mvee_REX {OptimalDesign}

Minimum-volume enclosing ellipsoid

Description

Computes the shape matrix H and the center z of the minimum-volume ellipsoid enclosing a finite set of data-points.

Usage

mvee_REX(Data, alg.AA="REX", eff=0.999999, it.max=Inf, t.max=60,
         picture=FALSE, echo=TRUE, track=TRUE)

Arguments

Data

the n times d (where d<n) matrix containing the d-dimensional data-vectors as rows.

alg.AA

the underlying computational method for approximate D-optimal design; possible values are "REX", "MUL" and "VDM".

eff

the minimum required efficiency.

it.max

a limit on the number of iterations of the underlying D-optimum approximate design algorithm.

t.max

a limit on the time of computation.

picture

Should a picture be plotted? (For the picture, the data need to be either two- or three-dimensional.)

echo

Print the call of the function?

track

Display the progress of the computation?

Details

The problem of the minimum-volume data-enclosing ellipsoid (MVEE) is computationally equivalent to the problem of D-optimal approximate design for an artificial problem based on the data. This procedure performs the computation and the proper conversion of the D-optimal approximate design to the MVEE parameters (the center and the shape matrix).

Value

Output is a list with components:

call

the call of the function

H

the shape matrix of the MVEE

z

the center of the MVEE

bpts

a set containing the boundary points of the MVEE

vol

the volume of the MVEE

eff.best

the actual precision of the result (1 is the perfect precision)

t.iter

the number of iterations of the underlying D-optimum design algorithm

t.act

the actual time of the computation

Note

Note: The affine hull of the rows of X should be the full space of dimension d. For the choice of the algorithm, see the comments in od_REX.

Author(s)

Radoslav Harman, Lenka Filova

References

Harman R, Filova L, Richtarik P (2019). A randomized exchange algorithm for computing optimal approximate designs of experiments. Journal of the American Statistical Association, 1-30.

See Also

od_REX

Examples

# Generate random 1000 points in a 3-dimensional space
# and compute the MVEE

Data <- matrix(rnorm(3000), ncol = 3)
mvee_REX(Data, picture = FALSE)