fafa2c464ce5a16a87760e9d67374e9a23278cf7
[valse.git] / pkg / R / initSmallEM.R
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 {
40 betaInit1[, , r, repet] <- MASS::ginv(crossprod(t(X[Z_indice, ]))) %*%
41 crossprod(t(X[Z_indice, ]), Y[Z_indice, ])
42 } else
43 {
44 betaInit1[, , r, repet] <- MASS::ginv(crossprod(X[Z_indice, ])) %*%
45 crossprod(X[Z_indice, ], Y[Z_indice, ])
46 }
47 sigmaInit1[, , r, repet] <- diag(m)
48 phiInit1[, , r, repet] <- betaInit1[, , r, repet] #/ sigmaInit1[,,r,repet]
49 rhoInit1[, , r, repet] <- solve(sigmaInit1[, , r, repet])
50 piInit1[repet, r] <- mean(Z == r)
51 }
52
53 for (i in 1:n)
54 {
55 for (r in 1:k)
56 {
57 dotProduct <- tcrossprod(Y[i, ] %*% rhoInit1[, , r, repet] - X[i,
58 ] %*% phiInit1[, , r, repet])
59 Gam[i, r] <- piInit1[repet, r] * det(rhoInit1[, , r, repet]) * exp(-0.5 *
60 dotProduct)
61 }
62 sumGamI <- sum(Gam[i, ])
63 gamInit1[i, , repet] <- Gam[i, ]/sumGamI
64 }
65
66 miniInit <- 10
67 maxiInit <- 11
68
69 init_EMG <- EMGLLF(phiInit1[, , , repet], rhoInit1[, , , repet], piInit1[repet,
70 ], gamInit1[, , repet], miniInit, maxiInit, gamma = 1, lambda = 0, X,
71 Y, eps = 1e-04, fast)
72 LLFEessai <- init_EMG$LLF
73 LLFinit1[repet] <- LLFEessai[length(LLFEessai)]
74 }
75 b <- which.min(LLFinit1)
76 phiInit <- phiInit1[, , , b]
77 rhoInit <- rhoInit1[, , , b]
78 piInit <- piInit1[b, ]
79 gamInit <- gamInit1[, , b]
80
81 return(list(phiInit = phiInit, rhoInit = rhoInit, piInit = piInit, gamInit = gamInit))
82 }