Robust Principal Component Analysis with Adaptive Selection for Tuning Parameters

The present paper discusses robustness against outliers in a principal component analysis (PCA). We propose a class of procedures for PCA based on the minimum psi principle, which unifies various approaches, including the classical procedure and recently proposed procedures. The reweighted matrix algorithm for off-line data and the gradient algorithm for on-line data are both investigated with respect to robustness. The reweighted matrix algorithm is shown to satisfy a desirable property with local convergence, and the on-line gradient algorithm is shown to satisfy an asymptotical stability of convergence. Some procedures in the class involve tuning parameters, which control sensitivity to outliers. We propose a shape-adaptive selection rule for tuning parameters using K-fold cross validation.