title: Relations Among Some Low-Rank Subspace Recovery Models.
abstract: Recovering intrinsic low-dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, a lot of work has modeled subspace recovery as low-rank minimization problems. We find that some representative models, such as robust principal component analysis (R-PCA), robust low-rank representation (R-LRR), and robust latent low-rank representation (R-LatLRR), are actually deeply connected. More specifically, we discover that once a solution to one of the models is obtained, we can obtain the solutions to other models in closed-form formulations. Since R-PCA is the simplest, our discovery makes it the center of low-rank subspace recovery models. Our work has two important implications. First, R-PCA has a solid theoretical foundation. Under certain conditions, we could find globally optimal solutions to these low-rank models at an overwhelming probability, although these models are nonconvex. Second, we can obtain significantly faster algorithms for these models by solving R-PCA first. The computation cost can be further cut by applying low-complexity randomized algorithms, for example, our novel l2,1 filtering algorithm, to R-PCA. Although for the moment the formal proof of our l2,1 filtering algorithm is not yet available, experiments verify the advantages of our algorithm over other state-of-the-art methods based on the alternating direction method.
authors.affiliation: Key Laboratory of Machine Perception, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China, and Cooperative Medianet Center, Shanghai Jiaotong University, Shanghai 200240, China hy_zh@pku.edu.cn.
authors.forename: Hongyang
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Key Laboratory of Machine Perception, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China, and Cooperative Medianet Center, Shanghai Jiaotong University, Shanghai 200240, China zlin@pku.edu.cn.
authors.forename: Zhouchen
authors.initials: Z
authors.lastname: Lin
authors.affiliation: Key Laboratory of Machine Perception, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China, and Cooperative Medianet Center, Shanghai Jiaotong University, Shanghai 200240, China chzhang@cis.pku.edu.cn.
authors.forename: Chao
authors.initials: C
authors.lastname: Zhang
authors.affiliation: School of Computing and Mathematics, Charles Sturt University, Bathurst, NSW 2795, Australia jbgao@csu.edu.au.
authors.forename: Junbin
authors.initials: J
authors.lastname: Gao