首页|Enhanced Acceleration for Generalized Nonconvex Low-Rank Matrix Learning

Enhanced Acceleration for Generalized Nonconvex Low-Rank Matrix Learning

扫码查看
原文链接
  • NETL
  • NSTL
  • IEEE
Matrix minimization techniques that employ the nuclear norm have gained recognition for their applicability in tasks like image inpainting, clustering, classification, and reconstruction. However, they come with inherent biases and computational burdens, especially when used to relax the rank function, making them less effective and efficient in real-world scenarios. To address these challenges, our research focuses on generalized nonconvex rank regularization problems in robust matrix completion, low-rank representation, and robust matrix regression. We introduce innovative approaches for effective and efficient low-rank matrix learning, grounded in generalized nonconvex rank relaxations inspired by various substitutes for the $\ell_{0}$-norm relaxed functions. These relaxations allow us to more accurately capture low-rank structures. Our optimization strategy employs a nonconvex and multi-variable alternating direction method of multipliers, backed by rigorous theoretical analysis for complexity and convergence. This algorithm iteratively updates blocks of variables, ensuring efficient convergence. Additionally, we incorporate the randomized singular value decomposition technique and/or other acceleration strategies to enhance the computational efficiency of our approach, particularly for large-scale constrained minimization problems. In conclusion, our experimental results across a variety of image vision-related application tasks unequivocally demonstrate the superiority of our proposed methodologies in terms of both efficacy and efficiency when compared to most other related learning methods.

Learning systemsImage recognitionMinimizationComputational efficiencyComplexity theoryMatrix decompositionOptimizationImage reconstructionSingular value decompositionConvergence

Hengmin Zhang、Jian Yang、Wenli Du、Bob Zhang、Zhiyuan Zha、Bihan Wen

展开 >

School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

School of Computer Science and Engineering, Nanjing, University of Science and Technology, Nanjing, China

School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China

Department of Electrical and Computer Engineering, University of Macau, Macau, China

展开 >

2025

10.23919/cje.2023.00.340

Chinese journal of electronics

Chinese journal of electronics

ISSN：
年,卷(期)：2025.34(1)
  • 73