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#' Update G in Semi-NMF
#'
#' @param X Data expression matrix need to be factorized
#' @param mf The basis matrix
#' @param mg The co-efficient matrix
#' @return \code{G} The basis matrix
#'
#' @details
#' By definition, G is a graph adjacency matrix. The \code{update_G} updates G
#' after every iteration.
#'
#' @author Haidong Yi, Ayush T. Raman
#' @export
#' @examples
#' X <- matrix(1:12,nrow=4)
#' mf <- matrix(1:8,nrow=4)
#' mg <- matrix(1:6,ncol=2)
#' mg <- update_G(X,mf,mg)
update_G <- function(X, mf, mg) {
n <- ncol(X)
k <- ncol(mf)
G <- matrix(nrow = n, ncol = k)
GFFP <- t(mf) %*% mf
GFFN <- t(mf) %*% mf
XF <- t(X) %*% mf
for (i in 1:k) {
for (j in 1:k) {
GFFP[i, j] <- 0.5 * (abs(GFFP[i, j]) + GFFP[i, j])
GFFN[i, j] <- 0.5 * (abs(GFFN[i, j]) - GFFN[i, j])
}
}
GFFP <- mg %*% GFFP
GFFN <- mg %*% GFFN
for (i in 1:n) {
for (j in 1:k) {
num <- 0.5 * (abs(XF[i, j]) + XF[i, j]) + GFFN[i, j]
den <- 0.5 * (abs(XF[i, j]) - XF[i, j]) + GFFP[i, j]
G[i, j] <- mg[i, j] * sqrt(num / den)
}
}
G
}
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