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

• URL: http://arxiv.org/abs/2010.07422v3
• Date: Sun, 7 Feb 2021 06:43:25 GMT
• Title: Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation
• Authors: HanQin Cai, Keaton Hamm, Longxiu Huang, Jiaqi Li, Tao Wang
• Abstract summary: We propose a novel non-RPC algorithm coined Iterated Robust CUR (IRCUR) IRCUR is able to process only small submatrices and avoid expensive computing on the full matrix through the entire algorithm. Numerical experiments establish the computational advantage of IRCUR on both synthetic and real-world datasets.
• Score: 8.169365031508885
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the computational efficiency in comparison with the existing algorithms. IRCUR achieves this acceleration by employing CUR decomposition when updating the low rank component, which allows us to obtain an accurate low rank approximation via only three small submatrices. Consequently, IRCUR is able to process only the small submatrices and avoid expensive computing on the full matrix through the entire algorithm. Numerical experiments establish the computational advantage of IRCUR over the state-of-art algorithms on both synthetic and real-world datasets.

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