Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose novel non-convex algorithm, coined Iterated CUR (IRCUR), solving RPCA problems, which dramatically improves the computational efficiency in comparison with existing algorithms. IRCUR achieves acceleration by employing decomposition when updating low rank component, allows us to obtain an accurate approximation via only three small submatrices. Consequently, able process submatrices and avoid expensive computing on full matrix through entire algorithm. Numerical experiments establish advantage of over state-of-art algorithms both synthetic real-world datasets.