Sparse Principal Component Analysis Based on Least Trimmed Squares

Sparse principal component analysis (PCA) is used to obtain stable and interpretable principal components (PCs) from high-dimensional data. A robust sparse PCA method is proposed to handle potential outliers in the data. The proposed method is based on the least trimmed squares PCA method which provides robust but non-sparse PC estimates. To obtain sparse solutions, our method incorporates a regularization penalty on the loading vectors. The principal directions are determined sequentially to avoid that outliers in the PC subspace destroy the sparse structure of the loadings. Simulation studies and real data examples show that the new method gives accurate estimates, even when the data are highly contaminated. Moreover, compared to existing robust sparse PCA methods the computation time is reduced to a great extent. Supplementary materials providing more simulation results and discussion, and an R package to compute the proposed method are available online.