Comparing Classical and Robust Sparse PCA

The main drawback of principal component analysis (PCA) especially for applications in high dimensions is that the extracted components are linear combinations of all input variables. To facilitate the interpretability of PCA various sparse methods have been proposed recently. However all these methods might suffer from the influence of outliers present in the data. An algorithm to compute sparse and robust PCA was recently proposed by Croux et al. We compare this method to standard (non-sparse) classical and robust PCA and several other sparse methods. The considered methods are illustrated on a real data example and compared in a simulation experiment. It is shown that the robust sparse method preserves the sparsity and at the same time provides protection against contamination.