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	Large-Scale Affine Matrix Rank Minimization With a Novel Nonconvex Regularizer
	Wang, Zhi1; Liu, Yu2; Luo, Xin3,4; Wang, Jianjun5; Gao, Chao1; Peng, Dezhong6; Chen, Wu1
	2021-02-27
摘要	Low-rank minimization aims to recover a matrix of minimum rank subject to linear system constraint. It can be found in various data analysis and machine learning areas, such as recommender systems, video denoising, and signal processing. Nuclear norm minimization is a dominating approach to handle it. However, such a method ignores the difference among singular values of target matrix. To address this issue, nonconvex low-rank regularizers have been widely used. Unfortunately, existing methods suffer from different drawbacks, such as inefficiency and inaccuracy. To alleviate such problems, this article proposes a flexible model with a novel nonconvex regularizer. Such a model not only promotes low rankness but also can be solved much faster and more accurate. With it, the original low-rank problem can be equivalently transformed into the resulting optimization problem under the rank restricted isometry property (rank-RIP) condition. Subsequently, Nesterov's rule and inexact proximal strategies are adopted to achieve a novel algorithm highly efficient in solving this problem at a convergence rate of O(1/K), with K being the iterate count. Besides, the asymptotic convergence rate is also analyzed rigorously by adopting the Kurdyka-Lojasiewicz (KL) inequality. Furthermore, we apply the proposed optimization model to typical low-rank problems, including matrix completion, robust principal component analysis (RPCA), and tensor completion. Exhaustively empirical studies regarding data analysis tasks, i.e., synthetic data analysis, image recovery, personalized recommendation, and background subtraction, indicate that the proposed model outperforms state-of-the-art models in both accuracy and efficiency.
关键词	Minimization Convergence Tensors Optimization Analytical models Data models Data analysis Inexact proximal step low-rank minimization matrix completion novel nonconvex regularizer robust principal component analysis (RPCA) tensor completion
DOI	10.1109/TNNLS.2021.3059711
发表期刊	IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
ISSN	2162-237X
页码	15
通讯作者	Wang, Jianjun(jjw@swu.edu.cn) ; Chen, Wu(chenwu@swu.edu.cn)
收录类别	SCI
WOS记录号	WOS:000733524900001
语种	英语