Low-Rank Approximation of Data Matrices Using Robust Sparse Principal Component Analysis

The estimation of principal components can be influenced by outlying observations, so-called row-wise outliers. For high-dimensional data, it becomes more and more likely that an observation contains outlying cells, which would lead to many row-wise outliers and to a breakdown of traditional robust methods. In this case, it is preferable to achieve protection against cell-wise outliers. We present various approaches for principal component analysis that lead to row-wise and cell-wise robustness. Moreover, we focus on sparse methods that enforce zeros in the loadings matrix and thus simplify the interpretation.