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matrix regression preserving projections for robust feature extraction

KNOWLEDGE-BASED SYSTEMS 2018年 161卷 35-46页

作者： Xie Luofeng Yin Ming Wang Ling Tan Feng Yin Guofu Sichuan Univ Sch Mfg Sci & Engn Chengdu 610065 Sichuan Peoples R China

Dimensionality reduction (DR) technique is a significant tool for feature extraction. In this paper, we propose an innovative two-dimensional (2D) algorithm for DR based on matrix regression model, termed matrix regression preserving projections (MRPP). Unlike many existing 2D algorithms, we construct weight matrix in the high-dimensional space based on nuclear norm (N-norm), which can well preserve the low-rank information of samples. Although MRPP is global in nature, it can also keep locality of data since it uses all training samples to reconstruct data. To make the distance metric more reliable and robust, we also replace F-norm with N-norm to calculate the reconstruction error in the projected space. Besides, L2,1-norm regularization is regularized on transformation matrix so that discrimination information can be learnt in the latent space. MRPP harnesses local and sparse preserving projections, and low rankness of high-dimensional data to build a graph. Therefore, it can learn a robust subspace from the corrupted data, i.e., illumination changes and occlusion. To verify the effectiveness of MRPP, we compare MRPP with a number of the state-of-the-art DR methods. Experiments on benchmark face datasets (Extend Yale B, CMU PIE, FERET, AR and LFW) demonstrate that MRPP outperforms the related state-of-the-arts with prominent results.

关键词： Feature extraction Image classification matrix regression Dimensionality reduction Subspace learning

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matrix regression heterogeneity analysis

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STATISTICS AND COMPUTING 2024年第3期34卷 1-12页

作者： Zhang, Fengchuan Zhang, Sanguo Li, Shi-Ming Ren, Mingyang Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China Chinese Acad Sci Key Lab Big Data Min & Knowledge Management Beijing Peoples R China Capital Med Univ Beijing Tongren Hosp Beijing Tongren Eye Ctr Beijing Key Lab Ophthalmol & Visual Sci Beijing Peoples R China Shanghai Jiao Tong Univ Sch Math Sci Shanghai Peoples R China

The development of modern science and technology has facilitated the collection of a large amount of matrix data in fields such as biomedicine. matrix data modeling has been extensively studied, which advances from the naive approach of flattening the matrix into a vector. However, existing matrix modeling methods mainly focus on homogeneous data, failing to handle the data heterogeneity frequently encountered in the biomedical field, where samples from the same study belong to several underlying subgroups, and different subgroups follow different models. In this paper, we focus on regression-based heterogeneity analysis. We propose a matrix data heterogeneity analysis framework, by combining matrix bilinear sparse decomposition and penalized fusion techniques, which enables data-driven subgroup detection, including determining the number of subgroups and subgrouping membership. A rigorous theoretical analysis is conducted, including asymptotic consistency in terms of subgroup detection, the number of subgroups, and regression coefficients. Numerous numerical studies based on simulated and real data have been constructed, showcasing the superior performance of the proposed method in analyzing matrix heterogeneous data.

关键词： Heterogeneity analysis matrix regression Penalized fusion Gene-environment interaction

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Single Image Self-Learning Super-Resolution with Robust matrix regression

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AATCC JOURNAL OF RESEARCH 2021年第1_SUPPL期8卷 135-142页

作者： Jian, Zhang Xu Tengteng Qian Jianjun Xiao, Yuchen Zhang, Heng Li, Hongran Li, Cunhua Jiangsu Ocean Univ Lianyungang Jiangsu Peoples R China China Univ Min & Technol Beijing Peoples R China Nanjing Univ Sci & Technol Nanjing Peoples R China

The similarity measure plays the key role in the self-learning framework for single image super-resolution. This paper involves matrix regression with properties of robustness and two-dimensional structure to measure the similarity between image blocks and enhance the effect of super-resolution. Specifically, we use the minimal nuclear norm of representation error as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the similarity between high- and low-resolution image blocks. Evaluation on several images with different interference and experimental results of super-resolution images clearly demonstrate the advantages of our proposed method in visual robustness and super-resolution effects.

关键词： Computer Vision Fabric Imaging Processing Image Super-Resolution matrix regression Similarity Measure

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Image deblurring with matrix regression and gradient evolution

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PATTERN RECOGNITION 2012年第6期45卷 2164-2179页

作者： Xiang, Shiming Meng, Gaofeng Wang, Ying Pan, Chunhong Zhang, Changshui Chinese Acad Sci Natl Lab Pattern Recognit Inst Automat Beijing 100190 Peoples R China Tsinghua Univ Tsinghua Natl Lab Informat Sci & Technol TNList Dept Automat Beijing 100084 Peoples R China

This paper presents a supervised learning algorithm for image deblurring. The task is addressed into the conceptual framework of matrix regression and gradient evolution. Specifically, given pairs of blurred image patches and their corresponding clear ones, an optimization framework of matrix regression is proposed to learn a matrix mapping. For an image to be deblurred, the learned matrix mapping will be employed to map each of its image patches directly to be a new one with more sharp details. The mapped result is then analyzed in terms of edge profiles, and the image is finally deblurred in way of gradient evolution. The algorithm is fast, and easy to be implemented. Comparative experiments on diverse natural images and the applications to interactive deblurring of real-world out-of-focus images illustrate the validity of our method. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Image deblurring Interactive deblurring matrix regression Gradient evolution Supervised learning

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Low-rank matrix regression for image feature extraction and feature selection

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INFORMATION SCIENCES 2020年 522卷 214-226页

作者： Yuan, Haoliang Li, Junyu Lai, Loi Lei Tang, Yuan Yan Guangdong Univ Technol Sch Automat Guangzhou Guangdong Peoples R China Univ Macau Zhuhai Sci & Technol Res Inst Macau Peoples R China UOW Coll Hong Kong Fac Sci & Technol Hong Kong Peoples R China

In many image processing and pattern recognition problems, the input data is commonly the images. The image could be represented as the matrix form. The natural structure information of the matrix is useful for data analysis and representation. However, most of existing methods commonly convert the image as a vector form, which destroys the natural structure of the image. To fully utilize this kind of structure information, we propose a low-rank matrix regression model for feature extraction and feature selection. To efficiently solve the objective functions of the proposed methods, we develop an optimization algorithm based on the alternating direction method of multipliers method. Promising experimental results have demonstrated the effectiveness of our proposed methods. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Feature extraction Feature selection Low-rank matrix regression

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Nonnegative spectral clustering and adaptive graph-based matrix regression for unsupervised image feature selection

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MULTIMEDIA TOOLS AND APPLICATIONS 2021年第21-23期80卷 32885-32904页

作者： Chen, Xiuhong Zhu, Xingyu Jiangnan Univ Sch Artificial Intelligence & Comp Sci Wuxi Jiangsu Peoples R China Jiangnan Univ Jiangsu Key Lab Media Design & Software Technol Wuxi Jiangsu Peoples R China

matrix regression model can directly take matrix data as input data, and its loss function is defined by left and right regression matrices. The spectral clustering-based matrix regression model can perform feature selection for unsupervised images. However, the graph weight matrix used in the existing spectral clustering models is predefined, which is often inaccurate, especially for noisy images. Moreover, they do not consider the preservation of local structure of image samples in transformation space. To this end, we propose a nonnegative spectral clustering and adaptive graph-based matrix regression model for unsupervised image feature selection. This model can make the prediction label matrix as smooth as possible on the whole graph, and the graph weight matrix can be adaptively learned instead of being predefined as fixed matrix. Thus, the accurate local structure of the sample data is preserved in transformation space and the discriminative information of these pseudo class labels can be revealed. Finally, we devise an efficient optimization algorithm to solve the proposed problem and analyze the computational complexity and convergence of the algorithm. Some experimental results on several datasets also show the effectiveness and superiority of our proposed method.

关键词： matrix regression Nonnegative spectral clustering Adaptive graph Unsupervised feature selection Convergence and complexity

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Bilateral Two-Dimensional matrix regression Preserving Discriminant Embedding for Corrupted Image Recognition

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IEEE ACCESS 2019年 7卷 13803-13816页

作者： Zhang, Jianbo Wang, Jinkuan Li, Mingwei Northeastern Univ Sch Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China Northeastern Univ Qinhuangdao Sch Math & Stat Qinhuangdao 066004 Peoples R China

Nuclear-norm-based matrix regression (NMR) methods have been successfully applied for the recognition of corrupted images. However, most of these methods do not consider the label information and are classified as unsupervised learning methods. In this paper, we propose a new regression-based algorithm, named bilateral two-dimensional matrix regression preserving discriminant embedding (B2DMRPDE). The proposed algorithm constructs the within-reconstruction graph and between-reconstruction graph using NMR. Then, B2DMRPDE aims to seek a subspace in which the within-class reconstructive residual is minimized and the between-class reconstructive residual is maximized based on Fisher's criterion. Hence, B2DMRPDE can capture the potential discriminative information for classification. To enhance the classification effectiveness, we present a new NMR-based classifier to determine the class label of the testing sample. Extensive experiments on face image databases were performed, and the results validate the effectiveness of the proposed method.

关键词： Corrupted image face recognition low-rank matrix regression nuclear-norm

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Locality-Constrained Discriminative matrix regression for Robust Face Identification

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022年第3期33卷 1254-1268页

作者： Zhang, Chao Li, Huaxiong Qian, Yuhua Chen, Chunlin Zhou, Xianzhong Nanjing Univ Dept Control & Syst Engn Nanjing 210093 Peoples R China Shanxi Univ Inst Big Data Sci & Ind Taiyuan 030006 Peoples R China Shanxi Univ Minist Educ Key Lab Computat Intelligence & Chinese Informat Taiyuan 030006 Peoples R China

regression-based methods have been widely applied in face identification, which attempts to approximately represent a query sample as a linear combination of all training samples. Recently, a matrix regression model based on nuclear norm has been proposed and shown strong robustness to structural noises. However, it may ignore two important issues: the label information and local relationship of data. In this article, a novel robust representation method called locality-constrained discriminative matrix regression (LDMR) is proposed, which takes label information and locality structure into account. Instead of focusing on the representation coefficients, LDMR directly imposes constraints on representation components by fully considering the label information, which has a closer connection to identification process. The locality structure characterized by subspace distances is used to learn class weights, and the correct class is forced to make more contribution to representation. Furthermore, the class weights are also incorporated into a competitive constraint on the representation components, which reduces the pairwise correlations between different classes and enhances the competitive relationships among all classes. An iterative optimization algorithm is presented to solve LDMR. Experiments on several benchmark data sets demonstrate that LDMR outperforms some state-of-the-art regression-based methods.

关键词： Training Nuclear magnetic resonance Face recognition Robustness matrix converters Collaboration Optimization Class competitions locality constraints matrix regression robust face identification (FI)

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Nuclear norm-based matrix regression preserving embedding for face recognition

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NEUROCOMPUTING 2018年 311卷 279-290页

作者： Deng, Yang-Jun Li, Heng-Chao Wang, Qi Du, Qian Southwest Jiaotong Univ Sichuan Prov Key Lab Informat Coding & Transmiss Chengdu 611756 Sichuan Peoples R China Northwestern Polytech Univ Sch Comp Sci Xian 710072 Peoples R China Northwestern Polytech Univ Ctr OPT IMagery Anal & Learning OPTIMAL Xian 710072 Peoples R China Mississippi State Univ Dept Elect & Comp Engn Mississippi State MS 39762 USA

Recently, using linear reconstruction technique to construct intrinsic graph for projection-based dimensionality reduction (DR) has aroused broad interest in face recognition. However, current methods either lack robustness to corruptions or require to perform vectorization which causes loss of local geometrical information of images. To this end, a novel nuclear norm-based matrix regression preserving embedding (NN-MRPE) method is proposed in this paper. First, NN-MRPE constructs an intrinsic graph by using the nuclear norm to evaluate the residual errors to resist data corruptions. Second, a matrix-based embedding cost function is formulated to seek two transformation matrices which can preserve the geometrical structure reflected by the intrinsic graph exactly. Finally, based on the linear regression theory, we summarize a general DR framework called linear regression preserving embedding that preserves the intrinsic structure of data by recovering the reconstruction relationship in the original space. Specifically, many existing approaches are the special cases of the linear regression preserving embedding. Experiments on five public face databases with different types of corruptions are conducted to demonstrate the efficiency of the proposed NN-MRPE method. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Nuclear norm matrix regression Dimensionality reduction Face recognition

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Double fused Lasso penalized LAD for matrix regression

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APPLIED MATHEMATICS AND COMPUTATION 2019年 357卷 119-138页

作者： Li, Mei Kong, Lingchen Beijing Jiaotong Univ Dept Appl Math Beijing 100044 Peoples R China

More complex data are generated with a response on vector and matrix predictors in statistics and machine learning. Recently, Zhou and Li (2014) proposed matrix regression based on least squares (LS) method but they mainly considered the regularized matrix regression with nuclear norm penalty when the distribution of noise is with mean 0 and covariance being fixed. In practice, noises may be heavy-tailed or the distribution is unknown. In this case, it is well known that least absolute deviation (LAD) method yields better performances than LS method. Considering structures of predictors, we propose the double fused Lasso penalized LAD for matrix regression in this paper. The new penalty term combines fused Lasso and matrix-type fused Lasso. We achieve the strong duality theorem between the double fused Lasso penalized LAD and its dual. Based on it, we design a highly scalable symmetric Gauss-Seidel based Alternating Direction Method of Multipliers (sGS-ADMM) algorithm to solve the dual problem. Moreover, we give the global convergence and Q-linear rate of convergence. Finally, effectiveness of our method is demonstrated by numerical experiments on simulation and real datasets. (c) 2019 ElsevierInc. All rights reserved.

关键词： matrix regression Double fused Lasso LAD sGS-ADMM Q-linear rate of convergence

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