Two Proposals for Robust PCA using Semidefinite Programming

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, \emph{maximum mean absolute deviation rounding} (\mdr), seeks directions of large spread in the data while damping the effect of outliers. The second method produces a \emph{low-leverage decomposition} (\lld) of the data that attempts to form a low-rank model for the data by separating out corrupted observations. This paper also presents efficient computational methods for solving these SDPs. Numerical experiments confirm the value of these new techniques.