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AddIndiv2LogBiplotGD <- function(LB, X, freq = matrix(1, nrow(X), 1), tolerance = 1e-04, penalization=0.01,
num_max_iters=100, RotVarimax = FALSE, seed = 0, OptimMethod="CG", Initial="random",
Orthogonalize=FALSE, Algorithm = "Joint", ...) {
X=as.matrix(X)
indnames=rownames(X)
varnames=colnames(X)
n <- nrow(X)
p <- ncol(X)
# Estimation of parameters A and B
r=LB$Dimension
if (!is.null(LB$Seed)) set.seed(LB$Seed)
B=LB$ColumnParameters
A=X %*% B[,-1]
parA=vec(A)$v
resbipA <- optim(parA, fn=JLogBiplotRegA, gr=grLogBiplotRegA, method=LB$OptimMethod, X=X, B=B, lambda=LB$Penalization)
parA=resbipA$par
A=matrix(parA,n,r)
rownames(A)=rownames(X)
H=sigmoide(cbind(rep(1,n),A) %*% t(B))
J=sum(-1*X*log(H)-(1-X)*log(1-H), na.rm = TRUE)/2 + LB$Penalization*sum(A^2, na.rm = TRUE)/2 + LB$Penalization*sum(B[,-1]^2, na.rm = TRUE)/2
}
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