-#' initialization of the EM algorithm
+#' initSmallEM
+#'
+#' 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 fast boolean to enable or not the C function call
+#'
+#' @return a list with phiInit (the regression parameter reparametrized),
+#' rhoInit (the covariance parameter reparametrized), piInit (the proportion parameter is the
+#' mixture model), gamInit (the conditional expectation)
#'
-#' @return a list with phiInit, rhoInit, piInit, gamInit
-#' @export
-#' @importFrom methods new
#' @importFrom stats cutree dist hclust runif
-initSmallEM <- function(k, X, Y, fast = TRUE)
+#'
+#' @export
+initSmallEM <- function(k, X, Y, fast)
{
- n <- nrow(Y)
- m <- ncol(Y)
+ n <- nrow(X)
p <- ncol(X)
+ m <- ncol(Y)
nIte <- 20
Zinit1 <- array(0, dim = c(n, nIte))
betaInit1 <- array(0, dim = c(p, m, k, nIte))
piInit1 <- matrix(0, nIte, k)
gamInit1 <- array(0, dim = c(n, k, nIte))
LLFinit1 <- list()
-
+
# require(MASS) #Moore-Penrose generalized inverse of matrix
for (repet in 1:nIte)
{
distance_clus <- dist(cbind(X, Y))
tree_hier <- hclust(distance_clus)
Zinit1[, repet] <- cutree(tree_hier, k)
-
+
for (r in 1:k)
{
Z <- Zinit1[, repet]
- Z_indice <- seq_len(n)[Z == r] #renvoit les indices où Z==r
- if (length(Z_indice) == 1)
- {
- betaInit1[, , r, repet] <- MASS::ginv(crossprod(t(X[Z_indice, ]))) %*%
+ Z_indice <- seq_len(n)[Z == r] #renvoit les indices ou Z==r
+ if (length(Z_indice) == 1) {
+ betaInit1[, , r, repet] <- MASS::ginv(crossprod(t(X[Z_indice, ]))) %*%
crossprod(t(X[Z_indice, ]), Y[Z_indice, ])
- } else
- {
- betaInit1[, , r, repet] <- MASS::ginv(crossprod(X[Z_indice, ])) %*%
+ } else {
+ betaInit1[, , r, repet] <- MASS::ginv(crossprod(X[Z_indice, ])) %*%
crossprod(X[Z_indice, ], Y[Z_indice, ])
}
sigmaInit1[, , r, repet] <- diag(m)
rhoInit1[, , r, repet] <- solve(sigmaInit1[, , r, repet])
piInit1[repet, r] <- mean(Z == r)
}
-
+
for (i in 1:n)
{
for (r in 1:k)
{
- dotProduct <- tcrossprod(Y[i, ] %*% rhoInit1[, , r, repet] - X[i,
- ] %*% phiInit1[, , r, repet])
- Gam[i, r] <- piInit1[repet, r] * det(rhoInit1[, , r, repet]) * exp(-0.5 *
- dotProduct)
+ dotProduct <- tcrossprod(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, ])
+ # TODO: next line is a division by zero if dotProduct is big
gamInit1[i, , repet] <- Gam[i, ]/sumGamI
}
-
+
miniInit <- 10
maxiInit <- 11
-
- init_EMG <- EMGLLF(phiInit1[, , , repet], rhoInit1[, , , repet], piInit1[repet,
- ], gamInit1[, , repet], miniInit, maxiInit, gamma = 1, lambda = 0, X,
- Y, eps = 1e-04, fast)
- LLFEessai <- init_EMG$LLF
- LLFinit1[repet] <- LLFEessai[length(LLFEessai)]
+
+ init_EMG <- EMGLLF(phiInit1[, , , repet], rhoInit1[, , , repet], piInit1[repet, ],
+ gamInit1[, , repet], miniInit, maxiInit, gamma = 1, lambda = 0, X, Y,
+ eps = 1e-04, fast)
+ LLFinit1[[repet]] <- init_EMG$llh
}
b <- which.min(LLFinit1)
phiInit <- phiInit1[, , , b]
rhoInit <- rhoInit1[, , , b]
piInit <- piInit1[b, ]
gamInit <- gamInit1[, , b]
-
- return(list(phiInit = phiInit, rhoInit = rhoInit, piInit = piInit, gamInit = gamInit))
+
+ list(phiInit = phiInit, rhoInit = rhoInit, piInit = piInit, gamInit = gamInit)
}