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 p-dimensional 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` as well. |

`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, `ret.wt` specifying the
weights, `ret.sqdist` the and squared
distances`ret.pr` the final probabilities
in the algorithms. |

`digits,...` |
the usual arguments to `print` methods. |

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` |
p-dimensional location of the ellipsoid center. |

`d2` |
average squared radius. |

`wt` |
the vector of weights iff `ret.wt` was true. |

`sqdist` |
the vector of squared distances iff `ret.sqdist` was true. |

`prob` |
the vector of algorithm probabilities iff `ret.pr` was true. |

`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; `0` means ok. |

`conv` |
logical indicating if the converged. This is defined as
`it < maxit && ierr == 0` . |

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.

A version of this is available as technical report from
http://win-www.uia.ac.be/u/statis/abstract/Disclu99.htm

D.N. 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.

`predict.ellipsoid`

which is also the
`predict`

method for `ellipsoid`

objects.

`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) lines(predict(exy)) 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 points round(exy$wt[ii],3); sum(exy$wt[ii]) # sum to 1

[Package *cluster* version 1.10.2 Index]