Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants
Efficient Optimization Algorithms for Robust Principal Component Analysis and Its Variants
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DOI：
10.1109/jproc.2018.2846606
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发表时间：
2018-06
影响因子：
20.6
通讯作者：
Shiqian Ma;N. Aybat
中科院分区：
文献类型：
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作者：
Shiqian Ma;N. Aybat
鲁棒主成分分析（RPCA）在过去十年中因其在众多应用领域的成功而引起了极大的关注，从生物信息学、统计学、机器学习到计算机视觉中的图像和视频处理。RPCA及其变体，如稀疏主成分分析和稳定主成分分析，可以表述为具有可利用的特殊结构的优化问题。为了解决鲁棒主成分分析和相关问题，已经提出了许多专门的高效优化方法。本文综述了求解RPCA的凸松弛和非凸松弛/变异体的现有优化方法，讨论了它们的优缺点，并阐述了它们的收敛性。我们还对未来可能的研究方向提供了一些见解，包括可能适合在多处理器设置上实现以处理大规模问题的新算法框架。
Robust principal component analysis (RPCA) has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bioinformatics, statistics, and machine learning to image and video processing in computer vision. RPCA and its variants such as sparse PCA and stable PCA can be formulated as optimization problems with exploitable special structures. Many specialized efficient optimization methods have been proposed to solve robust PCA and related problems. In this paper, we review existing optimization methods for solving convex and nonconvex relaxations/variants of RPCA, discuss their advantages and disadvantages, and elaborate on their convergence behaviors. We also provide some insights for possible future research directions including new algorithmic frameworks that might be suitable for implementing on multiprocessor setting to handle large-scale problems.