Multiple outlier detection in multivariate data using projection pursuit techniques

Abstract

Abstract Using projection pursuit techniques, in this paper we propose a procedure to detect multiple outliers in multivariate data. The basic idea behind this procedure is to project the multivariate data to univariate observations and then to apply an appropriate univariate outlier identifier to the projected data. The projected outlier identifier forms a centered Gaussian process on the high-dimensional unit sphere. When a set of directions is generated on the unit sphere, the projected outlier identifier on these directions then follows a multivariate normal distribution. In this way, an outlier identifier in the multivariate data with χ2-distribution is constructed. In order to have the outlier identifier revealing much information on multivariate outliers, the directions should be scattered uniformly on the unit sphere as much as possible, which can be implemented in terms of the quasi-Monte Carlo methods. For illustration, three practical data sets are analyzed and compared with existing methods. Also, a simulation is conducted to study the null properties of the multivariate outlier identifier.