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Efficient algorithms of box-constrained nonnegative matrix factorization and its applications in image clustering

APPLIED NUMERICAL MATHEMATICS 2025年 208卷 176-188页

作者： Guo, Jie Li, Ting Wan, Zhong Li, Jiaoyan Xiao, Yamei Changsha Normal Univ Sch Math Sci Changsha 410111 Hunan Peoples R China Zhejiang Lab Res Ctr Data Hub & Secur Hangzhou 311121 Zhejiang Peoples R China Cent South Univ Sch Math & Stat Changsha 410083 Hunan Peoples R China Hunan Normal Univ Coll Life Sci Changsha 410081 Hunan Peoples R China

nonnegative matrix factorization (NMF) provides an important approach of unsupervising learning, but it faces computational challenges when applied into clustering of high-dimensional datasets. In this paper, a class of novel nonmonotone gradient-descent algorithms are developed for solving box-constrained NMF problems. Unlike existing algorithms in the literature that update each matrix factor individually by fixing another one, our algorithms simultaneously update the paired matrix factors by leveraging adaptive projected Barzilai-Borwein directions and appropriate step sizes generated by the developed nonmonotone line search rules. Theoretically, it is proved that the developed algorithms are well defined and globally convergent. Extensive numerical tests on public image datasets demonstrate that the developed algorithms in this paper outperform the state-of-the-art ones, in terms of clustering performance, computational efficiency, and robustness of mining noisy data.

关键词： Image clustering Optimization modeling Algorithms nonnegative matrix factorization

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Weighted symmetric nonnegative matrix factorization and graph-boosting to improve the attributed graph clustering

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 142卷

作者： Li, Shunlei Wan, Lili Zhang, Yin Luo, Lixia Chinese Univ Hong Kong Multiscale Med Robot Ctr Ltd Hong Kong Peoples R China Wuhan Donghu Univ Sch Mech & Elect Engn Wuhan 430212 Hubei Peoples R China Wuhan Polytech Univ Sch Elect & Elect Engn Wuhan 430023 Hubei Peoples R China Guilin Univ Elect Technol Sch Optoelect Engn Guilin 541004 Guangxi Peoples R China Hunan Univ Informat Technol Sch Comp Sci & Engn Changsha 410148 Hunan Peoples R China

Graph clustering is a critical task in network analysis, aimed at grouping nodes based on their structural or attributed similarities. In particular, attributed graph clustering, which considers both structural links and node attributes, is essential for complex networks where additional node information is available. nonnegative matrix factorization (NMF) has shown promise in graph clustering;however, it faces limitations when applied to attributed graph clustering, such as an inability to detect outliers, distortion of geometric data point structures, and disregard for attributed information. Moreover, many existing attributed graph clustering methods overlook distant node relationships due to network sparsity, which hinders further performance improvements. To address these challenges, this paper introduces Weighted Symmetric NMF with graph-Boosting for attributed Graph Clustering (WSBGC), an innovative extension of NMF. WSBGC leverages attribute similarity among nodes to create a weighted version of NMF, enabling outlier detection while preserving the geometric structure of data points. Additionally, WSBGC employs graph-boosting, leveraging attribute information to account for distant node relationships and improve clustering accuracy. A graph attention auto-encoder is then used to construct the final clustering model. The effectiveness of WSBGC is validated through extensive experiments on real-world datasets. Notably, our algorithm improves accuracy by 2.5% compared to the best available method, demonstrating its superior clustering performance in attributed graphs.

关键词： Attributed graph Graph clustering Graph-boosting nonnegative matrix factorization Weighted symmetric

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A projected hybridization of the Hestenes-Stiefel and Dai-Yuan conjugate gradient methods with application to nonnegative matrix factorization

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2024年第1期71卷 551-571页

作者： Khoshsimaye-Bargard, Maryam Ashrafi, Ali Semnan Univ Dept Math Fac Math Stat & Comp Sci Semnan Iran

Hybrid conjugate gradient methods are considered as an efficient family of conjugate gradient methods to solve unconstrained optimization problems. In this work, based on the memoryless BFGS update, a convex hybridization of the Hestenes-Stiefel and Dai-Yuan conjugate parameters is presented. To put in place safeguards to protect the sufficient descent property, the given search direction is projected to the orthogonal subspace to the gradient of the objective function. The convergence analysis of the proposed method is addressed under standard assumptions for general functions. The practical merits of the proposed method are computationally demonstrated on a set of CUTEr test functions as well as the well-known nonnegative matrix factorization problem.

关键词： Nonlinear programming Hybrid conjugate gradient method Projecting strategy Sufficient descent property Global convergence nonnegative matrix factorization

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Semi-supervised structured nonnegative matrix factorization for anchor graph embedding

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NEUROCOMPUTING 2025年 639卷

作者： Li, Xiangli Mei, Jianping Mo, Yuanjian Guilin Univ Elect Technol Sch Math & Comp Sci Guilin 541004 Guangxi Peoples R China Guangxi Coll & Univ Key Lab Data Anal & Computat Guilin 541004 Guangxi Peoples R China Ctr Appl Math Guangxi Guilin 541004 Guangxi Peoples R China

Semi-supervised nonnegative matrix factorization (NMF) has been widely used in various clustering tasks due to its reliable performance. The key is how to use effectively a small amount of label information to obtain a more discriminative low-dimensional representation of data. In order to improve the clustering performance of semi-supervised NMF more effectively, this paper proposes a new semi-supervised NMF method, namely semi-supervised structured NMF for anchor graph embedding (AESSNMF). Specifically, AESSNMF uses three kinds of supervision information simultaneously, namely, pointwise constraints, pairwise constraints, and negative label information. Also, in order to handle mixed-sign data, AESSNMF uses a convex NMF form and only imposes nonnegative constraints on the coefficient matrix. AESSNMF constructs an anchor graph to embed the matrix factorization process, rather than performing the matrix factorization directly on the original data. We use the alternating iterative algorithm to optimize the objective function of AESSNMF. We also discuss the relationship between several related NMF based algorithms and AESSNMF. A large number of experimental results show that AESSNMF is superior to other related algorithms.

关键词： Anchor point nonnegative matrix factorization Semi-supervised clustering Label information

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Multi-view data representation via adaptive label propagation nonnegative matrix factorization

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INFORMATION SCIENCES 2025年 700卷

作者： Li, Hui Leng, Chengcai Peng, Jinye Pei, Zhao Basu, Anup Northwest Univ Sch Math Xian 710127 Peoples R China Northwest Univ Sch Informat Sci & Technol Xian 710127 Peoples R China Shaanxi Normal Univ Sch Comp Sci Xian 710119 Peoples R China Univ Alberta Dept Comp Sci Edmonton AB T6G 2E8 Canada

nonnegative matrix factorization (NMF) integrating label propagation (LP) algorithm can enhance the discrimination ability of low-dimensional representations. However, traditional LP-based NMF approaches require the construction of a k-nearest neighbor graph in advance to obtain the weight matrix for LP. This increases the burden of adjusting the neighborhood parameter k and leads to a suboptimal weight matrix. To address these issues, an Adaptive Label Propagation NMF (ALPNMF) framework is designed by jointly minimizing the data reconstruction error and the predicted soft label reconstruction error. First, ALPNMF completes neighbor selection and weight calculation simultaneously, without adjusting the neighborhood parameter k. Second, ALPNMF takes into account the dependence between the graph weight learning and LP, thereby yielding the globally optimal graph weight matrix for LP and the more accurate predicted soft label matrix for guiding the decomposition process. Finally, with the aim of combining the information from diverse views to acquire more efficient low-dimensional representations, we extend ALPNMF to a new multi-view NMF approach named Multi-view data representation via Adaptive Label Propagation NMF (MALPNMF). Experimental results on five benchmark multi-view datasets demonstrate that MALPNMF outperforms other state-of-the-art multi-view NMF methods.

关键词： Multi-view data representation nonnegative matrix factorization Adaptive label propagation Self-expressiveness

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Solving an Augmented nonnegative matrix factorization Model by Modified Scaled Nonmonotone Memoryless BFGS Methods Devised Based on the Ellipsoid Vector Norm

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年第8期48卷 9088-9097页

作者： Dargahi, Fatemeh Babaie-Kafaki, Saman Aminifard, Zohre Berenjestanaki, Mohammad Hajian Semnan Univ Dept Math Semnan Iran Free Univ Bozen Bolzano Fac Engn Bolzano Italy UCLouvain Inst Informat & Commun Technol Elect & Appl Math Louvain La Neuve Belgium

We suggest a modified version of the nonnegative matrix factorization problem, adding penalty terms to the model with the aim of taking control of the condition number of the decomposition elements. This measure is taken to reinforce computational stability in the solution path of the relevant optimization model. Then, using the ellipsoid vector norm in the Barzilai-Borwein least-squares model, we gain scaling parameters for the memoryless BFGS updating formula. Therefore, two augmented versions of the Oren-Spedicato self-scaling parameter are proposed when the BFGS and DFP formulas for the Hessian are employed as the matrix index of the ellipsoid norm. A similar analysis is conducted to obtain two augmented versions of the Oren-Luenberger self-scaling parameter using the mentioned quasi-Newton formulas for the inverse Hessian. We address the global convergence of the method under a modified version of a nonmonotone backtracking line search. Then, we discuss accelerating the method using a local memoryless quadratic model considering the given scaling parameters as scalar approximations of the Hessian. Finally, the computational merits of the given augmented nonnegative matrix factorization model as well as the effectiveness of the proposed scaling parameters are assessed on some standard and randomly generated test problems, and also, a classic database of facial images. The outputs generally support our analytical spectrum.

关键词： ellipsoid norm nonnegative matrix factorization scaled BFGS method nonmonotone line search unconstrained optimization

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A double sided deep nonnegative matrix factorization network for feature extraction of two dimensional data

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 271卷

作者： Karimpour, Mehdi Rezghi, Mansoor Tarbiat Modares Univ Dept Comp Sci Tehran Iran

nonnegative matrix factorization (NMF) has become a powerful and popular tool in data dimensionality reduction with outstanding performance on learning tasks. In recent years, its deep version has also been introduced, which is a kind of deep latent factor models. However, NMF and deep NMF are vector-based methods and only work on one-dimensional data. This means that, to use these methods, two dimensional data such as images should be reshaped as a vector. This vectorization of data leads to the loss of spatial relationships of features, increasing complexity and also the possibility of overfitting. This paper proposes a double sided NMF model that overcomes these drawbacks by considering the data in their original format, unlike the traditional NMF method. In addition to preserving the structure of data, the proposed method has fewer parameters and less computational complexity than the traditional NMF method. Furthermore, two deep linear and nonlinear versions of our method are introduced to extract hierarchical features of data. We investigate the clustering performance of our methods on two real-world image databases and compare them with the vector-based methods NMF and deep NMF. Numerical experiments confirm that the proposed algorithms are more efficient.

关键词： Dimensionality reduction nonnegative matrix factorization Deep NMF Double sided NMF Clustering

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Semi-supervised pivotal-aware nonnegative matrix factorization with label and pairwise constraint propagation for data clustering

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PATTERN RECOGNITION 2025年 157卷

作者： Yang, Xiaojun Zhu, Tuoji Peng, Siyuan Nie, Feiping Lin, Zhiping Guangdong Univ Technol Sch Informat Engn Guangzhou 510006 Peoples R China Guangdong Univ Technol Key Lab Photon Technol Integrated Sensing & Commu Minist Educ China Guangzhou 510006 Peoples R China Guangdong Univ Technol Guangdong Prov Key Lab Informat Photon Technol Guangzhou 510006 Peoples R China Northwestern Polytech Univ Sch Comp Sci Xian 710072 Peoples R China Northwestern Polytech Univ Ctr OPT IMagery Anal & Learning Xian 710072 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

Semi-supervised nonnegative matrix factorization (NMF) methods have found extensive utility in data clustering applications. However, these existing methods encounter challenges in effectively leveraging the limited supervisory information to enhance the performance of clustering. In particular, the majority of these methods tend to solely utilize either the label information or the pairwise constraint information, neglecting the potential benefits of their joint utilization. To address this issue, a novel algorithm named semi-supervised pivotal-aware nonnegative matrix factorization (SPNMF) is proposed in this paper, which utilizes the label information and the pairwise constraint information simultaneously to enhance the performance in data clustering tasks. The proposed method has two main innovations: (1) adopting the dual constraint propagation (DCP) algorithm (i.e., label propagation and pairwise constraint propagation) to effectively utilize a meager amount of label information for learning a compact data representation;(2) incorporating the pivotal-aware technique to mitigate the negative impact of outliers. Notably, the DCP algorithm not only propagates limited label information to a multitude of unlabeled samples, but also disseminates the pairwise constraint supervisory information obtained from the labels to unconstrained samples, allowing for the acquisition of richer supervisory information in the form of pointwise and pairwise constraints. Furthermore, a comprehensive analysis of SPNMF is conducted. Extensive experimental results are executed on eight real-world image datasets. The results underscore the superior performance of SPNMF in comparison to several state-of-the-art methods.

关键词： nonnegative matrix factorization Semi-supervised learning Dual constraint propagation Data clustering

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Accelerated SVD-based initialization for nonnegative matrix factorization

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COMPUTATIONAL & APPLIED MATHEMATICS 2024年第6期43卷 1-16页

作者： Esposito, Flavia Atif, Syed Muhammad Gillis, Nicolas Univ Bari Aldo Moro Dept Math Bari Italy Ziauddin Univ Coll Comp & Software Engn Karachi Pakistan Univ Mons Fac Polytech Dept Math & Operat Res Mons Belgium

nonnegative matrix factorization (NMF) is a popular dimensionality reduction technique. NMF is typically cast as a non-convex optimization problem solved via standard iterative schemes, such as coordinate descent methods. Hence the choice of the initialization for the variables is crucial as it will influence the factorization quality and the convergence speed. Different strategies have been proposed in the literature, the most popular ones rely on singular value decomposition (SVD). In particular, Atif et al. (Pattern Recognit Lett 122:53-59, 2019) have introduced a very efficient SVD-based initialization, namely NNSVD-LRC, that overcomes the drawbacks of previous methods, namely, it guarantees that (i) the error decreases as the factorization rank increases, (ii) the initial factors are sparse, and (iii) the computational cost is low. In this paper, we improve upon NNSVD-LRC by using the low-rank structure of the residual matrix;this allows us to obtain NMF initializations with similar quality to NNSVD-LRC (in terms of error and sparsity) while reducing the computational load. We evaluate our proposed solution over other NMF initializations on several real dense and sparse datasets.

关键词： nonnegative matrix factorization Singular value decomposition Nesterov accelerated gradient Initialization

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Identification of key nodes in complex networks by using a joint technique of nonnegative matrix factorization and regularization

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PHYSICAL COMMUNICATION 2024年 65卷

作者： Lu, Pengli Yang, Junxia Liu, Wenzhi Lanzhou Univ Technol Sch Comp & Commun Lanzhou 730050 Peoples R China

Identifying key nodes in complex networks is essential to deeply understand and fully utilize the properties and functions of complex systems. Currently, existing traditional methods perform critical nodes identification by manually selecting important attribute features of nodes, but there are limitations in this approach. Manual selection of attribute features may overlook non -obvious features related to nodes criticality and correlations between attribute features. To compensate for the shortcomings of traditional methods, a Joint Technique for identifying critical nodes, called JTNMFR, is presented based on nonnegative matrix factorization and Regularization. factorization of weighted adjacency matrix is performed to obtain potential attribute features of nodes, and communicability network matrix and similarity matrix are introduced as regularization terms to control sparsity of the decomposition results. Ultimately, the importance of nodes is assessed by constructing an objective function that integrates these two aspects and utilizing alternative iteration to obtain the attribute matrix. To validate the accuracy and reliability of JTNMFR, we compare it with nine other identification approaches on eight real networks. Experimental results show that JTNMFR not only significantly outperforms the other algorithms in terms of accuracy of node importance, monotonicity, and node spreading ability but also provides a more accurate means of assessing node importance.

关键词： Complex networks Node centrality nonnegative matrix factorization Regularization

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