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[valse.git] / R / initSmallEM.R

#' initialization of the EM algorithm
#'
#' @param k number of components
#' @param X matrix of covariates (of size n*p)
#' @param Y matrix of responses (of size n*m)
#' @param tau threshold to stop EM algorithm
#'
#' @return a list with phiInit, rhoInit, piInit, gamInit
#' @export
initSmallEM = function(k,X,Y,tau)
{
  n = nrow(Y)
  m = ncol(Y)
  p = ncol(X)
  
  betaInit1 = array(0, dim=c(p,m,k,20))
  sigmaInit1 = array(0, dim = c(m,m,k,20))
  phiInit1 = array(0, dim = c(p,m,k,20))
  rhoInit1 = array(0, dim = c(m,m,k,20))
  piInit1 = matrix(0,20,k)
  gamInit1 = array(0, dim=c(n,k,20))
  LLFinit1 = list()
  
  require(MASS) #Moore-Penrose generalized inverse of matrix
  for(repet in 1:20)
  {
    clusters = hclust(dist(y)) #default distance : euclidean
    #cutree retourne les indices (? quel cluster indiv_i appartient) d'un clustering hierarchique
    clusterCut = cutree(clusters,k)
    Zinit1[,repet] = clusterCut
    
    for(r in 1:k)
    {
      Z = Zinit1[,repet]
      Z_bin = vec_bin(Z,r)
      Z_vec = Z_bin$Z #vecteur 0 et 1 aux endroits o? Z==r
      Z_indice = Z_bin$indice #renvoit les indices o? Z==r
      
      betaInit1[,,r,repet] =
        ginv(t(x[Z_indice,])%*%x[Z_indice,])%*%t(x[Z_indice,])%*%y[Z_indice,]
      sigmaInit1[,,r,repet] = diag(m)
      phiInit1[,,r,repet] = betaInit1[,,r,repet]/sigmaInit1[,,r,repet]
      rhoInit1[,,r,repet] = solve(sigmaInit1[,,r,repet])
      piInit1[repet,r] = sum(Z_vec)/n
    }
    
    for(i in 1:n)
    {
      for(r in 1:k)
      {
        dotProduct = (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet]) %*%
          (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet])
        Gam[i,r] = piInit1[repet,r]*det(rhoInit1[,,r,repet])*exp(-0.5*dotProduct)
      }
      sumGamI = sum(gam[i,])
      gamInit1[i,,repet]= Gam[i,] / sumGamI
    }
    
    miniInit = 10
    maxiInit = 11
    
    new_EMG = .Call("EMGLLF",phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],
                    gamInit1[,,repet],miniInit,maxiInit,1,0,x,y,tau)
    LLFEessai = new_EMG$LLF
    LLFinit1[repet] = LLFEessai[length(LLFEessai)]
  }
  
  b = which.max(LLFinit1)
  phiInit = phiInit1[,,,b]
  rhoInit = rhoInit1[,,,b]
  piInit = piInit1[b,]
  gamInit = gamInit1[,,b]
  
  return (list(phiInit=phiInit, rhoInit=rhoInit, piInit=piInit, gamInit=gamInit))
}