Computationally Easy Outlier Detection via Projection Pursuit with Finitely Many Directions

• Activity Number: 98
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Journal of Nonparmametric Statistics
• Author(s): Robert Serfling*+ and Robert Serfling
• Companies: The University of Texas at Dallas and The University of Texas at Dallas
• Keywords: Outlier detection ; Projection pursuit ; Nonparametric ; Multivariate ; Affine invariance

Abstract

Outlier detection methods are fundamental to all of data analysis. They are desirably robust, affine invariant, and computationally easy in any dimension. The powerful projection pursuit approach yields the "projection outlyingness", which is affine invariant and highly robust and does not impose ellipsoidal contours as with Mahalanobis distance. However, it is highly computationally intensive, taking suprema of univariate scaled deviation outlyingness over all projections of the data onto lines. Here we introduce an attractive quadratic form outlyingness function based on a vector of scaled deviations taken over only finitely many directions approximately uniform over the unit hypersphere. A preliminary strong invariant coordinate system transformation of the data makes such vectors affine invariant. We establish useful theory for such vectors and compare our method with the usual projection outlyingness and the Mahalanobis distance outlyingness using simulations and several real data sets. Other variants using finitely many projections have been formulated but give up affine invariance and/or entail random or data-driven directions and/or impose ellipsoidal contours.