论文标题
快速鲁棒的主成分分析：cur加速不切实际低等级估计
Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation
论文作者
论文摘要
鲁棒主成分分析（RPCA）是一种广泛使用的尺寸降低工具。在这项工作中，我们提出了一种新型的非凸算法，用于解决RPCA问题，该算法迭代了鲁棒性CUR（IRCUR），与现有算法相比，该问题显着提高了计算效率。 IRCUR在更新低级组件时采用CUR分解来实现此加速度，这使我们仅通过三个小型子膜即可获得准确的低级近似值。因此，IRCUR能够仅处理小型子膜片，并通过整个算法避免在完整矩阵上进行昂贵的计算。数值实验确定了IRCUR在合成数据集和现实世界中的最先进算法上的计算优势。
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.
