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 the expensive computing on 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.

中文翻译：

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快速鲁棒主成分分析：CUR 加速的不精确低秩估计

稳健主成分分析 (RPCA) 是一种广泛使用的降维工具。在这项工作中，我们提出了一种新的非凸算法，创造了迭代鲁棒 CUR (IRCUR)，用于解决 RPCA 问题，与现有算法相比，它显着提高了计算效率。IRCUR 通过在更新低秩分量时采用 CUR 分解来实现这种加速，这使我们能够仅通过三个小子矩阵获得准确的低秩近似。因此，IRCUR 能够只处理小子矩阵，并通过整个算法避免对完整矩阵进行昂贵的计算。数值实验证明了 IRCUR 在合成和现实世界数据集上优于最先进算法的计算优势。