论文标题
Riemannian CUR分解可用于鲁棒的主成分分析
Riemannian CUR Decompositions for Robust Principal Component Analysis
论文作者
论文摘要
近年来，健壮的主成分分析（PCA）受到了广泛的关注。它旨在从其总和中恢复一个低级别矩阵和稀疏矩阵。本文提出了一种新型的非凸强壮PCA算法，即Riemannian Cur（riecur），它利用了Riemannian优化和强大的CUR分解概念。该算法与迭代的鲁棒cur具有相同的计算复杂性，后者目前是最新的，但对离群值更强。 Riecur还能够忍受大量的异常值，并且与加速的交替预测相媲美，交替的预测具有较高的离群公差，但计算复杂性比提议的方法差。因此，所提出的算法在计算复杂性和异常耐受性方面都在鲁棒PCA上实现了最先进的性能。
Robust Principal Component Analysis (PCA) has received massive attention in recent years. It aims to recover a low-rank matrix and a sparse matrix from their sum. This paper proposes a novel nonconvex Robust PCA algorithm, coined Riemannian CUR (RieCUR), which utilizes the ideas of Riemannian optimization and robust CUR decompositions. This algorithm has the same computational complexity as Iterated Robust CUR, which is currently state-of-the-art, but is more robust to outliers. RieCUR is also able to tolerate a significant amount of outliers, and is comparable to Accelerated Alternating Projections, which has high outlier tolerance but worse computational complexity than the proposed method. Thus, the proposed algorithm achieves state-of-the-art performance on Robust PCA both in terms of computational complexity and outlier tolerance.
