Nothing
#' Robust Fréchet Mean of Manifold-valued Data
#'
#' Robust estimator for mean starts from dividing the data \eqn{\{x_i\}_{i=1}^n} into \eqn{k} equally sized
#' sets. For each subset, it first estimates Fréchet mean. It then follows a step to aggregate
#' \eqn{k} sample means by finding a geometric median.
#'
#' @param input a S3 object of \code{riemdata} class. See \code{\link{riemfactory}} for more details.
#' @param k number of subsets for which the data be divided into.
#' @param maxiter maximum number of iterations for gradient descent algorithm and Weiszfeld algorithm.
#' @param eps stopping criterion for the norm of gradient.
#' @param parallel a flag for enabling parallel computation.
#'
#' @return a named list containing
#' \describe{
#' \item{x}{an estimate geometric median.}
#' \item{iteration}{number of iterations until convergence.}
#' }
#'
#' @examples
#' \donttest{
#' ### Generate 100 data points on Sphere S^2 near (0,0,1).
#' ndata = 100
#' theta = seq(from=-0.99,to=0.99,length.out=ndata)*pi
#' tmpx = cos(theta) + rnorm(ndata,sd=0.1)
#' tmpy = sin(theta) + rnorm(ndata,sd=0.1)
#'
#' ### Wrap it as 'riemdata' class
#' data = list()
#' for (i in 1:ndata){
#' tgt = c(tmpx[i],tmpy[i],1)
#' data[[i]] = tgt/sqrt(sum(tgt^2)) # project onto Sphere
#' }
#' data = riemfactory(data, name="sphere")
#'
#' ### Compute Robust Fréchet Mean
#' out1 = rbase.robust(data)
#' out2 = rbase.robust(data,parallel=TRUE) # test parallel implementation
#' }
#'
#' @references
#' \insertRef{2011arXiv1112.3914L}{RiemBase}
#'
#' \insertRef{2013arXiv1308.1334M}{RiemBase}
#'
#' \insertRef{2014arXiv1409.5937F}{RiemBase}
#'
#' @seealso \code{\link[RiemBase]{rbase.mean}}, \code{\link[RiemBase]{rbase.median}}
#' @author Kisung You
#' @export
rbase.robust <- function(input, k=5, maxiter=496, eps=1e-6, parallel=FALSE){
#-------------------------------------------------------
# must be of 'riemdata' class
if ((class(input))!="riemdata"){
stop("* rbase.robust : the input must be of 'riemdata' class. Use 'riemfactory' first to manage your data.")
}
k = as.integer(k)
if (k<=1){
stop("* rbase.robust : when 'k' <= 1, there is no need to run this.")
}
# acquire manifold name
mfdname = tolower(input$name)
# stack data as 3d matrices
newdata = aux_stack3d(input)
if (is.matrix(newdata)){
output = list()
output$x = newdata
output$iteration = 0
return(output)
}
if (dim(newdata)[3]==1){
output = list()
output$x = matrix(newdata,nrow=nrow(newdata))
output$iteration = 0
return(output)
}
#-------------------------------------------------------
# generate cluster index and separate true data
nCores = parallel::detectCores()
clustidx = aux_rndivide(dim(newdata)[3], k)
partdata = list()
for (i in 1:length(clustidx)){
tmpdata = newdata[,,clustidx[[i]]]
if (length(dim(tmpdata))==2){
tmpdata = rmean_2to3(tmpdata)
}
if (length(dim(tmpdata))!=3){
stop("* rmean : something is wrong.")
}
partdata[[i]] = tmpdata
}
#-------------------------------------------------------
# let's run parallel for mean
tmpout = list()
for (i in 1:k){
if ((nCores==1)||is.na(nCores)||(parallel=FALSE)){
tmpoutput = rbase.mean.cube(partdata[[i]], mfdname, maxiter=maxiter, eps=eps)
} else {
tmpoutput = rbase.mean.cube(partdata[[i]], mfdname, maxiter=maxiter, eps=eps, parallel=TRUE)
}
tmpout[[i]] = tmpoutput$x
}
#-------------------------------------------------------
# it's time to run robust median problem
partmeans = rmean_lto3(tmpout)
if ((nCores==1)||(is.na(nCores))||(parallel=FALSE)){
partran = engine_mean(partmeans, mfdname, as.integer(maxiter), as.double(eps))
partinit = partran$x
output = engine_median(partmeans, mfdname, as.integer(maxiter), as.double(eps), partinit)
} else {
partran = engine_mean_openmp(partmeans, mfdname, as.integer(maxiter), as.double(eps), nCores)
partinit = partran$x
output = engine_median_openmp(partmeans, mfdname, as.integer(maxiter), as.double(eps), nCores, partinit)
}
#-------------------------------------------------------
# return output
return(output)
}
#' @keywords internal
#' @noRd
rmean_2to3 <- function(A){
m = nrow(A)
p = ncol(A)
output = array(0,c(m,1,p))
for (i in 1:p){
output[,,i] = A[,i]
}
return(output)
}
#' @keywords internal
#' @noRd
rmean_lto3 <- function(dlist){
p = length(dlist)
m = nrow(dlist[[1]])
n = ncol(dlist[[1]])
output = array(0,c(m,n,p))
for (i in 1:p){
output[,,i] = dlist[[i]]
}
return(output)
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.