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#' Find K-Nearest Neighbors
#'
#' Given \eqn{N} observations \eqn{X_1, X_2, \ldots, X_N \in \mathcal{M}},
#' \code{riem.knn} constructs \eqn{k}-nearest neighbors.
#'
#' @param riemobj a S3 \code{"riemdata"} class for \eqn{N} manifold-valued data.
#' @param k the number of neighbors to find.
#' @param geometry (case-insensitive) name of geometry; either geodesic (\code{"intrinsic"}) or embedded (\code{"extrinsic"}) geometry.
#'
#' @return a named list containing\describe{
#' \item{nn.idx}{an \eqn{(N \times k)} neighborhood index matrix.}
#' \item{nn.dists}{an \eqn{(N\times k)} distances from a point to its neighbors.}
#' }
#'
#' @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(2,3,4), each=10)
#'
#' ## K-NN CONSTRUCTION WITH K=5 & K=10
#' knn1 = riem.knn(myriem, k=5)
#' knn2 = riem.knn(myriem, k=10)
#'
#' ## MDS FOR VISUALIZATION
#' embed2 = riem.mds(myriem, ndim=2)$embed
#'
#' ## VISUALIZE
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,2), pty="s")
#' plot(embed2, pch=19, main="knn with k=4", col=mylabs)
#' for (i in 1:30){
#' for (j in 1:5){
#' lines(embed2[c(i,knn1$nn.idx[i,j]),])
#' }
#' }
#' plot(embed2, pch=19, main="knn with k=8", col=mylabs)
#' for (i in 1:30){
#' for (j in 1:10){
#' lines(embed2[c(i,knn2$nn.idx[i,j]),])
#' }
#' }
#' par(opar)
#'
#' @concept learning
#' @export
riem.knn <- function(riemobj, k=2, geometry=c("intrinsic","extrinsic")){
## PREPARE
DNAME = paste0("'",deparse(substitute(riemobj)),"'")
if (!inherits(riemobj,"riemdata")){
stop(paste0("* riem.knn : input ",DNAME," should be an object of 'riemdata' class."))
}
myk = max(0, round(k))
mygeom = ifelse(missing(geometry),"intrinsic",
match.arg(tolower(geometry),c("intrinsic","extrinsic")))
## COMPUTE PAIRWISE DISTANCE
distobj = as.matrix(basic_pdist(riemobj$name, riemobj$data, mygeom))
## COMPUTE AND RETURN
return(nearest_neighbor(distobj, myk))
}
#' @keywords internal
#' @noRd
nearest_neighbor <- function(dmat, k){
n = base::nrow(dmat)
nn.idx = array(0,c(n,k))
nn.dists = array(0,c(n,k))
for (i in 1:n){
tgt = as.vector(dmat[i,])
i_id = order(tgt)[2:(k+1)]
nn.idx[i,] = i_id
nn.dists[i,] = tgt[i_id]
}
output = list()
output$nn.idx = nn.idx
output$nn.dists = nn.dists
return(output)
}
# library(usmap)
# library(ggplot2)
# data("cities")
# mygeo = usmap_transform(data.frame(lon=cities$coord[,2], lat=cities$coord[,1]))
#
# myriem = riem.sphere(cities$cartesian)
#
# plot_usmap(regions="states") +
# geom_point(data=mygeo, aes(x=lon.1, y=lat.1), alpha=0.25)
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