文献类型：会议论文

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]Univ Macau, Dept Comp & Informat Sci, Taipa 999078, Macao, Peoples R China;[2]East China Univ Sci & Technol, Sch Informat Sci & Engn, Key Lab Adv Smart Mfg Energy Chem Proc, Minist Educ, Shanghai 200237, Peoples R China;[3]South China Agr Univ, Coll Math & Informat, Guangzhou 510642, Peoples R China;[4]Nanjing Univ Sci & Technol, Sch Comp Sci & Engn, Nanjing 210094, Peoples R China

会议论文集：11th International Conference on Image and Graphics (ICIG)

会议日期：AUG 06-08, 2021

会议地点：China Soc Image & Graph, Haikou, PEOPLES R CHINA

主办单位：China Soc Image & Graph

语种：英文

外文关键词：Low rank matrix recovery; Nonconvex rank regularization; Convergence analysis; Nonconve ADMM; KKT conditions

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.