#' EMGLLF
#'
-#' Description de EMGLLF
+#' Run a generalized EM algorithm developped for mixture of Gaussian regression
+#' models with variable selection by an extension of the Lasso estimator (regularization parameter lambda).
+#' Reparametrization is done to ensure invariance by homothetic transformation.
+#' It returns a collection of models, varying the number of clusters and the sparsity in the regression mean.
#'
#' @param phiInit an initialization for phi
#' @param rhoInit an initialization for rho
#' @param Y matrix of responses (of size n*m)
#' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4
#'
-#' @return A list ... phi,rho,pi,LLF,S,affec:
-#' phi : parametre de moyenne renormalisé, calculé par l'EM
-#' rho : parametre de variance renormalisé, calculé par l'EM
-#' pi : parametre des proportions renormalisé, calculé par l'EM
-#' LLF : log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
-#' S : ...
-#' affec : ...
+#' @return A list (corresponding to the model collection) defined by (phi,rho,pi,LLF,S,affec):
+#' phi : regression mean for each cluster
+#' rho : variance (homothetic) for each cluster
+#' pi : proportion for each cluster
+#' LLF : log likelihood with respect to the training set
+#' S : selected variables indexes
+#' affec : cluster affectation for each observation (of the training set)
#'
#' @export
EMGLLF <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,