pkg/R/initSmallEM.R

   1 #' initSmallEM
   2 #'
   3 #' initialization of the EM algorithm
   4 #'
   5 #' @param k number of components
   6 #' @param X matrix of covariates (of size n*p)
   7 #' @param Y matrix of responses (of size n*m)
   8 #' @param fast boolean to enable or not the C function call
   9 #'
  10 #' @return a list with phiInit, rhoInit, piInit, gamInit
  11 #'
  12 #' @importFrom stats cutree dist hclust runif
  13 #'
  14 #' @export
  15 initSmallEM <- function(k, X, Y, fast)
  16 {
  17   n <- nrow(X)
  18   p <- ncol(X)
  19   m <- ncol(Y)
  20   nIte <- 20
  21   Zinit1 <- array(0, dim = c(n, nIte))
  22   betaInit1 <- array(0, dim = c(p, m, k, nIte))
  23   sigmaInit1 <- array(0, dim = c(m, m, k, nIte))
  24   phiInit1 <- array(0, dim = c(p, m, k, nIte))
  25   rhoInit1 <- array(0, dim = c(m, m, k, nIte))
  26   Gam <- matrix(0, n, k)
  27   piInit1 <- matrix(0, nIte, k)
  28   gamInit1 <- array(0, dim = c(n, k, nIte))
  29   LLFinit1 <- list()
  30
  31   # require(MASS) #Moore-Penrose generalized inverse of matrix
  32   for (repet in 1:nIte)
  33   {
  34     distance_clus <- dist(cbind(X, Y))
  35     tree_hier <- hclust(distance_clus)
  36     Zinit1[, repet] <- cutree(tree_hier, k)
  37
  38     for (r in 1:k)
  39     {
  40       Z <- Zinit1[, repet]
  41       Z_indice <- seq_len(n)[Z == r]  #renvoit les indices ou Z==r
  42       if (length(Z_indice) == 1) {
  43         betaInit1[, , r, repet] <- MASS::ginv(crossprod(t(X[Z_indice, ]))) %*%
  44           crossprod(t(X[Z_indice, ]), Y[Z_indice, ])
  45       } else {
  46         betaInit1[, , r, repet] <- MASS::ginv(crossprod(X[Z_indice, ])) %*%
  47           crossprod(X[Z_indice, ], Y[Z_indice, ])
  48       }
  49       sigmaInit1[, , r, repet] <- diag(m)
  50       phiInit1[, , r, repet] <- betaInit1[, , r, repet]  #/ sigmaInit1[,,r,repet]
  51       rhoInit1[, , r, repet] <- solve(sigmaInit1[, , r, repet])
  52       piInit1[repet, r] <- mean(Z == r)
  53     }
  54
  55     for (i in 1:n)
  56     {
  57       for (r in 1:k)
  58       {
  59         dotProduct <- tcrossprod(Y[i, ] %*% rhoInit1[, , r, repet]
  60           - X[i, ] %*% phiInit1[, , r, repet])
  61         Gam[i, r] <- piInit1[repet, r] *
  62           det(rhoInit1[, , r, repet]) * exp(-0.5 * dotProduct)
  63       }
  64       sumGamI <- sum(Gam[i, ])
  65       # TODO: next line is a division by zero if dotProduct is big
  66       gamInit1[i, , repet] <- Gam[i, ]/sumGamI
  67     }
  68
  69     miniInit <- 10
  70     maxiInit <- 11
  71
  72     init_EMG <- EMGLLF(phiInit1[, , , repet], rhoInit1[, , , repet], piInit1[repet, ],
  73       gamInit1[, , repet], miniInit, maxiInit, gamma = 1, lambda = 0, X, Y,
  74       eps = 1e-04, fast)
  75     LLFinit1[[repet]] <- init_EMG$llh
  76   }
  77   b <- which.min(LLFinit1)
  78   phiInit <- phiInit1[, , , b]
  79   rhoInit <- rhoInit1[, , , b]
  80   piInit <- piInit1[b, ]
  81   gamInit <- gamInit1[, , b]
  82
  83   list(phiInit = phiInit, rhoInit = rhoInit, piInit = piInit, gamInit = gamInit)
  84 }