RAP: Scalable RPCA for low-rank matrix recovery

Recovering low-rank matrices is a problem common in many applications of data mining and machine learning, such as matrix completion and image denoising. Robust Principal Component Analysis (RPCA) has emerged for handling such kinds of problems; however, the existing RPCA approaches are usually computationally expensive, due to the fact that they need to obtain the singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA approach that eliminates the need for SVD of large matrices. Scalable algorithms are designed for several variants of our approach, which are crucial for real world applications on large scale data. Extensive experimental results confirm the effectiveness of our approach both quantitatively and visually.