Efficient image classification via structured low-rank matrix factorization regression

In real-world applications involving sparse coding and low-rank matrix recovery problems, linear regression methods usually struggle to effectively capture the structured correlations present in data matrices. This limitation arises from representation approaches that treat images as vectors and han...

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Main Authors: Zhang, Hengmin, Yang, Jian, Qian, Jianjun, Gao, Guangwei, Lan, Xiangyuan, Zha, Zhiyuan, Wen, Bihan
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2024
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Online Access:https://hdl.handle.net/10356/173295
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1732952024-01-23T06:00:26Z Efficient image classification via structured low-rank matrix factorization regression Zhang, Hengmin Yang, Jian Qian, Jianjun Gao, Guangwei Lan, Xiangyuan Zha, Zhiyuan Wen, Bihan School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Low-Rank Matrix Regression Matrix Factorization In real-world applications involving sparse coding and low-rank matrix recovery problems, linear regression methods usually struggle to effectively capture the structured correlations present in data matrices. This limitation arises from representation approaches that treat images as vectors and handle testing samples individually, overlooking these correlations. To address these challenges, we propose a novel approach that leverages the low-rank property to capture the global and intrinsic structure of residual and coefficient matrices, departing from the assumption of independent and identically distributed (I.I.D) data. Our method introduces nonconvex and nonsmooth low-rank matrix regression models guided by the extended matrix variate power exponential distribution (M.P.E.D). By incorporating factorization strategies into the regression coefficient matrix and utilizing the Schatten- p norm with three distinct values of p , we enhance computational efficiency. Our formulation enables efficient subproblem solving through the introduction of auxiliary variables and the use of singular value threshold operators. We achieve closed-form solutions using the proposed multi-variable alternating direction method of multipliers (ADMM). Theoretical analysis establishes the local convergence properties and computational complexity of our optimization algorithm. Furthermore, we conduct numerical experiments on various image datasets, including face, object, and digital, to demonstrate the superior performance and computational efficiency of our methods compared to several related regression approaches. The source codes for our method are available at https://github.com/ZhangHengMin/TIFS_SLRMFR. Ministry of Education (MOE) This work was supported in part by the Ministry of Education, Republic of Singapore, through its Start-Up Grant and Academic Research Fund Tier 1 under Grant RG61/22; in part by the National Natural Science Fund (NSF) of China under Grant 61906067, Grant 61972212, and Grant 62176124; in part by the Peng Cheng Laboratory Key Project under Grant PCL2023A08; in part by the China Post-Doctoral Science Foundation under Grant 2019M651415 and Grant 2020T130191; and in part by the Fundamental Research Funds for the Central Universities under Grant 30918014108. 2024-01-23T06:00:26Z 2024-01-23T06:00:26Z 2024 Journal Article Zhang, H., Yang, J., Qian, J., Gao, G., Lan, X., Zha, Z. & Wen, B. (2024). Efficient image classification via structured low-rank matrix factorization regression. IEEE Transactions On Information Forensics and Security, 19, 1496-1509. https://dx.doi.org/10.1109/TIFS.2023.3337717 1556-6013 https://hdl.handle.net/10356/173295 10.1109/TIFS.2023.3337717 2-s2.0-85179119622 19 1496 1509 en RG61/22 IEEE Transactions on Information Forensics and Security © 2023 IEEE. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Low-Rank Matrix Regression
Matrix Factorization
spellingShingle Engineering::Electrical and electronic engineering
Low-Rank Matrix Regression
Matrix Factorization
Zhang, Hengmin
Yang, Jian
Qian, Jianjun
Gao, Guangwei
Lan, Xiangyuan
Zha, Zhiyuan
Wen, Bihan
Efficient image classification via structured low-rank matrix factorization regression
description In real-world applications involving sparse coding and low-rank matrix recovery problems, linear regression methods usually struggle to effectively capture the structured correlations present in data matrices. This limitation arises from representation approaches that treat images as vectors and handle testing samples individually, overlooking these correlations. To address these challenges, we propose a novel approach that leverages the low-rank property to capture the global and intrinsic structure of residual and coefficient matrices, departing from the assumption of independent and identically distributed (I.I.D) data. Our method introduces nonconvex and nonsmooth low-rank matrix regression models guided by the extended matrix variate power exponential distribution (M.P.E.D). By incorporating factorization strategies into the regression coefficient matrix and utilizing the Schatten- p norm with three distinct values of p , we enhance computational efficiency. Our formulation enables efficient subproblem solving through the introduction of auxiliary variables and the use of singular value threshold operators. We achieve closed-form solutions using the proposed multi-variable alternating direction method of multipliers (ADMM). Theoretical analysis establishes the local convergence properties and computational complexity of our optimization algorithm. Furthermore, we conduct numerical experiments on various image datasets, including face, object, and digital, to demonstrate the superior performance and computational efficiency of our methods compared to several related regression approaches. The source codes for our method are available at https://github.com/ZhangHengMin/TIFS_SLRMFR.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Zhang, Hengmin
Yang, Jian
Qian, Jianjun
Gao, Guangwei
Lan, Xiangyuan
Zha, Zhiyuan
Wen, Bihan
format Article
author Zhang, Hengmin
Yang, Jian
Qian, Jianjun
Gao, Guangwei
Lan, Xiangyuan
Zha, Zhiyuan
Wen, Bihan
author_sort Zhang, Hengmin
title Efficient image classification via structured low-rank matrix factorization regression
title_short Efficient image classification via structured low-rank matrix factorization regression
title_full Efficient image classification via structured low-rank matrix factorization regression
title_fullStr Efficient image classification via structured low-rank matrix factorization regression
title_full_unstemmed Efficient image classification via structured low-rank matrix factorization regression
title_sort efficient image classification via structured low-rank matrix factorization regression
publishDate 2024
url https://hdl.handle.net/10356/173295
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