ellipsoidhull {cluster}  R Documentation 
Compute the “ellipsoid hull” or “spanning ellipsoid”, i.e. the ellipsoid of minimal volume (‘area’ in 2D) such that all given points lie just inside or on the boundary of the ellipsoid.
ellipsoidhull(x, tol=0.01, maxit=5000, ret.wt = FALSE, ret.sqdist = FALSE, ret.pr = FALSE) ## S3 method for class 'ellipsoid' print(x, digits = max(1, getOption("digits")  2), ...)
x 
the n pdimensional points asnumeric n x p matrix. 
tol 
convergence tolerance for Titterington's algorithm.
Setting this to much smaller values may drastically increase the number of
iterations needed, and you may want to increas 
maxit 
integer giving the maximal number of iteration steps for the algorithm. 
ret.wt, ret.sqdist, ret.pr 
logicals indicating if additional
information should be returned, 
digits,... 
the usual arguments to 
The “spanning ellipsoid” algorithm is said to stem from
Titterington(1976), in Pison et al (1999) who use it for
clusplot.default
.
The problem can be seen as a special case of the “Min.Vol.”
ellipsoid of which a more more flexible and general implementation is
cov.mve
in the MASS
package.
an object of class "ellipsoid"
, basically a list
with several components, comprising at least
cov 
p x p covariance matrix description the ellipsoid. 
loc 
pdimensional location of the ellipsoid center. 
d2 
average squared radius. Further, d2 = t^2, where
t is “the value of a tstatistic on the ellipse
boundary” (from 
wt 
the vector of weights iff 
sqdist 
the vector of squared distances iff 
prob 
the vector of algorithm probabilities iff 
it 
number of iterations used. 
tol, maxit 
just the input argument, see above. 
eps 
the achieved tolerance which is the maximal squared radius minus p. 
ierr 
error code as from the algorithm; 
conv 
logical indicating if the converged. This is defined as

Martin Maechler did the present class implementation; Rousseeuw et al did the underlying code.
Pison, G., Struyf, A. and Rousseeuw, P.J. (1999)
Displaying a Clustering with CLUSPLOT,
Computational Statistics and Data Analysis, 30, 381–392.
D.M. Titterington (1976) Algorithms for computing Doptimal design on finite design spaces. In Proc.\ of the 1976 Conf.\ on Information Science and Systems, 213–216; John Hopkins University.
predict.ellipsoid
which is also the
predict
method for ellipsoid
objects.
volume.ellipsoid
for an example of ‘manual’
ellipsoid
object construction;
further ellipse
from package ellipse
and ellipsePoints
from package sfsmisc.
chull
for the convex hull,
clusplot
which makes use of this; cov.mve
.
x < rnorm(100) xy < unname(cbind(x, rnorm(100) + 2*x + 10)) exy < ellipsoidhull(xy) exy # >> calling print.ellipsoid() plot(xy, main = "ellipsoidhull(<Gauss data>)  'spanning points'") lines(predict(exy), col="blue") points(rbind(exy$loc), col = "red", cex = 3, pch = 13) exy < ellipsoidhull(xy, tol = 1e7, ret.wt = TRUE, ret.sq = TRUE) str(exy) # had small `tol', hence many iterations (ii < which(zapsmall(exy $ wt) > 1e6)) ## > only about 4 to 6 "spanning ellipsoid" points round(exy$wt[ii],3); sum(exy$wt[ii]) # weights summing to 1 points(xy[ii,], pch = 21, cex = 2, col="blue", bg = adjustcolor("blue",0.25))