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Semi-supervised non-negative matrix factorization with structure preserving for image clustering

NEURAL NETWORKS 2025年 187卷 107340页

作者： Jing, Wenjing Lu, Linzhang Ou, Weihua Guizhou Normal Univ Sch Math Sci Guiyang 550025 Peoples R China Xiamen Univ Sch Math Sci Xiamen 361005 Peoples R China Guizhou Normal Univ Sch Big Data & Comp Sci Guiyang 550025 Peoples R China

Semi-supervised learning methods have wide applications thanks to the reasonable utilization for a part of label information of data. In recent years, non-negative matrix factorization (NMF) has received considerable attention because of its interpretability and practicality. Based on the advantages of semi-supervised learning and NMF, many semi-supervised NMF methods have been presented. However, these existing semi-supervised NMF methods construct a label matrix only containing elements 1 and 0 to represent the labeled data and further construct a label regularization, which neglects an intrinsic structure of NMF. To address the deficiency, in this paper, we propose a novel semi-supervised NMF method with structure preserving. Specifically, we first construct a new label matrix with weights and further construct a label constraint regularizer to both utilize the label information and maintain the intrinsic structure of NMF. Then, based on the label constraint regularizer, the basis images of labeled data are extracted for monitoring and modifying the basis images learning of all data by establishing a basis regularizer. Finally, incorporating the label constraint regularizer and the basis regularizer into NMF, we propose a new semi-supervised NMF method. To solve the optimization problem, a multiplicative updating algorithm is developed. The proposed method is applied to image clustering to test its performance. Experimental results on eight data sets demonstrate the effectiveness of the proposed method in contrast with state-of-the-art unsupervised and semi-supervised algorithms.

关键词： non-negative matrix factorization Semi-supervised Graph Label information Clustering

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Semi-supervised correntropy-based non-negative matrix factorization with hypergraph regularization

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2025年 1-20页

作者： Luo, Mengjie Li, Songtao Tao, Jun Vladimirovich, Pavlovskiy Pavel Jianghan Univ Sch Artificial Intelligence Wuhan 430056 Peoples R China Moscow State Management Univ Sch Informat Management Moscow Russia

non-negative matrix factorization (NMF) stands as a potent technique for reducing dimensionality, renowned especially for its prowess in clustering. However, it often disregards the crucial a priori labeling information inherent in diverse datasets. In this study, we introduce a semi-supervised approach named SCNMFH, leveraging hypergraph regularization to address these aforementioned challenges. Specifically, we integrate correntropy into the loss function of SCNMFH, replacing the conventional Euclidean metric. This alteration is aimed at fortifying the robustness of our algorithm. Furthermore, we incorporate hypergraph regularization into the objective function to capture higher-order geometric relationships among data samples. Additionally, recognizing NMF's inherent operation as an unsupervised matrix factorization technique, we employ limited label information as supervision to enhance the discriminative capacity of the matrix factorization. Consequently, our algorithm enhances clustering performance without substantially increasing complexity. Through extensive experimentation across nine image datasets, we have demonstrated the effectiveness and superiority of the proposed algorithm. Comparative analyses, involving several state-of-the-art algorithms, were conducted, thereby elucidating the efficacy and superiority of our approach.

关键词： non-negative matrix factorization Semi-supervised learning Correntropy Hypergraph regularization Clustering

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Self-supervised star graph optimization embedding non-negative matrix factorization

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INFORMATION PROCESSING & MANAGEMENT 2025年第2期62卷

作者： Li, Songtao Wang, Qiancheng Luo, MengJie Li, Yang Tang, Chang Jianghan Univ State Key Lab Precis Blasting Wuhan 430056 Peoples R China Jianghan Univ Sch Artificial Intelligence Wuhan 430056 Peoples R China Wuhan Univ Sci & Technol Engn Res Ctr Met Automat & Measurement Technol Minist Educ Wuhan 430080 Peoples R China China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China

Labeling expensive and graph structure fuzziness are recognized as indispensable prerequisites for solving practical problems in semi-supervised graph learning. This paper proposes a novel approach: a non-negative matrix factorization algorithm based on self-supervised star graph optimal embedding, utilizing the progressive spontaneous strategy of anchor graphs. The model considers the feature assignment rules in unlabeled samples and constructs a corresponding probabilistic extension model to extract pseudo-labeled information from the samples. It also constructs self-supervised hard constraints accordingly to enhance the learning process. In addition, inspired by the graph structure filter, we propose a star graph optimization method. It smooths the association relationships between nodes in the graph structure and improves the accuracy of the graph regularization term in describing the association relationships of the original data. Finally, we give the objective function of the model with the multiplicative update rule and analyze the convergence of the algorithm under this rule. Clustering experiments on several standard image datasets and electroencephalography datasets show that the proposed algorithm improves over the current state-of-the-art benchmark algorithms by 6.9% on average. This indicates that the proposed model has excellent self-supervised label discovery and data representation capabilities.

关键词： Self-supervised learning Star graph embedding non-negative matrix factorization Data representation Clustering

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ChromaFactor: Deconvolution of single-molecule chromatin organization with non-negative matrix factorization

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PLOS COMPUTATIONAL BIOLOGY 2025年第2期21卷 e1012841页

作者： Gunsalus, Laura M. Keiser, Michael J. Pollard, Katherine S. Gladstone Inst Data Sci & Biotechnol Gladstone Inst San Francisco CA 94158 USA Univ Calif San Francisco Bakar Computat Hlth Sci Inst San Francisco CA 94143 USA Univ Calif San Francisco Dept Bioengn & Therapeut Sci San Francisco CA 94143 USA Univ Calif San Francisco Kavli Inst Fundamental Neurosci San Francisco CA USA Univ Calif San Francisco Dept Pharmaceut Chem San Francisco CA USA Univ Calif San Francisco Dept Epidemiol & Biostat San Francisco CA USA Univ Calif San Francisco Inst Neurodegenerat Dis San Francisco CA 94158 USA Chan Zuckerberg Biohub SF Investigator Program San Francisco CA 94158 USA

The investigation of chromatin organization in single cells holds great promise for identifying causal relationships between genome structure and function. However, analysis of single-molecule data is hampered by extreme yet inherent heterogeneity, making it challenging to determine the contributions of individual chromatin fibers to bulk trends. To address this challenge, we propose ChromaFactor, a novel computational approach based on non-negative matrix factorization that deconvolves single-molecule chromatin organization datasets into their most salient primary components. ChromaFactor provides the ability to identify trends accounting for the maximum variance in the dataset while simultaneously describing the contribution of individual molecules to each component. Applying our approach to two single-molecule imaging datasets across different genomic scales, we find that these primary components demonstrate significant correlation with key functional phenotypes, including active transcription, enhancer-promoter distance, and genomic compartment. Also, we find that some bulk trends exist at the single-cell level, but only in a small fraction of cells, suggesting that critical changes in genome organization may be driven by specific rare subpopulations rather than occurring uniformly across all cells. ChromaFactor offers a robust tool for understanding the complex interplay between chromatin structure and function on individual DNA molecules, pinpointing which subpopulations drive functional changes and fostering new insights into cellular heterogeneity and its implications for bulk genomic phenomena.

关键词： non-negative matrix factorization

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Multispectral Land Surface Reflectance Reconstruction Based on non-negative matrix factorization: Bridging Spectral Resolution Gaps for GRASP TROPOMI BRDF Product in Visible

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REMOTE SENSING 2025年第6期17卷 1053-1053页

作者： Hou, Weizhen Liu, Xiong Wang, Jun Chen, Cheng Xu, Xiaoguang Ctr Astrophys Harvard & Smithsonian Atom & Mol Phys Div Cambridge MA 02138 USA Univ Iowa Iowa Technol Inst Ctr Global & Reg Environm Res Dept Chem & Biochem Engn Iowa City IA 52242 USA Univ Lille Lab Opt Atmospher F-59655 Villeneuve Dascq France GRASP SAS Remote Sensing Dev F-59260 Lezennes France Univ Maryland Baltimore Cty Earth & Space Inst Baltimore MD 21250 USA Univ Maryland Baltimore Cty GESTAR2 Baltimore MD 21250 USA

In satellite remote sensing, mixed pixels commonly arise in medium- and low-resolution imagery, where surface reflectance is a combination of various land cover types. The widely adopted linear mixing model enables the decomposition of mixed pixels into constituent endmembers, effectively bridging spectral resolution gaps by retrieving the spectral properties of individual land cover types. This study introduces a method to enhance multispectral surface reflectance data by reconstructing additional spectral information, particularly in the visible spectral range, using the TROPOMI BRDF product generated by the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm. Employing non-negative matrix factorization (NMF), the approach extracts spectral basis vectors from reference spectral libraries and reconstructs key spectral features using a limited number of wavelength bands. The comprehensive test results show that this method is particularly effective in supplementing surface reflectance information for specific wavelengths where gas absorption is strong or atmospheric correction errors are significant, demonstrating its applicability not only within the 400-800 nm range but also across the broader spectral range of 400-2400 nm. While not a substitute for hyperspectral observations, this approach provides a cost-effective means to address spectral resolution gaps in multispectral datasets, facilitating improved surface characterization and environmental monitoring. Future research will focus on refining spectral libraries, improving reconstruction accuracy, and expanding the spectral range to enhance the applicability and robustness of the method for diverse remote sensing applications.

关键词： surface reflectance reconstruction non-negative matrix factorization bidirectional reflectance distribution function isotropic coefficient GRASP TROPOMI linear mixing

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A semi-supervised non-negative matrix factorization model for scRNA-seq data analysis

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APPLIED SOFT COMPUTING 2025年 174卷

作者： Lan, Junjie Zhuo, Xiaoling Ye, Siman Deng, Jin South China Agr Univ Coll Math & Informat Guangzhou 510642 Peoples R China Pazhou Lab Guangzhou 510330 Peoples R China

Single-cell RNA sequencing (scRNA-seq) technology enables the measurement of cellular gene expression at the single-cell level, thus facilitating cell clustering at the gene level. Despite numerous dimensionality reduction methods developed for scRNA-seq data, many are limited to analyzing individual gene expression matrices and struggle to address false positives and false zero expression entries effectively. Moreover, existing methods often underutilize prior knowledge of similarity and dissimilarity between multi-omics data, leading to the loss of intercellular correlations and shared structural information, thus hindering desired dimensionality reduction outcomes. To address these limitations, a novel model termed joint non-negative matrix factorization with similarity and dissimilarity constraints (SDJNMF) was proposed to tailor for scRNA-seq data clustering. The model leverages prior knowledge of similarity and dissimilarity across multiple gene expression matrices, facilitating joint non-negative matrix factorization to extract common features from multi-omics data. By preserving shared structural and cellular relevance information, SDJNMF enhances the clustering of similar cells while effectively separating dissimilar ones. Furthermore, the SDJNMF model incorporates sparse Singular Value Decomposition during initialization to mitigate noise and redundancy and ensure robust dimensionality reduction. The experimental results demonstrate that the SDJNMF model exhibits superior performance on the 10 datasets, not only outperforming the other 14 algorithms in terms of clustering accuracy on the 9 datasets, but also enhancing the ARI of SDJNMF by an average of 0.0687 in comparison to the second-best algorithm on each dataset. In the visual representation, the model is able to efficiently and accurately cluster similar cells and effectively discriminate different classes of cells from each other. Additionally, the SDJNMF model was applied to identify informative ge

关键词： scRNA-seq non-negative matrix factorization Dimensionality reduction Clustering Omics

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Cross-domain human activity recognition based on deviation-graph constrained non-negative matrix factorization

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 152卷

作者： Li, Yue Zhi, Yuxing Wang, Huaijun Guo, Yufan Wang, Kan Yu, Lei Fei, Rong Li, Junhuai Xian Univ Technol Sch Comp Sci & Engn Xian 710048 Shaanxi Peoples R China Shaanxi Key Lab Network Comp & Secur Technol Xian 710048 Shaanxi Peoples R China

Sensor-based human activity recognition (HAR) often faces challenges associated with domain shift and limited labeled samples. Many studies have been done to address these cross-domain issues in HAR. nonetheless, there are two main limitations of the existing methods on the cross-person HAR problem. First, the influence of noise or outliers within the original feature space is often overlooked, potentially adversely affecting the classification accuracy of target samples. Second, the local graph constructed from the source domain sample labels may contain redundancies, which can lead to the transfer of incorrect knowledge to the target domain. To cope with these two limitations, we propose cross-domain human activity recognition approach based on Deviation-Graph Constrained non-negative matrix factorization. We introduce a deviation constraint strategy to mitigate the partial impact of noise and outliers on overall feature space. We also create a novel local graph to avoid redundant information from the source domain affecting local manifold structures, thereby enhancing the effectiveness of knowledge transfer. Then, we perform joint non-negative matrix factorization on the samples from both domains. Under the constraint of the new local manifold structure, samples of the same category from different domains can iteratively approach, thereby enhancing the performance of correct knowledge transfer. We conducted comprehensive experiments on Daily and Sports Activities Dataset. The results demonstrate that our method outperforms comparison methods by 3.41%-24.49% in single-source tasks and 4.62%-42.34% in multi-source tasks.

关键词： Human activity recognition Domain adaptation non-negative matrix factorization Manifold learning

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Collaborative filtering recommendation based on K-nearest neighbor and non-negative matrix factorization algorithm

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JOURNAL OF SUPERCOMPUTING 2025年第1期81卷 1-45页

作者： Sun, Yu Liu, Qicheng Yantai Univ Sch Comp & Control Engn Yantai 264005 Peoples R China

Traditional collaborative filtering recommendation algorithms suffer from low recommendation efficiency and poor accuracy when calculating similarities between users or items. To address this issue and improve the efficiency of recommendation systems, the paper introduces an algorithm called K-nearest neighbors and non-negative matrix factorization (KNNCNMF) collaborative filtering recommendation algorithm. When calculating the similarity between users or items, the algorithm extracts the latent factors of users and items through matrix decomposition, constructs a low-dimensional dense "user-item factor" matrix, and inputs it into the classifier for rating prediction, which replaces the complex similarity calculation and further improves the efficiency of the user-item similarity calculation. We use performance metrics such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Precision, and Recall to measure our method. The experimental results show that compared to other algorithms, our method improves the MAE metric by 1.78% on average, the RMSE metric by 4.48% on average, the Precision metric by 4.66% on average, and the Recall metric by 7.95% on average. It proves the effectiveness of our proposed method.

关键词： K-nearest neighbor non-negative matrix factorization Latent factors Collaborative filtering Recommender system Hybrid algorithm

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Unravelling patterns of food tolerance to pesticide residues via non-negative matrix factorization

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JOURNAL OF FOOD SCIENCE 2025年第2期90卷 e70029页

作者： Mei, Suyu Shenyang Normal Univ Software Coll Shenyang 110034 Peoples R China

Gaining knowledge about the maximum residue limits (MALs) of pesticides on fresh or processed foods is critical to the process of pre-harvest cultivation, post-harvest processing and storage, and the downstream safety surveillance of food commodities. In this study, we explore the available MALs of 643 pesticides on 128 foods via non-negative matrix factorization (NMF) and hierarchical clustering to gain insights into the patterns of how similar pesticides exhibit similar MALs profiles on foods. Meanwhile, NMF predicts the MALs for untested foods via the implicitly-learnt patterns without conducting in vivo testing that potentially violates ethic regulations. Clustering results show that foods with closer NMF weights commonly exhibit closer residue tolerance profiles, and pesticides with closer MALs profiles exhibit higher structural similarities. These patterns help food experts to assess the MALs of pesticides concerned on untested foods, and the determination of MRLs on foods has its mechanistic basis. Using the reverse process of NMF decomposition, we provide the predicted MALs for 24.31% pesticide-food pairs, and NMF achieves 0.9 R2 on more than 75.78% foods in terms of recreating the experimental MALs values. Only 8.6% foods achieve less than 0.7 R2. These predicted MALs are supposed to provide practical or theoretical reference to benefit the surveillance of pesticide applications and food safety control.

关键词： food safety maximum residue limits non-negative matrix factorization pesticide management Tanimoto similarity

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A model of feature extraction for well logging data based on graph regularized non-negative matrix factorization with optimal estimation

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COMPLEX & INTELLIGENT SYSTEMS 2025年第4期11卷 1-16页

作者： Yuan, Kehong Shang, Youlin Guo, Haixiang Dong, Yongsheng Liu, Zhonghua Henan Univ Sci & Technol Coll Informat Engn Luoyang 471000 Peoples R China Luoyang Inst Sci & Technol Dept Math & Phys Luoyang 471023 Peoples R China Henan Univ Sci & Technol Sch Math & Stat Luoyang 471000 Peoples R China China Univ Geosci Coll Econ & Management Wuhan 430074 Peoples R China Zhejiang Ocean Univ Sch Informat Engn Zhoushan 316022 Peoples R China

Reservoir oil-bearing recognition is the process of predicting reservoir types based on well logging data, which determines the accuracy of recognition. However, the original well logging data is multidimensional and contains potential noise, which can influence the performance of sequent processing, such as clustering and classification. It is crucial to obtain key low-dimensional features and study an accurate automatic recognition algorithm under unsupervised condition. To solve this problem, we propose a feature extraction method named graph regularized non-negative matrix factorization with optimal estimation (GNMF-OE) according to the characteristics of well logging data in this paper. Firstly, the low dimensional embedding dimension of high-dimensional well logging data is modeled and estimated, which enables the method to obtain the appropriate number of features that reflect the data structure. Secondly, local features are optimized by structured initial vectors in the framework of GNMF, which encourages the basis matrix to have clear reservoir category characteristics. These two approaches are meaningful and beneficial to construct an appropriate basis matrix that discovers the intrinsic structure of well logging data. The visualized experimental results on real datasets from Jianghan oilfield in China show that the proposed method has significant clustering performance for reservoir oil-bearing recognition.

关键词： non-negative matrix factorization Low rank matrix recovery Feature extraction Reservoir

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