-library(MASS) #generalized inverse of matrix Monroe-Penrose
-
-vec_bin = function(X,r){
- Z = c()
- indice = c()
- j=1
- for(i in 1:length(X)){
- if(X[i] == r){
- Z[i] = 1
- indice[j] = i
- j=j+1
- }
- else{
- Z[i] = 0
- }
- }
- return(list(Z,indice))
-}
+#' 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 tau threshold to stop EM algorithm
+#'
+#' @return a list with phiInit, rhoInit, piInit, gamInit
+#' @export
+initSmallEM = function(k,X,Y,tau)
+{
+ n = nrow(Y)
+ m = ncol(Y)
+ p = ncol(X)
+
+ Zinit1 = array(0, dim=c(n,20))
+ betaInit1 = array(0, dim=c(p,m,k,20))
+ sigmaInit1 = array(0, dim = c(m,m,k,20))
+ phiInit1 = array(0, dim = c(p,m,k,20))
+ rhoInit1 = array(0, dim = c(m,m,k,20))
+ Gam = matrix(0, n, k)
+ piInit1 = matrix(0,20,k)
+ gamInit1 = array(0, dim=c(n,k,20))
+ LLFinit1 = list()
-initSmallEM = function(k,X,Y,tau){
- n = nrow(Y)
- m = ncol(Y)
- p = ncol(X)
+ require(MASS) #Moore-Penrose generalized inverse of matrix
+ for(repet in 1:20)
+ {
+ distance_clus = dist(X)
+ tree_hier = hclust(distance_clus)
+ Zinit1[,repet] = cutree(tree_hier, k)
- betaInit1 = array(0, dim=c(p,m,k,20))
- sigmaInit1 = array(0, dim = c(m,m,k,20))
- phiInit1 = array(0, dim = c(p,m,k,20))
- rhoInit1 = array(0, dim = c(m,m,k,20))
- piInit1 = matrix(0,20,k)
- gamInit1 = array(0, dim=c(n,k,20))
- LLFinit1 = list()
-
-
- for(repet in 1:20){
- clusters = hclust(dist(y)) #default distance : euclidean
- clusterCut = cutree(clusters,k)
- Zinit1[,repet] = clusterCut #retourne les indices (à quel cluster indiv_i appartient) d'un clustering hierarchique (nb de cluster = k)
-
- for(r in 1:k){
- Z = Zinit1[,repet]
- Z_bin = vec_bin(Z,r)
- Z_vec = Z_bin[[1]] #vecteur 0 et 1 aux endroits où Z==r
- Z_indice = Z_bin[[2]] #renvoit les indices où Z==r
-
- betaInit1[,,r,repet] = ginv(t(x[Z_indice,])%*%x[Z_indice,])%*%t(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] = sum(Z_vec)/n
- }
-
- for(i in 1:n){
- for(r in 1:k){
- dotProduct = (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet]) %*% (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
-
- new_EMG = EMGLLF(phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],gamInit1[,,repet],miniInit,maxiInit,1,0,x,y,tau)
- ##.C("EMGLLF", phiInit = phiInit, rhoInit = rhoInit, ...)
- LLFEessai = new_EMG[[4]]
- LLFinit1[[repet]] = LLFEessai[[length(LLFEessai)]]
- }
-
- b = which.max(LLFinit1)
-
- phiInit = phiInit1[,,,b]
- rhoInit = rhoInit1[,,,b]
- piInit = piInit1[b,]
- gamInit = gamInit1[,,b]
-
- return(list(phiInit, rhoInit, piInit, gamInit))
-}
+ for(r in 1:k)
+ {
+ Z = Zinit1[,repet]
+ Z_indice = seq_len(n)[Z == r] #renvoit les indices où Z==r
+
+ betaInit1[,,r,repet] = 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
+
+ new_EMG = .Call("EMGLLF_core",phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],
+ gamInit1[,,repet],miniInit,maxiInit,1,0,X,Y,tau)
+ LLFEessai = new_EMG$LLF
+ LLFinit1[repet] = LLFEessai[length(LLFEessai)]
+ }
+ b = which.max(LLFinit1)
+ phiInit = phiInit1[,,,b]
+ rhoInit = rhoInit1[,,,b]
+ piInit = piInit1[b,]
+ gamInit = gamInit1[,,b]
+ return (list(phiInit=phiInit, rhoInit=rhoInit, piInit=piInit, gamInit=gamInit))
+}