Minimum Volume Ellipsoid estimation

Download executable JAR file (double click after saving to run it)

Webstart

For the version performing first a PCA to deal with singular matrices, see PCA-MVE.

See the Applied Usage of the Minimum-Volume Ellipsoid paper for more details.

This method is used for robust outlier detection in multivariate space. The algorithm takes subsamples of the dataset and calculates the Volume of the Ellipsoid representing that subsample. Outliers increase the volume dramatically, so the Minimum Volume Ellipsoid (MVE) will correspond with the actual core of the dataset. After this, data points exceeding the cut-off value for the Mahalanobis distance will be designated outliers.

This method was developed by Peter J. Rousseeuw of the Antwerp Group On Robust & Applied Statistics and published in 1985 (Rousseeuw P.J., Multivariate estimation with high breakdown point. In: Grossman W., Pflug G., Vincze I., Wertz W. (eds.) Mathematical Statistics and Applications. Reidel, Dordrecht, The Netherlands, p. 283) and improved later in Rousseeuw P.J. & Leroy A., (1987), Robust regression and outlier detection. New York, John Wiley.

They developed a fortran program that does the job, and the method isimplemented in S-PLUS (as the function cov.mve ) and in SAS /IML Version 6.12 and later ( as the call MVE ) and supposingly also in R.

Based on the fortran code and the 1987 publication, I have developed a java class that calculates the MVE of a given dataset. The program was tested on thier brainlog data set . The output of thier fortran implementation and this java implementation are available.

The program needs the Java Runtime Environment available from the java site of SUN

There are two options:

• either download it as jar file which enables you to load and save files. To execute it use <path to jar file>/java -jar rma.jar or let for example windows handle it from the download dialog box (works wonders under my Mozilla and win XP system).
• or use the java webstart option. As java webstart programs run in a so-called sandbox, it can not access files on the hard disk so it works with an input dialog and can not save the results.

Cite this as:
Kim van der Linde (2004) MVE: Minimum Volume Ellipsoid estimation for robust outlier detection in multivariate space, Java version. Website: http://www.kimvdlinde.com/professional/mve.html.

Cited in:

• Neil J. Cornish, Tyson B. Littenberg (2007) Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

Version History:

• Version 1.0 (28 October 2004):
  • released.
• Version 1.1 (28 November 2004):
  • added sorted output option.