Given \(N\) observations \(X_1, X_2, \ldots, X_N \in \mathcal{M}\), find the smallest enclosing ball.
Usage
riem.seb(riemobj, method = c("aa2013"), ...)Arguments
- riemobj
a S3
"riemdata"class for \(N\) manifold-valued data.- method
(case-insensitive) name of the algorithm to be used as follows;
"aa2013"Arnaudon and Nielsen (2013).
- ...
extra parameters including
- maxiter
maximum number of iterations to be run (default:50).
- eps
tolerance level for stopping criterion (default: 1e-5).
Value
a named list containing
- center
a matrix on \(\mathcal{M}\) that minimizes the radius.
- radius
the minimal radius with respect to the
center.
Validation status
This retained legacy interface is experimental. Its full numerical and
statistical contract has not been independently verified across supported
inputs. See riem-method-contracts and the installed contract
table for method-specific assumptions, restrictions, and evidence scope.
References
Bâdoiu M, Clarkson KL (2003). “Smaller core-sets for balls.” In Proceedings of the fourteenth annual ACM-SIAM symposium on discrete algorithms, SODA '03, 801–802. ISBN 0-89871-538-5.
Arnaudon M, Nielsen F (2013). “On approximating the Riemannian 1-center.” Computational Geometry, 46(1), 93–104. ISSN 09257721.
Examples
#-------------------------------------------------------------------
# Euclidean Example : samples from Standard Normal in R^2
#-------------------------------------------------------------------
## GENERATE 25 OBSERVATIONS FROM N(0,I)
ndata = 25
mymats = array(0,c(ndata, 2))
mydata = list()
for (i in 1:ndata){
mydata[[i]] = stats::rnorm(2)
mymats[i,] = mydata[[i]]
}
myriem = wrap.euclidean(mydata)
## COMPUTE
sebobj = riem.seb(myriem)
center = as.vector(sebobj$center)
radius = sebobj$radius
## VISUALIZE
# 1. prepare the circle for drawing
theta = seq(from=0, to=2*pi, length.out=100)
coords = radius*cbind(cos(theta), sin(theta))
coords = coords + matrix(rep(center, each=100), ncol=2)
# 2. draw
opar <- par(no.readonly=TRUE)
par(pty="s")
plot(coords, type="l", lwd=2, col="red",
main="Euclidean SEB", xlab="x", ylab="y")
points(mymats, pch=19) # data
points(center[1], center[2], pch=19, col="blue") # center
par(opar)