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Robust non-negative matrix factorization with Supervised Graph Embedding for Image Classification

KSII TRANSACTIONS ON INTERNET AND INFORMATION SYSTEMS 2025年第3期19卷 950-972页

作者： Wan, Minghua Gu, Weiyu Yang, Guowei Tan, Hai Nanjing Audit Univ Sch Comp Sci Sch Intelligent Auditing Nanjing 211815 Peoples R China Qingdao Univ Sch Elect & Informat Qingdao 266071 Peoples R China

In recent years, non-negative matrix factorization (NMF) methods based on graph embedding have been widely applied in the field of image classification. Despite their significant success, these methods have some limitations: 1) Existing methods are sensitive to noise interference and occlusion;2) They do not fully account for intra-class compactness and inter-class separability;3) Some models arbitrarily assume that the subspace distribution of samples within the same class is identical;4) Traditional graph embedding methods often necessitate the introduction of additional regularization parameters, thereby reducing the algorithm's interpretability. To address these issues, this paper proposes a novel method called robust non-negative matrix factorization with supervised graph embedding (RNMF-SGE). RNMF-SGE integrates label information, graph embedding structures, & ell;2,1-norm sparsity constraint, and NMF method into a unified optimization framework. Firstly, we employ & ell;2,1-norm constraint to reduce sensitivity to noise interference. Secondly, we utilize a weight matrix to ensure that the subspace distribution of samples within the same class is similar but not necessarily identical. To fully consider intra-class compactness and inter-class separability, we impose constraints on the learning of the weight matrix using label information. Lastly, to avoid introducing additional regularization terms, we integrate the supervised weight matrix into the NMF model in a parameter-free manner. Comprehensive experiments demonstrate that RNMF-SGE exhibits enhanced robustness, superior classification performance, and improved generalization capability compared to a series of advanced NMF algorithms.

关键词： non-negative matrix factorization & ell 2 1-norm supervised weight matrix image classification robustness

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Deep Learning-Based Image Watermarking Using Catalan Transform and non-negative matrix factorization

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IEEE Access 2025年 13卷 68995-69020页

作者： Fahim Hossain Saikat, Md. Provath, Md. Al-Mamun Deb, Kaushik Dhar, Pranab Kumar Shimamura, Tetsuya Department of Computer Science and Engineering Chittagong4349 Bangladesh Saitama University Department of Information and Computer Sciences Saitama338-8570 Japan

In the digital age, embedding imperceptible data into images for authenticating ownership and content integrity through watermarking has gained immense importance. Existing watermarking methods struggle to balance imperceptibility, robustness, and security, resulting in suboptimal peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), normalized correlation (NC) values, along with higher time complexity. To overcome these constraints, this study proposes a new method for image watermarking that uses deep learning and operates within the YIQ color space. The main contribution of the proposed method is its new combination of the Catalan transform (CT) and non-negative matrix factorization (NMF) with an artificial neural network (ANN) for enhanced watermark embedding and extraction. CT enhances pixel intensity while NMF extracts the most significant features from each (m x m) block (with m= 2 in simulations), improving the method's robustness and imperceptibility. Before embedding, the watermark undergoes a new scrambling technique combining adaptive diffusion and non-linear transform, significantly enhancing security. A new embedding equation integrates the watermark into the non-negative elements of the host image blocks. Statistical features from watermarked blocks are used to create a dataset for extraction, and an ANN model trained on this dataset enables accurate watermark recovery. The proposed method achieves a PSNR of 66.43 to 77.02 dB (31.91% improvement), SSIM of 0.99 to 1.00 (1.02% improvement), and NC of 0.99 to 1.00 (1.88% improvement). Its computational complexity is O(n2), a 33.33% reduction compared to traditional O(n3) methods. Security metrics include RE = 0.3094, UACI = 34.21%, and NPCR = 99.15%, demonstrating superior robustness and efficiency over existing approaches. © 2013 IEEE.

关键词： non-negative matrix factorization

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Pairwisely constrained symmetric non-negative matrix factorization for link prediction in complex networks using degree-related clustering coefficient and improved closeness centrality

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Cluster Computing 2025年第5期28卷 1-26页

作者： Chen, Guangfu Xie, Bin Li, Xiaofei Zhao, Jizhi School of Mathematics and Computer Science Wuyi University Fujian Wuyishan354300 China School of Information Engineering Jiangxi University of Science and Technology Jiangxin Ganzhou341000 China School of Business Wuyi University Fujian Wuyishan354300 China

The aim of link prediction is to predict missing links or eliminate spurious links and new links in future network. Among different types of link prediction algorithms, non-negative matrix factorization(NMF)-based methods have become a promising and competitive algorithm with the advantages of dimension reduction and higher prediction accuracy. However, existing NMF-based algorithms have some problems as follows: (1) NMF failure directly captures the neighbor capability of the node;(2) most NMF-based methods do not guarantee that the additional information can effectively improve the performance. To dismiss the above limitations, a novel link prediction model named Pairwisely Constrained Symmetric non-negative matrix factorization via Degree-related clustering coefficient and Improved closeness centrality (PCSNMF_DI) is proposed in this paper. Specifically, PCSNMF_DI has the following features: (1) the pairwisely constrained graph regularized coupled with degree-related clustering coefficients and improved closeness centrality to maintain both local and global information;and (2) an ablation study is employed to analyse and discuss the necessity of the proposed model for attaching local and global information. In addition, the proof of convergence and the computational complexity for PCSNMF_DI are presented. PCSNMF_DI and baseline methods are evaluated on sixteen real-world networks and the results demonstrate that PCSNMF_DI significantly outperforms state-of-the-art link prediction approaches. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： non-negative matrix factorization

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JSNMFuP: a unsupervised method for the integrative analysis of single-cell multi-omics data based on non-negative matrix factorization

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BMC GENOMICS 2025年第1期26卷 1-10页

作者： Zhang, Bai Nan, Mengdi Wang, Liugen Wu, Hanwen Chen, Xiang Shi, Yongle Ma, Yibing Gao, Jie Jiangnan Univ Sch Sci Wuxi Jiangsu Peoples R China JiangNan Univ Sch Artificial Intelligence & Comp Sci Wuxi Jiangsu Peoples R China

With the rapid advancement of sequencing technology, the increasing availability of single-cell multi-omics data from the same cells has provided us with unprecedented opportunities to understand the cellular phenotypes. Integrating multi-omics data has the potential to enhance the ability to reveal cellular heterogeneity. However, data integration analysis is extremely challenging due to the different characteristics and noise levels of different molecular modalities in single-cell data. In this paper, an unsupervised integration method (JSNMFuP) based on non-negative matrix factorization is proposed. This method integrates the information extracted from the latent variables of each omic through a consensus graph. High-dimensional geometrical structure is captured in the original data and biologically-related feature links across modalities are incorporated into the model using regularization terms. JSNMFuP can be utilized for data visualization and clustering, facilitating marker characterization and gene ontology enrichment analysis, providing rich biological insights for downstream analysis. The application on real datasets shows that JSNMFuP has superior performance in cell clustering. The factors are interpretable, making it an effective method for analyzing cell heterogeneity using single-cell multi-omics data.

关键词： Single-cell multi-omics data non-negative matrix factorization Data integration

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Bayesian multi-study non-negative matrix factorization for mutational signatures

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GENOME BIOLOGY 2025年第1期26卷 1-23页

作者： Grabski, Isabella N. Trippa, Lorenzo Parmigiani, Giovanni New York Genome Ctr New York NY USA Dana Farber Canc Inst Dept Data Sci Boston MA 02215 USA

Mutational signatures are typically identified from tumor genome sequencing data using non-negative matrix factorization (NMF). However, existing NMF techniques only decompose a single dataset, limiting rigorous comparisons of signatures across conditions. We propose a Bayesian NMF method that jointly decomposes multiple datasets to identify signatures and their sharing pattern across conditions. We propose a fully unsupervised "discovery-only" model and a semi-supervised "recovery-discovery" model that simultaneously estimates known and novel signatures, and extend both to estimate covariate effects. We demonstrate our approach on extensive simulations, and apply our method to answer questions related to colorectal cancer and early-onset breast cancer.

关键词： Mutational signatures non-negative matrix factorization Dimension reduction

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Blind Modal Parameter Identification Using non-negative matrix factorization and Generalized Complexity Pursuit Algorithms 13th

Blind Modal Parameter Identification Using Non-Negative Matr...

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13th Structural Engineering Convention, SEC 2023

作者： Banerjee, Subhajit Saravanan, T. Jothi School of Infrastructure Indian Institute of Technology Bhubaneswar Bhubaneswar India

ISBN: (纸本)9789819760664

Operational modal analysis (OMA) has attracted a lot of interest in the field of civil engineering during the past 15 years, to monitor structural health of large-scale infrastructure. Traditional contact-based modal analysis techniques require physically attached sensors for data collection and vibration-based monitoring which can impose mass-loading as well as financial constraints upon installation and maintenance of such devices. Recently, non-contact video-based modal analysis methods for structures with arbitrary complexity using advanced computer vision techniques such as video motion magnification and optical flow have gained much importance. However, these techniques require prior information about the natural frequency ranges of the structure and utilize steerable pyramids which are complex multi-scale image decomposition filters. To address these issues, a technique is suggested in this study to extract the modal parameters (modal frequencies and mode shapes) blindly from the recorded structural vibration video signal using an unsupervised machine learning algorithm called non-negative matrix factorization (NNMF) integrated with a blind source separation technique called Generalized Complexity Pursuit (GCP). NNMF algorithm can be directly applied to the raw pixel-time series formed from the video data to obtain the temporal components, which can be demixed using GCP to identify the individual modal frequencies and mode shapes. The above algorithm is first validated on an 8-degree of freedom (DOF) numerical model and then implemented on laboratory-scale models (multi-storey shear frame model) as well as on real-world recorded structural vibration video like the Tacoma Narrows bridge to determine its noise sensitivity. The modal parameters extracted are compared with those from available literature for validation. The estimation errors obtained from all the validations are well below 1%, which makes the technique quite suitable and reliable for structural v

关键词： non-negative matrix factorization

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From Evolutionary Game Dynamics to non-negative matrix factorization: Acceleration with Hessian Geometry 18th

From Evolutionary Game Dynamics to Non-negative Matrix Fact...

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18th International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom, IJTCS-FAW 2024

作者： Liang, Huili Wang, Xiao Wei, Yechao Wu, Pingfan Shanghai University of Finance and Economics Shanghai China North East Normal University Changchun China Key Laboratory of Interdisciplinary Research of Computation and Economics Shanghai China

ISBN: (纸本)9789819777518

Optimization on Riemannian manifolds has attracted the attention of many in the machine learning community due to its potential in solving constrained optimization problems. However, high cost of geodesic-based retraction algorithms often limits the applications of Riemannian optimization algorithm in practical problems that are intensely resource consuming. We focus on the positive orthant constrained optimization problems, a special type of constraint that are present in many application areas from evolutionary game theory to non-negative matrix factorization. We propose an accelerated natural gradient descent algorithm modified from evolutionary game dynamics and show that our algorithm converges to second-order stationary points. Our theoretical analysis and experiments verify that a geodesic free acceleration scheme has the potential to balance the convergence guarantee and computational efficiency in constrained non-convex optimization problems like non-negative matrix factorization. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： non-negative matrix factorization

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Dynamic Fusion and non-negative matrix factorization-based Multi-view clustering method 4

Dynamic Fusion and Non-negative matrix Factorization-based M...

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4th International Conference on Computer Vision, Application, and Algorithm, CVAA 2024

作者： Gui, Hanlin Jiang, Yu Chengdu University of Information Technology Chengdu China

ISBN: (数字)9781510687622

ISBN: (纸本)9781510687615

Aiming at the problem that most of the current multi-view clustering methods only focus on the information of a single view, ignoring the correlation between views, and failing to fully explore the potential structure of the data, a multi-view clustering method combining dynamic fusion and non-negative matrix factorization is proposed. First, we extract low-dimensional feature representations for each view using non-negative matrix factorization and enhance feature consistency across different views through contrastive learning. Second, we apply a continual learning strategy to dynamically update the model, adapting to changes in new view data and improving model robustness and adaptability. Finally, we use a dynamic fusion strategy to weight and integrate features from all views, obtaining a common feature representation for multi-view data. Experimental results demonstrate that our proposed method significantly outperforms existing methods in clustering performance on several public datasets. © 2025 SPIE.

关键词： non-negative matrix factorization

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Music Recommender System using non-negative matrix factorization

Music Recommender System using Non-Negative Matrix Factoriza...

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2025 International Conference on Advancement in Data Science, E-learning and Information System, ICADEIS 2025

作者： Athari, Syafreza Hanif Baizal, Z.K.A. School of Computing Telkom University Bandung Indonesia

ISBN: (纸本)9798331513320

Recommender systems play a crucial role in music streaming services like Spotify to help users discover music that aligns with their preferences. The goal of this research is to create a music recommendation system that utilizes collaborative filtering with non-negative matrix factorization (NMF). matrix factorization decomposes user-music interactions into smaller matrices to predict user preferences for songs they have not listened to yet. This method will be compared with SVD to see if NMF is better at recommending music that match their likes and preferences. NMF imposes a non-negativity constraint on the decomposed matrices, making the resulting factors easier to interpret. Performance evaluation is conducted using RMSE (Root Mean Squared Error) and MAE (Mean Absolute Error) metrics to find out how good the method provides recommendations. Based on the test results, the NMF method with an RMSE value of 0.4727 and MAE value 0.3693, indicating its effectiveness in providing music recommendations. © 2025 IEEE.

关键词： non-negative matrix factorization

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Multi-view clustering based on pairwise co-regularization and robust dual graph non-negative matrix factorization

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NEUROCOMPUTING 2025年 611卷

作者： Tang, Huiguo Liu, Shihu Tang, Yi Yu, Fusheng Yunnan Minzu Univ Sch Math & Comp Sci Kunming 650504 Peoples R China Beijing Normal Univ Sch Math Sci Beijing 100875 Peoples R China

Multi-view clustering has been a hotspot in the field of machine learning and pattern recognition, and methods based on non-negative matrix factorization have gained attention for their simplicity and interpretability. Despite these methods achieving great clustering performance, there may also be some limitations, such as the full structural information of data and the similarity between different views not being considered. This paper proposes a novel multi-view clustering algorithm based on pairwise co-regularization and robust dual graph non-negative matrix factorization. Firstly, the L-2,L-p -norm is applied in non-negative matrix factorization framework to enhance model robustness. Next, pairwise co-regularization is utilized to extract the inter-view information of all views. Then, graph dual regularization is applied to preserve the structure information of the data and feature spaces. Lastly, an auto-weighted strategy is introduced to assign appropriate weights to each view. In addition, an iterative updating optimization scheme for the proposed algorithm is developed, and the convergence proof of the scheme is provided. The experimental results on twelve real-world datasets show that the proposed algorithm is both effective and efficient, compared with three classical and six state-of-the-art algorithms.

关键词： Multi-view clustering Pairwise co-regularization Graph dual regularization non-negative matrix factorization L-2,L-p-norm

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