A Comparison of Three Procedures for Robust PCA in High Dimensions

• Main Authors: S. Engelen, M. Hubert, K. Vanden Branden
• Format: Article
• Language: English
• Published: Austrian Statistical Society 2016-04-01
• Series: Austrian Journal of Statistics
• Online Access: http://www.ajs.or.at/index.php/ajs/article/view/405

In this paper we compare three procedures for robust Principal Components Analysis (PCA). The first method is called ROBPCA (see Hubert et al., 2005). It combines projection pursuit ideas with robust covariance estimation. The original algorithm for its computation is designed to construct an optimal PCA subspace of a fixed dimension k. If instead the optimal PCA subspace is searched within a whole range of dimensions k, this algorithm is not computationally efficient. Hence we present an adjusted algorithm that yields several PCA models in one single run. A different approach is the LTS-subspace estimator (see Wolbers, 2002; Maronna, 2005). It seeks for the subspace that minimizes an objective function based on the squared orthogonal distances of the observations to this subspace. It can be computed in analogy with the computation of the LTS regression estimator (see Rousseeuw and Van Driessen, 2000). The three approaches are compared by means of a simulation study.