Detecting multivariate outliers using projection pursuit with particle swarm optimization

Detecting outliers in the context of multivariate data is known as an important but difficult task and there already exist several detection methods. Most of the proposed methods are based either on the Mahalanobis distance of the observations to the center of the distribution or on a projection pursuit (PP) approach. In the present paper we focus on the one-dimensional PP approach which may be of particular interest when the data are not elliptically symmetric. We give a survey of the statistical literature on PP for multivariate outliers detection and investigate the pros and cons of the different methods. We also propose the use of a recent heuristic optimization algorithm called Tribes for multivariate outliers detection in the projection pursuit context.