A comparison of robust principal component analysis in high dimensions

It is rare for high-dimensional data to be clean in reality. There is a great need for robust principal component analysis (PCA) in high dimensional data analysis. However, most of the existing robust PCA methods are constructed based on the rowwise assumption. This assumption is too restrictive as it assumes that all the components are completely contaminated in an observation vector. It is more flexible and realistic to make the cellwise assumption in practice that only some components rather than all the components are contaminated in the observation vector. The objective of this paper is to extent the robust PCA method to the case with cellwise contaminated data and to compare with the existing rowwise methods. The proposed method can make use of information in clean elements of contaminated data, compared to the latter. The simulation results favor the proposed method.