# R/visualization_mds.R In Riemann: Learning with Data on Riemannian Manifolds

#### Documented in riem.mds

#' Multidimensional Scaling
#'
#' Given \eqn{N} observations \eqn{X_1, X_2, \ldots, X_N \in \mathcal{M}},
#' apply multidimensional scaling to get low-dimensional embedding
#' in Euclidean space. Usually, \code{ndim=2,3} are chosen for visualization.
#'
#' @param riemobj a S3 \code{"riemdata"} class for \eqn{N} manifold-valued data.
#' @param ndim an integer-valued target dimension (default: 2).
#' @param geometry (case-insensitive) name of geometry; either geodesic (\code{"intrinsic"}) or embedded (\code{"extrinsic"}) geometry.
#'
#' @return a named list containing \describe{
#' \item{embed}{an \eqn{(N\times ndim)} matrix whose rows are embedded observations.}
#' \item{stress}{discrepancy between embedded and original distances as a measure of error.}
#' }
#'
#' @examples
#' #-------------------------------------------------------------------
#' #          Example on Sphere : a dataset with three types
#' #
#' # 10 perturbed data points near (1,0,0) on S^2 in R^3
#' # 10 perturbed data points near (0,1,0) on S^2 in R^3
#' # 10 perturbed data points near (0,0,1) on S^2 in R^3
#' #-------------------------------------------------------------------
#' ## GENERATE DATA
#' mydata = list()
#' for (i in 1:10){
#'   tgt = c(1, stats::rnorm(2, sd=0.1))
#'   mydata[[i]] = tgt/sqrt(sum(tgt^2))
#' }
#' for (i in 11:20){
#'   tgt = c(rnorm(1,sd=0.1),1,rnorm(1,sd=0.1))
#'   mydata[[i]] = tgt/sqrt(sum(tgt^2))
#' }
#' for (i in 21:30){
#'   tgt = c(stats::rnorm(2, sd=0.1), 1)
#'   mydata[[i]] = tgt/sqrt(sum(tgt^2))
#' }
#' myriem = wrap.sphere(mydata)
#' mylabs = rep(c(1,2,3), each=10)
#'
#' ## MDS EMBEDDING WITH TWO GEOMETRIES
#' embed2int = riem.mds(myriem, geometry="intrinsic")$embed #' embed2ext = riem.mds(myriem, geometry="extrinsic")$embed
#'
#' ## VISUALIZE
#' par(mfrow=c(1,2), pty="s")
#' plot(embed2int, main="intrinsic MDS", ylim=c(-2,2), col=mylabs, pch=19)
#' plot(embed2ext, main="extrinsic MDS", ylim=c(-2,2), col=mylabs, pch=19)
#' par(opar)
#'
#' @references
#' \insertRef{torgerson_multidimensional_1952a}{Riemann}
#'
#' @concept visualization
#' @export
riem.mds <- function(riemobj, ndim=2, geometry=c("intrinsic","extrinsic")){
## PREPARE
DNAME = paste0("'",deparse(substitute(riemobj)),"'")
if (!inherits(riemobj,"riemdata")){
stop(paste0("* riem.mds : input ",DNAME," should be an object of 'riemdata' class."))
}
myndim = max(2, round(ndim))
mygeom = ifelse(missing(geometry),"intrinsic",
match.arg(tolower(geometry),c("intrinsic","extrinsic")))

# ## OLD PART : FUNCTION IMPORT FROM MAOTAI
# distobj = stats::as.dist(basic_pdist(riemobj$name, riemobj$data, mygeom))
#
# ## COMPUTE MDS AND RETURN
# func.import = utils::getFromNamespace("hidden_cmds", "maotai")
# out.cmds    = func.import(distobj, ndim=myndim)
# return(out.cmds)

# COMPUTE WITH CPP
return(visualize_cmds(riemobj$name, mygeom, riemobj$data, myndim))
}

## Try the Riemann package in your browser

Any scripts or data that you put into this service are public.

Riemann documentation built on March 18, 2022, 7:55 p.m.