# R/gdmf.r In dml: Distance Metric Learning in R

#' Global Distance Metric Learning
#'
#' Performs Global Distance Metric Learning (GDM) on the given data, learning a full matrix.
#'
#' Put GdmFull function details here.
#'
#' @param data \code{n * d} data matrix. \code{n} is the number of data points,
#'             \code{d} is the dimension of the data.
#'             Each data point is a row in the matrix.
#' @param simi \code{n * 2} matrix describing the similar constrains.
#'              Each row of matrix is serial number of a similar pair in the original data.
#'				For example, pair(1, 3) represents the first observation is similar the 3th observation in the original data.
#' @param dism \code{n * 2} matrix describing the dissimilar constrains as \code{simi}.
#'				Each row of matrix is serial number of a dissimilar pair in the original data.
#' @param maxiter numeric, the number of iteration.
#'
#' @return list of the GdmDiag results:
#' \item{newData}{GdmDiag transformed data}
#' \item{fullA}{suggested Mahalanobis matrix}
#' \item{dmlA}{matrix to transform data, square root of diagonalA }
#' \item{converged}{whether the iteration-projection optimization is converged or not}
#'
#' For every two original data points (x1, x2) in newData (y1, y2):
#'
#' \eqn{(x2 - x1)' * A * (x2 - x1) = || (x2 - x1) * B ||^2 = || y2 - y1 ||^2}
#'
#' @keywords GDM global distance metirc learning transformation mahalanobis metric
#'
#' @import MASS
#'
#' @export GdmFull
#'
#' @note Be sure to check whether the dimension of original data and constrains' format are valid for the function.
#'
#' @author Gao Tao <\url{http://www.gaotao.name}>
#'
#' @references
#' Steven C.H. Hoi, W. Liu, M.R. Lyu and W.Y. Ma (2003).
#' Distance metric learning, with application to clustering with side-information.
#  in \emph{Proc. NIPS}.
#'
#' @examples
#' \dontrun{
#' set.seed(123)
#' library(MASS)
#' library(scatterplot3d)
#'
#' # generate simulated Gaussian data
#' k = 100
#' m <- matrix(c(1, 0.5, 1, 0.5, 2, -1, 1, -1, 3), nrow =3, byrow = T)
#' x1 <- mvrnorm(k, mu = c(1, 1, 1), Sigma = m)
#' x2 <- mvrnorm(k, mu = c(-1, 0, 0), Sigma = m)
#' data <- rbind(x1, x2)
#'
#' # define similar constrains
#' simi <- rbind(t(combn(1:k, 2)), t(combn((k+1):(2*k), 2)))
#'
#' temp <-  as.data.frame(t(simi))
#' tol <- as.data.frame(combn(1:(2*k), 2))
#'
#' # define disimilar constrains
#' dism <- t(as.matrix(tol[!tol %in% simi]))
#'
#' # transform data using GdmFull
#' result <- GdmFull(data, simi, dism)
#' newData <- result$newData #' # plot original data #' color <- gl(2, k, labels = c("red", "blue")) #' par(mfrow = c(2, 1), mar = rep(0, 4) + 0.1) #' scatterplot3d(data, color = color, cex.symbols = 0.6, #' xlim = range(data[, 1], newData[, 1]), #' ylim = range(data[, 2], newData[, 2]), #' zlim = range(data[, 3], newData[, 3]), #' main = "Original Data") #' # plot GdmFull transformed data #' scatterplot3d(newData, color = color, cex.symbols = 0.6, #' xlim = range(data[, 1], newData[, 1]), #' ylim = range(data[, 2], newData[, 2]), #' zlim = range(data[, 3], newData[, 3]), #' main = "Transformed Data") #' } #' GdmFull <- function(data, simi, dism, maxiter = 100) { data <- as.matrix(data) N <- dim(data)[1] d <- dim(data)[2] new.simi <- unique(t(apply(simi, 1, sort))) new.dism <- unique(t(apply(dism, 1, sort))) A <- diag(1, d) * 0.1 W <- mat.or.vec(d, d) dij <- mat.or.vec(1, d) # sphereMult = cov(data)^(-0.5); # spheredata = data %*% sphereMult dist1.simi <- data[new.simi[, 1], ] - data[new.simi[, 2], ] dist2.ij <- t(apply(dist1.simi, 1, function(x) outer(x, x))) W <- matrix(apply(dist2.ij, 2, sum), ncol = d, byrow = TRUE) w <- matrix(W, ncol = 1) t0 <- as.numeric(crossprod(w, matrix(A, ncol = 1))/100) IterProjection <- function(data, simi, dism, A, w, t0 , maxiter = 100) { data <- as.matrix(data) N = dim(data)[1] # number of examples d = dim(data)[2] # dimensionality of examples # S1 <- mat.or.vec(N, N) # D1 <- mat.or.vec(N, N) # simi <- rbind(simi, simi[, c(2, 1)]) # dism <- rbind(dism, dism[, c(2, 1)]) # S1[simi] <- 1 # D1[dism] <- 1 new.simi <- unique(t(apply(simi, 1, sort))) new.dism <- unique(t(apply(dism, 1, sort))) # error1=1e5 threshold2 <- 0.01 # error-bound of main A-update iteration epsilon <- 0.01 # error-bound of iterative projection on C1 and C2 maxcount <- 200 w1 <- w/norm(w, "F") # make 'w' a unit vector t1 <- t0/norm(w, "F") count <- 1 alpha <- 0.1 # initial step size along gradient GradProjection <- function(grad1, grad2, d) { g1 <- matrix(grad1, ncol = 1) g2 <- matrix(grad2, ncol = 1) g2 <- g2/norm(g2, "F") gtemp <- g1 - as.numeric(crossprod(g2, g1)) * g2 gtemp <- gtemp/norm(gtemp, "F") grad.proj <- matrix(gtemp, d, d) return(grad.proj) } fS1 <- function(data, new.simi, A, N, d, fudge = 0.000001) { dist1.simi <- data[new.simi[, 1], ] - data[new.simi[, 2], ] dist2.ij <- t(apply(dist1.simi, 1, function(x) outer(x, x))) fs.1d <- matrix(apply(dist2.ij, 2, sum), ncol = d, byrow = TRUE) return(fs.1d) } fD1 <- function(data, new.simi, A, N, d, fudge = 0.000001) { dist1.dism <- data[new.dism[, 1], ] - data[new.dism[, 2], ] dist.ij <- numeric(dim(dist1.dism)[1]) for (i in 1:dim(dist1.dism)[1]) { dist.ij[i] <- sqrt(t(dist1.dism[i, ]) %*% A %*% t(t(dist1.dism[i, ]))) } sum.dist <- sum(dist.ij) + 0.000001 Mij <- t(apply(dist1.dism, 1, function(x) outer(x, x))) temp <- cbind(Mij, t(t(dist.ij))) deri.ij <- 0.5 * temp[, 1:(d^2)]/(temp[, d^2 + 1] + (temp[, d^2 + 1] == 0) * fudge) sum.deri <- matrix(apply(deri.ij, 2, sum), ncol = d, byrow = TRUE) fd.1d <- sum.deri/sum.dist return(fd.1d) } fD <- function(data, new.dism, A, N, d) { dist1.dism <- data[new.dism[, 1], ] - data[new.dism[, 2], ] dist.ij <- numeric(dim(dist1.dism)[1]) for (i in 1:dim(dist1.dism)[1]) { dist.ij[i] <- sqrt(t(dist1.dism[i, ]) %*% A %*% t(t(dist1.dism[i, ]))) } fd <- sum(dist.ij) + 0.000001 fd <- log(fd) return(fd) } grad1 <- fS1(data, new.simi, A, N, d); # gradient of similarity constraint function grad2 <- fD1(data, new.dism, A, N, d); # gradient of dissimilarity constraint func. M <- GradProjection(grad1, grad2, d); # gradient of fD1 orthognal to fS1 A.last <- A # initial A done <- 0 delta <- 0 converged <- 0 while (done == 0) { projection.iters <- 0 satisfy <- 0 while (projection.iters < maxiter & satisfy == 0) { A0 <- A x0 <- matrix(A0, ncol = 1) if(crossprod(w, x0) <= t0) A <- A0 else { x <- x0 + as.numeric(t1 - crossprod(w1, x0)) * w1 A <- matrix(x, 3, 3) } A <- (A + t(A))/2 vl <- eigen(A) vl[[1]][vl[[1]] < 0] = 0 A <- vl[[2]] %*% diag(vl[[1]], d) %*% t(vl[[2]]) fDC2 <- crossprod(w, matrix(A, ncol = 1)) error1 <- as.numeric((fDC2 - t0)/t0) projection.iters <- projection.iters + 1 satisfy <- as.numeric(ifelse(error1 > epsilon, 0, 1)) } obj.previous <- fD(data, new.dism, A.last, N, d) obj <- fD(data, new.dism, A, N, d) if (obj > obj.previous & satisfy == 1) { alpha <- alpha * 1.05 A.last <- A grad2 <- fS1(data, new.simi, A, N, d) grad1 <- fD1(data, new.dism, A, N, d) M <- GradProjection(grad1, grad2, d) A <- A + alpha * M } else{ alpha <- alpha/2 A <- A.last + alpha * M } delta <- norm(alpha * M, "F")/norm(A.last, "F") count <- count + 1 done <- ifelse(delta < threshold2 | count == maxcount, 1, 0) } converged <- ifelse(delta > threshold2, 0, 1) return(list("converged" = ifelse(converged == 1, "Yes", "No"), "fullA" = A)) } iterproj <- IterProjection(data, simi, dism, A, w, t0) eigenvalue <- eigen(iterproj$fullA)
dml <- eigenvalue[[2]] %*% sqrt(diag(eigenvalue[[1]], d))
newData <- data %*% dml
return(list("newData" = newData, "fullA" = iterproj[[2]], "dmlA" = dml, "converged" = iterproj[[1]]))
}


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dml documentation built on May 2, 2019, 6:35 a.m.