Residual-Based Sampling for Online Outlier-Robust PCA

Outlier-robust principal component analysis (ORPCA) has been broadly applied in scientific discovery in the last decades. In this paper, we study online ORPCA, an important variant that addresses the practical challenge that the data points arrive in a sequential manner and the goal is to recover the underlying subspace of the clean data with one pass of the data. Our main contribution is the first provable algorithm that enjoys comparable recovery guarantee to the best known batch algorithm, while significantly improving upon the state-of-the-art online ORPCA algorithms. The core technique is a robust version of the residual norm which, informally speaking, leverages not only the importance of a data point, but also how likely it behaves as an outlier.