,,r,repet] =
  39         ginv(t(x[Z_indice,])%*%x[Z_indice,])%*%t(x[Z_indice,])%*%y[Z_indice,]
  40       sigmaInit1[,,r,repet] = diag(m)
  41       phiInit1[,,r,repet] = betaInit1[,,r,repet]/sigmaInit1[,,r,repet]
  42       rhoInit1[,,r,repet] = solve(sigmaInit1[,,r,repet])
  43       piInit1[repet,r] = sum(Z_vec)/n
  44     }
  45
  46     for(i in 1:n)
  47     {
  48       for(r in 1:k)
  49       {
  50         dotProduct = (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet]) %*%
  51           (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet])
  52         Gam[i,r] = piInit1[repet,r]*det(rhoInit1[,,r,repet])*exp(-0.5*dotProduct)
  53       }
  54       sumGamI = sum(gam[i,])
  55       gamInit1[i,,repet]= Gam[i,] / sumGamI
  56     }
  57
  58     miniInit = 10
  59     maxiInit = 11
  60
  61     new_EMG = .Call("EMGLLF",phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],
  62                     gamInit1[,,repet],miniInit,maxiInit,1,0,x,y,tau)
  63     LLFEessai = new_EMG$LLF
  64     LLFinit1[repet] = LLFEessai[length(LLFEessai)]
  65   }
  66
  67   b = which.max(LLFinit1)
  68   phiInit = phiInit1[,,,b]
  69   rhoInit = rhoInit1[,,,b]
  70   piInit = piInit1[b,]
  71   gamInit = gamInit1[,,b]
  72
  73   return (list(phiInit=phiInit, rhoInit=rhoInit, piInit=piInit, gamInit=gamInit))
  74 }