pkg/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, fast = TRUE)
  12 {
  13   n <- nrow(Y)
  14   m <- ncol(Y)
  15   p <- ncol(X)
  16   nIte <- 20
  17   Zinit1 <- array(0, dim = c(n, nIte))
  18   betaInit1 <- array(0, dim = c(p, m, k, nIte))
  19   sigmaInit1 <- array(0, dim = c(m, m, k, nIte))
  20   phiInit1 <- array(0, dim = c(p, m, k, nIte))
  21   rhoInit1 <- array(0, dim = c(m, m, k, nIte))
  22   Gam <- matrix(0, n, k)
  23   piInit1 <- matrix(0, nIte, k)
  24   gamInit1 <- array(0, dim = c(n, k, nIte))
  25   LLFinit1 <- list()
  26
  27   # require(MASS) #Moore-Penrose generalized inverse of matrix
  28   for (repet in 1:nIte)
  29   {
  30     distance_clus <- dist(cbind(X, Y))
  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] <- MASS::ginv(crossprod(t(X[Z_indice, ]))) %*%
  40           crossprod(t(X[Z_indice, ]), Y[Z_indice, ])
  41       } else {
  42         betaInit1[, , r, repet] <- MASS::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]
  56           - X[i, ] %*% phiInit1[, , r, repet])
  57         Gam[i, r] <- piInit1[repet, r]
  58           * det(rhoInit1[, , r, repet]) * exp(-0.5 * dotProduct)
  59       }
  60       sumGamI <- sum(Gam[i, ])
  61       gamInit1[i, , repet] <- Gam[i, ]/sumGamI
  62     }
  63
  64     miniInit <- 10
  65     maxiInit <- 11
  66
  67     init_EMG <- EMGLLF(phiInit1[, , , repet], rhoInit1[, , , repet], piInit1[repet, ],
  68       gamInit1[, , repet], miniInit, maxiInit, gamma = 1, lambda = 0, X, Y,
  69       eps = 1e-04, fast)
  70     LLFEessai <- init_EMG$LLF
  71     LLFinit1[repet] <- LLFEessai[length(LLFEessai)]
  72   }
  73   b <- which.min(LLFinit1)
  74   phiInit <- phiInit1[, , , b]
  75   rhoInit <- rhoInit1[, , , b]
  76   piInit <- piInit1[b, ]
  77   gamInit <- gamInit1[, , b]
  78
  79   return(list(phiInit = phiInit, rhoInit = rhoInit, piInit = piInit, gamInit = gamInit))
  80 }