EMGLLF_R = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau)
{
- #matrix dimensions
- n = dim(X)[1]
- p = dim(phiInit)[1]
- m = dim(phiInit)[2]
- k = dim(phiInit)[3]
-
- #init outputs
- phi = phiInit
- rho = rhoInit
- pi = piInit
- LLF = rep(0, maxi)
- S = array(0, dim=c(p,m,k))
-
- gam = gamInit
- Gram2 = array(0, dim=c(p,p,k))
- ps2 = array(0, dim=c(p,m,k))
- b = rep(0, k)
- X2 = array(0, dim=c(n,p,k))
- Y2 = array(0, dim=c(n,m,k))
- dist = 0
- dist2 = 0
- ite = 1
- pi2 = rep(0, k)
- ps = matrix(0, m,k)
- nY2 = matrix(0, m,k)
- ps1 = array(0, dim=c(n,m,k))
- Gam = matrix(0, n,k)
- EPS = 1E-15
-
- while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
+ # Matrix dimensions
+ n = dim(X)[1]
+ p = dim(phiInit)[1]
+ m = dim(phiInit)[2]
+ k = dim(phiInit)[3]
+
+ # Outputs
+ phi = phiInit
+ rho = rhoInit
+ pi = piInit
+ llh = -Inf
+ S = array(0, dim=c(p,m,k))
+
+ # Algorithm variables
+ gam = gamInit
+ Gram2 = array(0, dim=c(p,p,k))
+ ps2 = array(0, dim=c(p,m,k))
+ X2 = array(0, dim=c(n,p,k))
+ Y2 = array(0, dim=c(n,m,k))
+ EPS = 1e-15
+
+ for (ite in 1:maxi)
{
- Phi = phi
- Rho = rho
- Pi = pi
+ # Remember last pi,rho,phi values for exit condition in the end of loop
+ Phi = phi
+ Rho = rho
+ Pi = pi
- #calcul associé à Y et X
- for(r in 1:k)
+ # Calcul associé à Y et X
+ for (r in 1:k)
{
- for (mm in 1:m)
- Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
- for (i in 1:n)
- X2[i,,r] = sqrt(gam[i,r]) * X[i,]
- for (mm in 1:m)
- ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
- for (j in 1:p)
+ for (mm in 1:m)
+ Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
+ for (i in 1:n)
+ X2[i,,r] = sqrt(gam[i,r]) * X[i,]
+ for (mm in 1:m)
+ ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
+ for (j in 1:p)
{
- for (s in 1:p)
- Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
- }
- }
-
- ##########
- #Etape M #
- ##########
-
- #pour pi
- for (r in 1:k)
- b[r] = sum(abs(phi[,,r]))
- gam2 = colSums(gam)
- a = sum(gam %*% log(pi))
-
- #tant que les props sont negatives
- kk = 0
- pi2AllPositive = FALSE
- while (!pi2AllPositive)
+ for (s in 1:p)
+ Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
+ }
+ }
+
+ ##########
+ #Etape M #
+ ##########
+
+ # Pour pi
+ b = sapply( 1:k, function(r) sum(abs(phi[,,r])) )
+ gam2 = colSums(gam)
+ a = sum(gam %*% log(pi))
+
+ # Tant que les props sont negatives
+ kk = 0
+ pi2AllPositive = FALSE
+ while (!pi2AllPositive)
{
- pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
- pi2AllPositive = all(pi2 >= 0)
- kk = kk+1
- }
+ pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
+ pi2AllPositive = all(pi2 >= 0)
+ kk = kk+1
+ }
- #t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
- while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
+ # t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
+ while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
-sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) )
{
- pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
- kk = kk + 1
- }
- t = 0.1^kk
- pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
-
- #Pour phi et rho
- for (r in 1:k)
+ pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
+ kk = kk + 1
+ }
+ t = 0.1^kk
+ pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
+
+ #Pour phi et rho
+ for (r in 1:k)
{
- for (mm in 1:m)
+ for (mm in 1:m)
{
- for (i in 1:n)
- {
- ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
- }
- ps[mm,r] = sum(ps1[,mm,r])
- nY2[mm,r] = sum(Y2[,mm,r]^2)
- rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r])
+ ps = 0
+ for (i in 1:n)
+ ps = ps + Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
+ nY2 = sum(Y2[,mm,r]^2)
+ rho[mm,mm,r] = (ps+sqrt(ps^2+4*nY2*gam2[r])) / (2*nY2)
}
- }
+ }
- for (r in 1:k)
+ for (r in 1:k)
{
- for (j in 1:p)
+ for (j in 1:p)
{
- for (mm in 1:m)
+ for (mm in 1:m)
{
- S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
+ S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
if (abs(S[j,mm,r]) <= n*lambda*(pi[r]^gamma))
- phi[j,mm,r]=0
- else if(S[j,mm,r] > n*lambda*(pi[r]^gamma))
- phi[j,mm,r] = (n*lambda*(pi[r]^gamma)-S[j,mm,r]) / Gram2[j,j,r]
- else
- phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r]
- }
- }
- }
-
- ##########
- #Etape E #
- ##########
-
- sumLogLLF2 = 0
- for (i in 1:n)
+ phi[j,mm,r]=0
+ else if(S[j,mm,r] > n*lambda*(pi[r]^gamma))
+ phi[j,mm,r] = (n*lambda*(pi[r]^gamma)-S[j,mm,r]) / Gram2[j,j,r]
+ else
+ phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r]
+ }
+ }
+ }
+
+ ##########
+ #Etape E #
+ ##########
+
+ # Precompute det(rho[,,r]) for r in 1...k
+ detRho = sapply(1:k, function(r) det(rho[,,r]))
+
+ sumLogLLH = 0
+ for (i in 1:n)
{
- #precompute sq norms to numerically adjust their values
- sqNorm2 = rep(0,k)
- for (r in 1:k)
- sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )
-
- #compute Gam[,]
- sumLLF1 = 0.0;
- for (r in 1:k)
+ # Update gam[,]
+ sumGamI = 0
+ for (r in 1:k)
{
- Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r]) * det(rho[,,r])
- sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2)
- }
- sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
- sumGamI = sum(Gam[i,])
- if(sumGamI > EPS)
- gam[i,] = Gam[i,] / sumGamI
- else
- gam[i,] = rep(0,k)
- }
-
- sumPen = sum(pi^gamma * b)
- LLF[ite] = -sumLogLLF2/n + lambda*sumPen
- dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
- Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) )
- Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
- Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) )
- dist2 = max(Dist1,Dist2,Dist3)
-
- ite = ite+1
- }
-
- affec = apply(gam, 1, which.max)
- return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S, "affec" = affec ))
+ gam[i,r] = pi[r]*exp(-0.5*sum((Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2))*detRho[r]
+ sumGamI = sumGamI + gam[i,r]
+ }
+ sumLogLLH = sumLogLLH + log(sumGamI) - log((2*base::pi)^(m/2))
+ if (sumGamI > EPS) #else: gam[i,] is already ~=0
+ gam[i,] = gam[i,] / sumGamI
+ }
+
+ sumPen = sum(pi^gamma * b)
+ last_llh = llh
+ llh = -sumLogLLH/n + lambda*sumPen
+ dist = ifelse( ite == 1, llh, (llh-last_llh) / (1+abs(llh)) )
+ Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) )
+ Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
+ Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) )
+ dist2 = max(Dist1,Dist2,Dist3)
+
+ if (ite >= mini && (dist >= tau || dist2 >= sqrt(tau)))
+ break
+ }
+
+ affec = apply(gam, 1, which.max)
+ list( "phi"=phi, "rho"=rho, "pi"=pi, "llh"=llh, "S"=S, "affec"=affec )
}
projects / valse.git / blobdiff