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Applied Usage of the Minimum-Volume Ellipsoid

Kim van der Linde & David Houle

Abstract: The minimum volume ellipsoid (MVE) method is a powerful algorithm for detecting multivariate outliers. We report here extensions to the method that facilitate its use when variance-covariance matrices may be singular and when outliers can be checked to determine whether they are caused by measurement error or a truly anomalous observation. Before applying MVE, we perform a principal-components analysis and retain only those eigenvectors with positive eigenvalues. To facilitate the investigation of outliers, we rank them from the highest distance score to the lowest. In our application, the highest scores are almost inevitably erroneous measurements that should be corrected, whereas the lowest scores arise from slight departures from multivariate normality and are not removed. Elements of this approach are applicable to many other sets of multivariate data.

Availability: Platform independent Java implementations of PCA-MVE (http://www.kimvdlinde.com/professional/pcamve.html) and MVE (http://www.kimvdlinde.com/professional/mve.html) are available. They can be used directly from the website (with copy-paste data entry) or downloaded (with file import data entry) for offline use.