ellipsoidhull {cluster} | R Documentation |
Compute the Ellipsoid Hull or Spanning Ellipsoid of a Point Set
Description
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.
Usage
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), ...)
Arguments
x |
the |
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 |
Details
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.
Value
an object of class "ellipsoid"
, basically a list
with several components, comprising at least
cov |
|
loc |
|
d2 |
average squared radius. Further, |
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 |
ierr |
error code as from the algorithm; |
conv |
logical indicating if the converged. This is defined as
|
Author(s)
Martin Maechler did the present class implementation; Rousseeuw et al did the underlying original code.
References
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 D-optimal design on finite design spaces. In Proc.\ of the 1976 Conf.\ on Information Science and Systems, 213–216; John Hopkins University.
See Also
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
.
Examples
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 = 1e-7, ret.wt = TRUE, ret.sq = TRUE)
str(exy) # had small 'tol', hence many iterations
(ii <- which(zapsmall(exy $ wt) > 1e-6))
## --> 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))