Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art algorithms usually need to solve singular value decomposition of large matrices, which generally has at least a quadratic or even cubic complexity. This drawback has limited the application of RPCA in solving real world problems. To combat this drawback, in this paper we propose a new type of RPCA method, RES-PCA, which is linearly efficient and scalable in both data size and dimension. For comparison purpose, AltProj, an existing scalable approach to RPCA requires the precise knowlwdge of the true rank; otherwise, it may fail to recover low-rank matrices. By contrast, our method works with or without knowing the true rank; even when both methods work, our method is faster. Extensive experiments have been performed and testified to the effectiveness of proposed method quantitatively and in visual quality, which suggests that our method is suitable to be employed as a light-weight, scalable component for RPCA in any application pipelines.
翻译:主要主要组成部分分析(RPCA)因其恢复低级矩阵的强大能力以及在各种现实世界问题中的成功应用而引起人们的极大关注。目前最先进的算法通常需要解决大型矩阵的单值分解问题,而大矩阵通常至少具有二次或甚至立方复杂程度。这一缺陷限制了RPCA在解决现实世界问题方面的应用。为了克服这一缺陷,我们在本文件中提出了一种新的RPCA方法,RES-PCA,该方法在数据大小和维度上均具有线性效率且可伸缩。为比较起见,AltProj,现有对RPCA的可伸缩方法需要准确了解真实等级;否则,它可能无法恢复低级矩阵。相比之下,我们的方法与真实等级或不知道真实等级一起工作;即使两种方法都工作有效,我们的方法也比较快。进行了广泛的实验,并证明拟议的方法在定量和视觉质量上都具有效力,这表明我们的方法在任何RPCA的任何应用中都适合用作轻度、可伸缩的管道组件。