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 (the regression parameter reparametrized),
  11 #' rhoInit (the covariance parameter reparametrized), piInit (the proportion parameter is the
  12 #' mixture model), gamInit (the conditional expectation)
  13 #'
  14 #' @importFrom stats cutree dist hclust runif
  15 #'
  16 #' @export
  17 initSmallEM <- function(k, X, Y, fast)
  18 {
  19   n <- nrow(X)
  20   p <- ncol(X)
  21   m <- ncol(Y)
  22   nIte <- 20
  23   Zinit1 <- array(0, dim = c(n, nIte))
  24   betaInit1 <- array(0, dim = c(p, m, k, nIte))
  25   sigmaInit1 <- array(0, dim = c(m, m, k, nIte))
  26   phiInit1 <- array(0, dim = c(p, m, k, nIte))
  27   rhoInit1 <- array(0, dim = c(m, m, k, nIte))
  28   Gam <- matrix(0, n, k)
  29   piInit1 <- matrix(0, nIte, k)
  30   gamInit1 <- array(0, dim = c(n, k, nIte))
  31   LLFinit1 <- list()
  32
  33   # require(MASS) #Moore-Penrose generalized inverse of matrix
  34   for (repet in 1:nIte)
  35   {
  36     distance_clus <- dist(cbind(X, Y))
  37     tree_hier <- hclust(distance_clus)
  38     Zinit1[, repet] <- cutree(tree_hier, k)
  39
  40     for (r in 1:k)
  41     {
  42       Z <- Zinit1[, repet]
  43       Z_indice <- seq_len(n)[Z == r]  #renvoit les indices ou Z==r
  44       if (length(Z_indice) == 1) {
  45         betaInit1[, , r, repet] <- MASS::ginv(crossprod(t(X[Z_indice, ]))) %*%
  46           crossprod(t(X[Z_indice, ]), Y[Z_indice, ])
  47       } else {
  48         betaInit1[, , r, repet] <- MASS::ginv(crossprod(X[Z_indice, ])) %*%
  49           crossprod(X[Z_indice, ], Y[Z_indice, ])
  50       }
  51       sigmaInit1[, , r, repet] <- diag(m)
  52       phiInit1[, , r, repet] <- betaInit1[, , r, repet]  #/ sigmaInit1[,,r,repet]
  53       rhoInit1[, , r, repet] <- solve(sigmaInit1[, , r, repet])
  54       piInit1[repet, r] <- mean(Z == r)
  55     }
  56
  57     for (i in 1:n)
  58     {
  59       for (r in 1:k)
  60       {
  61         dotProduct <- tcrossprod(Y[i, ] %*% rhoInit1[, , r, repet]
  62           - X[i, ] %*% phiInit1[, , r, repet])
  63         Gam[i, r] <- piInit1[repet, r] *
  64           det(rhoInit1[, , r, repet]) * exp(-0.5 * dotProduct)
  65       }
  66       sumGamI <- sum(Gam[i, ])
  67       # TODO: next line is a division by zero if dotProduct is big
  68       gamInit1[i, , repet] <- Gam[i, ]/sumGamI
  69     }
  70
  71     miniInit <- 10
  72     maxiInit <- 11
  73
  74     init_EMG <- EMGLLF(phiInit1[, , , repet], rhoInit1[, , , repet], piInit1[repet, ],
  75       gamInit1[, , repet], miniInit, maxiInit, gamma = 1, lambda = 0, X, Y,
  76       eps = 1e-04, fast)
  77     LLFinit1[[repet]] <- init_EMG$llh
  78   }
  79   b <- which.min(LLFinit1)
  80   phiInit <- phiInit1[, , , b]
  81   rhoInit <- rhoInit1[, , , b]
  82   piInit <- piInit1[b, ]
  83   gamInit <- gamInit1[, , b]
  84
  85   list(phiInit = phiInit, rhoInit = rhoInit, piInit = piInit, gamInit = gamInit)
  86 }