Sparse PCA for High-Dimensional Data With Outliers

Abstract

A new sparse PCA algorithm is presented, which is robust against outliers. The approach is based on the ROBPCA algorithm that generates robust but nonsparse loadings. The construction of the new ROSPCA method is detailed, as well as a selection criterion for the sparsity parameter. An extensive simulation study and a real data example are performed, showing that it is capable of accurately finding the sparse structure of datasets, even when challenging outliers are present. In comparison with a projection pursuit-based algorithm, ROSPCA demonstrates superior robustness properties and comparable sparsity estimation capability, as well as significantly faster computation time.

• Dimension reduction
• Outlier detection
• Robustness.

ACKNOWLEDGMENTS

Mia Hubert acknowledges the financial support of the Internal Fund of KU Leuven and of the IAP Research Network P7/06 of the Belgian Science Policy.