#' 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) #' #' @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) { n = nrow(Y) m = ncol(Y) p = ncol(X) nIte = 20 Zinit1 = array(0, dim=c(n,nIte)) betaInit1 = array(0, dim=c(p,m,k,nIte)) sigmaInit1 = array(0, dim = c(m,m,k,nIte)) phiInit1 = array(0, dim = c(p,m,k,nIte)) rhoInit1 = array(0, dim = c(m,m,k,nIte)) Gam = matrix(0, n, k) 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,]))) %*% crossprod(t(X[Z_indice,]), Y[Z_indice,]) } else { betaInit1[,,r,repet] = MASS::ginv(crossprod(X[Z_indice,])) %*% crossprod(X[Z_indice,], Y[Z_indice,]) } sigmaInit1[,,r,repet] = diag(m) phiInit1[,,r,repet] = betaInit1[,,r,repet] #/ sigmaInit1[,,r,repet] 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) } sumGamI = sum(Gam[i,]) 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-4, fast) LLFEessai = init_EMG$LLF LLFinit1[repet] = LLFEessai[length(LLFEessai)] } 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)) }