| The minimum volume ellipsoid (MVE) is a useful construct for computing robust multivariate outlier diagnostics and robust covariance matrix estimates. Exact computation of the MVE is impractical for all but the smallest data sets. A variety of approaches have been developed for approximating the MVE. We review these approaches, and propose a new approach, a direct search of the ellipsoid space. An original, matrix-based genetic algorithm is developed for performing this search. Algorithm settings are tuned using designed experiments. Evidence is provided to document the performance of the new genetic algorithm compared to existing techniques. The new matrix-based genetic algorithm is found to be capable of detecting outliers in high contamination data sets where other approaches fail. |
