| 1 | #' initialization of the EM algorithm |
| 2 | #' |
| 3 | #' @param k number of components |
| 4 | #' @param X matrix of covariates (of size n*p) |
| 5 | #' @param Y matrix of responses (of size n*m) |
| 6 | #' |
| 7 | #' @return a list with phiInit, rhoInit, piInit, gamInit |
| 8 | #' @export |
| 9 | #' @importFrom methods new |
| 10 | #' @importFrom stats cutree dist hclust runif |
| 11 | initSmallEM = function(k,X,Y, fast=TRUE) |
| 12 | { |
| 13 | n = nrow(Y) |
| 14 | m = ncol(Y) |
| 15 | p = ncol(X) |
| 16 | nIte = 20 |
| 17 | Zinit1 = array(0, dim=c(n,nIte)) |
| 18 | betaInit1 = array(0, dim=c(p,m,k,nIte)) |
| 19 | sigmaInit1 = array(0, dim = c(m,m,k,nIte)) |
| 20 | phiInit1 = array(0, dim = c(p,m,k,nIte)) |
| 21 | rhoInit1 = array(0, dim = c(m,m,k,nIte)) |
| 22 | Gam = matrix(0, n, k) |
| 23 | piInit1 = matrix(0,nIte,k) |
| 24 | gamInit1 = array(0, dim=c(n,k,nIte)) |
| 25 | LLFinit1 = list() |
| 26 | |
| 27 | #require(MASS) #Moore-Penrose generalized inverse of matrix |
| 28 | for(repet in 1:nIte) |
| 29 | { |
| 30 | distance_clus = dist(cbind(X,Y)) |
| 31 | tree_hier = hclust(distance_clus) |
| 32 | Zinit1[,repet] = cutree(tree_hier, k) |
| 33 | |
| 34 | for(r in 1:k) |
| 35 | { |
| 36 | Z = Zinit1[,repet] |
| 37 | Z_indice = seq_len(n)[Z == r] #renvoit les indices où Z==r |
| 38 | if (length(Z_indice) == 1) { |
| 39 | betaInit1[,,r,repet] = MASS::ginv(crossprod(t(X[Z_indice,]))) %*% |
| 40 | crossprod(t(X[Z_indice,]), Y[Z_indice,]) |
| 41 | } else { |
| 42 | betaInit1[,,r,repet] = MASS::ginv(crossprod(X[Z_indice,])) %*% |
| 43 | crossprod(X[Z_indice,], Y[Z_indice,]) |
| 44 | } |
| 45 | sigmaInit1[,,r,repet] = diag(m) |
| 46 | phiInit1[,,r,repet] = betaInit1[,,r,repet] #/ sigmaInit1[,,r,repet] |
| 47 | rhoInit1[,,r,repet] = solve(sigmaInit1[,,r,repet]) |
| 48 | piInit1[repet,r] = mean(Z == r) |
| 49 | } |
| 50 | |
| 51 | for(i in 1:n) |
| 52 | { |
| 53 | for(r in 1:k) |
| 54 | { |
| 55 | dotProduct = tcrossprod(Y[i,]%*%rhoInit1[,,r,repet]-X[i,]%*%phiInit1[,,r,repet]) |
| 56 | Gam[i,r] = piInit1[repet,r]*det(rhoInit1[,,r,repet])*exp(-0.5*dotProduct) |
| 57 | } |
| 58 | sumGamI = sum(Gam[i,]) |
| 59 | gamInit1[i,,repet]= Gam[i,] / sumGamI |
| 60 | } |
| 61 | |
| 62 | miniInit = 10 |
| 63 | maxiInit = 11 |
| 64 | |
| 65 | init_EMG = EMGLLF(phiInit1[,,,repet], rhoInit1[,,,repet], piInit1[repet,], |
| 66 | gamInit1[,,repet], miniInit, maxiInit, gamma=1, lambda=0, X, Y, eps=1e-4, fast) |
| 67 | LLFEessai = init_EMG$LLF |
| 68 | LLFinit1[repet] = LLFEessai[length(LLFEessai)] |
| 69 | } |
| 70 | b = which.min(LLFinit1) |
| 71 | phiInit = phiInit1[,,,b] |
| 72 | rhoInit = rhoInit1[,,,b] |
| 73 | piInit = piInit1[b,] |
| 74 | gamInit = gamInit1[,,b] |
| 75 | |
| 76 | return (list(phiInit=phiInit, rhoInit=rhoInit, piInit=piInit, gamInit=gamInit)) |
| 77 | } |