Enhanced Acceleration for Generalized Nonconvex Low-Rank Matrix Learning

ZHANG Hengmin; YANG Jian; DU Wenli; ZHANG Bob; ZHA Zhiyuan; WEN Bihan

doi:10.23919/cje.2023.00.340

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Hengmin ZHANG, Jian YANG, Wenli DU, et al., “Enhanced Acceleration for Generalized Nonconvex Low-Rank Matrix Learning,” Chinese Journal of Electronics, vol. x, no. x, pp. 1–16, xxxx doi: 10.23919/cje.2023.00.340

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Hengmin ZHANG, Jian YANG, Wenli DU, et al., “Enhanced Acceleration for Generalized Nonconvex Low-Rank Matrix Learning,” Chinese Journal of Electronics, vol. x, no. x, pp. 1–16, xxxx doi: 10.23919/cje.2023.00.340

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Enhanced Acceleration for Generalized Nonconvex Low-Rank Matrix Learning

doi: 10.23919/cje.2023.00.340

ZHANG Hengmin^1
,,
YANG Jian^2
,,
DU Wenli^3
,,
ZHANG Bob^4
,,
ZHA Zhiyuan^1
,,
WEN Bihan^{1
,
,}

1.
Nanyang Technological University, Singapore 639798, Singapore
2.
Nanjing University of Science and Technology, Nanjing 210094, China
3.
East China University of Science and Technology, Shanghai 200237, China
4.
University of Macau, Macau 999078, China

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Author Bio:
Hengmin ZHANG received a Ph.D. degree from the School of Computer Science and Engineering, Nanjing University of Science and Technology (NJUST), Nanjing, China, in 2019. He was a Post-Doctoral Fellow with the School of Information Science and Engineering, East China University of Science and Technology (ECUST), Shanghai, China, and also with a Post-Doctoral Fellow with the PAMI Research Group, Department of Computer and Information Science, University of Macau (UM), Macau, China, from 2019 to 2022. He is currently a Research Fellow with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore. He has published more than 30 technical papers at prominent journals and conferences. His research interests include sparse coding and low-rank matrix recovery, nonconvex optimizations, and large-scale representation learning methods. (Email: hengmin.zhang@ntu.edu.sg, hengmin.zhang@ntu.edu.sg)

Jian YANG received the Ph.D. degree in Pattern Recognition and Intelligence Systems from the Nanjing University of Science and Technology (NJUST), Nanjing, China, in 2002. In 2003, he was a Post-Doctoral Researcher with the University of Zaragoza, Zaragoza, Spain. From 2004 to 2006, he was a Post-Doctoral Fellow with the Biometrics Centre, The Hong Kong Polytechnic University, Hong Kong, China. From 2006 to 2007, he was a Post-Doctoral Fellow with the Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, USA. He is currently a Chang-Jiang Professor with the School of Computer Science and Engineering, NJUST. He has authored more than 400 scientific papers in pattern recognition, computer vision, and machine learning. His papers have been cited more than 41000 times in the Scholar Google. His research interests include pattern recognition, computer vision, and machine learning. Moreover, Prof. Yang is a fellow of International Association for Pattern Recognition, i.e., IAPR Fellow. He is/was an Associate Editor of Pattern Recognition, Pattern Recognition Letters, the IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, and Neurocomputing. (Email:csjyang@njust.edu.cn)

Wenli DU received the B.S. and M.S. degrees in Chemical Process Control from the Dalian University of Technology, Dalian, China, in 1997 and 2000, respectively, and the Ph.D. degree in Control Theory and Control Engineering from the East China University of Science and Technology, Shanghai, China, in 2005. She is currently a Professor of the College of Information Science and Engineering and serves as the Dean of Graduate School, East China University of Science and Technology, and is also the Vice-director of Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology. Her research interests include control theory and applications, system modeling, advanced control, and process optimization. (Email: wldu@ecust.edu.cn)

Bob ZHANG received the Ph.D. degree in Electrical and Computer Engineering from the University of Waterloo, Waterloo, ON, Canada, in 2011. He was with the Center for Pattern Recognition and Machine Intelligence and later was a Post-Doctoral Researcher with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA. He is currently an Associate Professor with the Department of Computer and Information Science, University of Macau, Macau, China. In addition, he is/was also a Technical Committee Member of the IEEE Systems, Man, and Cybernetics Society, and an Associate Editor of IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS, IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, Artificial Intelligence Review, and IET Computer Vision. His research interests include biometrics, pattern recognition, feature extraction/detection, and image processing. (Email: bobzhang@um.edu.mo)

Zhiyuan ZHA received the Ph.D. degree from the School of Electronic Science and Engineering, Nanjing University, Nanjing, China, in 2018. He is currently a Senior Post-Doctoral Research Fellow with Nanyang Technological University, Singapore. Dr. Zha was a recipient of the Platinum Best Paper Award and the Best Paper Runner-Up Award at the IEEE International Conference on Multimedia and Expo (ICME) in 2017 and 2020, respectively. He has been an Associate Editor of the visual computer since 2023. His research interests include inverse problems in image/video processing, sparse signal representation, and machine learning. (Email:zhiyuan.zha@ntu.edu.sg)

Bihan WEN received the B.S. degree in Electrical and Electronic Engineering from Nanyang Technological University, Singapore, Singapore, in 2012, and the M.S. and Ph.D. degrees in Electrical and Computer Engineering from the University of Illinois at Urbana-Champaign, Champaign, IL, USA, in 2015 and 2018, respectively. He is currently a Nanyang Assistant Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University. He was a recipient of the 2016 Yee Fellowship and the 2012 Professional Engineers Board Gold Medal, Singapore. He was also a recipient of the Best Paper Runner Up Award at the IEEE International Conference on Multimedia and Expo in 2020. He has been an Associate Editor of IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY since 2022, and an Associate Editor of MDPI MICROMACHINES since 2021. He is a Guest Editor for IEEE SIGNAL PROCESSING MAGAZINE from 2021 to 2023, and a Guest Editor for IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING from 2023 to 2025. His research interests include machine learning, computational imaging, computer vision, image and video processing, and big data applications. (Email: bihan.wen@ntu.edu.sg)
Corresponding author: Email: bihan.wen@ntu.edu.sg
Received Date: 2023-10-26
Accepted Date: 2024-01-10
Rev Recd Date: 2023-11-27

Available Online: 2024-03-02

Abstract

Abstract

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 (RMC), low-rank representation (LRR), and robust matrix regression (RMR). 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 (ADMM), 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 (RSVD) 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.

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References(72)

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