文献类型：期刊文献

英文题名：Robust Recovery of Low Rank Matrix by Nonconvex Rank Regularization

作者：Zhang, Hengmin[1,2]; Luo, Wei[3]; Du, Wenli[2]; Qian, Jianjun[4]; Yang, Jian[4]; Zhang, Bob[1]

机构：[1] Department of Computer and Information Science, University of Macau, 999078, China; [2] School of Information Science and Engineering, Key Laboratory of Advanced Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai, 200237, China; [3] College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China; [4] School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

年份：2021

卷号：12889 LNCS

起止页码：106

外文期刊名：Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

收录：EI(收录号：20214211031082)

语种：英文

外文关键词：Computer vision

摘要：As we know, nuclear norm based regularization methods have the real-world applications in pattern recognition and computer vision. However, there exists a biased estimator when nuclear norm relaxes the rank function. To solve this issue, we focus on studying nonconvex rank regularization problems for both robust matrix completion (RMC) and low rank representation (LRR), respectively. By extending both to a general low rank matrix minimization problem, we develop a nonconvex alternating direction method of multipliers (ADMM). Moreover, the convergence results, i.e., the variable sequence generated by the nonconvex ADMM is bounded and its subsequence converges to a stationary point. Meanwhile, its limiting point satisfies the Karush-Kuhn-Tucher (KKT) conditions provided under some milder assumptions. Numerical experiments can verify the convergence properties of the theoretical results and the performance shows its superiority on both image inpainting and subspace clustering. ? 2021, Springer Nature Switzerland AG.