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