| 1 | EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau) |
| 2 | { |
| 3 | #matrix dimensions |
| 4 | n = dim(X)[1] |
| 5 | p = dim(phiInit)[1] |
| 6 | m = dim(phiInit)[2] |
| 7 | k = dim(phiInit)[3] |
| 8 | |
| 9 | #init outputs |
| 10 | phi = phiInit |
| 11 | rho = rhoInit |
| 12 | pi = piInit |
| 13 | LLF = rep(0, maxi) |
| 14 | S = array(0, dim=c(p,m,k)) |
| 15 | |
| 16 | gam = gamInit |
| 17 | Gram2 = array(0, dim=c(p,p,k)) |
| 18 | ps2 = array(0, dim=c(p,m,k)) |
| 19 | b = rep(0, k) |
| 20 | pen = matrix(0, maxi, k) |
| 21 | X2 = array(0, dim=c(n,p,k)) |
| 22 | Y2 = array(0, dim=c(n,m,k)) |
| 23 | dist = 0 |
| 24 | dist2 = 0 |
| 25 | ite = 1 |
| 26 | pi2 = rep(0, k) |
| 27 | ps = matrix(0, m,k) |
| 28 | nY2 = matrix(0, m,k) |
| 29 | ps1 = array(0, dim=c(n,m,k)) |
| 30 | Gam = matrix(0, n,k) |
| 31 | EPS = 1E-15 |
| 32 | |
| 33 | while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau)))) |
| 34 | { |
| 35 | Phi = phi |
| 36 | Rho = rho |
| 37 | Pi = pi |
| 38 | |
| 39 | #calcul associé à Y et X |
| 40 | for(r in 1:k) |
| 41 | { |
| 42 | for (mm in 1:m) |
| 43 | Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm] |
| 44 | for (i in 1:n) |
| 45 | X2[i,,r] = sqrt(gam[i,r]) * X[i,] |
| 46 | for (mm in 1:m) |
| 47 | ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r]) |
| 48 | for (j in 1:p) |
| 49 | { |
| 50 | for (s in 1:p) |
| 51 | Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r]) |
| 52 | } |
| 53 | } |
| 54 | |
| 55 | ########## |
| 56 | #Etape M # |
| 57 | ########## |
| 58 | |
| 59 | #pour pi |
| 60 | for (r in 1:k){ |
| 61 | b[r] = sum(abs(phi[,,r]))} |
| 62 | gam2 = colSums(gam) |
| 63 | a = sum(gam %*% log(pi)) |
| 64 | |
| 65 | #tant que les props sont negatives |
| 66 | kk = 0 |
| 67 | pi2AllPositive = FALSE |
| 68 | while (!pi2AllPositive) |
| 69 | { |
| 70 | pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi) |
| 71 | pi2AllPositive = all(pi2 >= 0) |
| 72 | kk = kk+1 |
| 73 | } |
| 74 | |
| 75 | #t[m] la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante |
| 76 | while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) < |
| 77 | -sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) ) |
| 78 | { |
| 79 | pi2 = pi + 0.1^kk * (1/n*gam2 - pi) |
| 80 | kk = kk + 1 |
| 81 | } |
| 82 | t = 0.1^kk |
| 83 | pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi)) |
| 84 | |
| 85 | #Pour phi et rho |
| 86 | for (r in 1:k) |
| 87 | { |
| 88 | for (mm in 1:m) |
| 89 | { |
| 90 | for (i in 1:n) |
| 91 | { |
| 92 | ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r]) |
| 93 | } |
| 94 | ps[mm,r] = sum(ps1[,mm,r]) |
| 95 | nY2[mm,r] = sum(Y2[,mm,r]^2) |
| 96 | rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r]) |
| 97 | } |
| 98 | } |
| 99 | for (r in 1:k) |
| 100 | { |
| 101 | for (j in 1:p) |
| 102 | { |
| 103 | for (mm in 1:m) |
| 104 | { |
| 105 | S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p,j),r]) |
| 106 | if (abs(S[j,mm,r]) <= n*lambda*(pi[r]^gamma)) |
| 107 | phi[j,mm,r]=0 |
| 108 | else if(S[j,mm,r] > n*lambda*(pi[r]^gamma)) |
| 109 | phi[j,mm,r] = (n*lambda*(pi[r]^gamma)-S[j,mm,r]) / Gram2[j,j,r] |
| 110 | else |
| 111 | phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r] |
| 112 | } |
| 113 | } |
| 114 | } |
| 115 | |
| 116 | ########## |
| 117 | #Etape E # |
| 118 | ########## |
| 119 | sumLogLLF2 = 0 |
| 120 | for (i in 1:n) |
| 121 | { |
| 122 | #precompute sq norms to numerically adjust their values |
| 123 | sqNorm2 = rep(0,k) |
| 124 | for (r in 1:k){ |
| 125 | sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )} |
| 126 | |
| 127 | #compute Gam(:,:) using shift determined above |
| 128 | sumLLF1 = 0.0; |
| 129 | for (r in 1:k) |
| 130 | { |
| 131 | Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r])* det(rho[,,r]) |
| 132 | sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2) |
| 133 | } |
| 134 | sumLogLLF2 = sumLogLLF2 + log(sumLLF1) |
| 135 | sumGamI = sum(Gam[i,]) |
| 136 | if(sumGamI > EPS) |
| 137 | gam[i,] = Gam[i,] / sumGamI |
| 138 | else |
| 139 | gam[i,] = rep(0,k) |
| 140 | } |
| 141 | |
| 142 | sumPen = sum(pi^gamma * b) |
| 143 | LLF[ite] = -sumLogLLF2/n + lambda*sumPen |
| 144 | |
| 145 | dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) ) |
| 146 | |
| 147 | Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) ) |
| 148 | Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) ) |
| 149 | Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) ) |
| 150 | dist2 = max(Dist1,Dist2,Dist3) |
| 151 | |
| 152 | ite = ite+1 |
| 153 | } |
| 154 | |
| 155 | affec = apply(gam, 1,which.max) |
| 156 | return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S, "affec" = affec )) |
| 157 | } |