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Learning multi-level topology representation for multi-view clustering with deep non-negative matrix factorization

NEURAL NETWORKS 2025年 182卷 106856页

作者： Dou, Zengfa Peng, Nian Hou, Weiming Xie, Xianghua Ma, Xiaoke Qinghai Inst Technol Sch Comp & Informat Sci Xining Qinghai Peoples R China Xidian Univ Sch Comp Sci & Technol Xian Shaanxi Peoples R China Hebei Univ Sci & Technol Sch Informat Sci & Engn Shijiazhuang Hebei Peoples R China Swansea Univ Dept Comp Sci Swansea Wales

Clustering of multi-view data divides objects into groups by preserving structure of clusters in all views, requiring simultaneously takes into consideration diversity and consistency of various views, corresponding to the shared and specific components of various views. Current algorithms fail to fully characterize and balance diversity and consistency of various views, resulting in the undesirable performance. Here, a novel Multi-View Clustering with deep non-negative matrix factorization and Multi-Level Representation (MVC-DMLR) learning is proposed, which integrates feature learning, multi-level topology representation, and clustering of multi-view data. Specifically, MVC-DMLR first learns multi-level representation (also called deep features) of objects with deep nonnegative matrix factorization (DNMF), facilitating the exploitation of hierarchical structure of multi- view data. Then, it learns multi-level graphs for each view from multi-level representation, where relations between diversity and consistency are addressed at various resolutions. MVC-DMLR integrates multi-level representation learning, multi-level topology representation learning and clustering, which is formulated as an optimization problem. Experimental results show the superiority of MVC-DMLR to baselines in terms of accuracy, F1-score, normalized mutual information and adjusted rand index.

关键词： Multi-view clustering deep non-negative matrix factorization Self-representation learning Multi-layer networks

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deep non-negative matrix factorization with edge generator for link prediction in complex networks

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APPLIED INTELLIGENCE 2024年第1期54卷 592-613页

作者： Yao, Yabing He, Yangyang Huang, Zhentian Xu, Zhipeng Yang, Fan Tang, Jianxin Gao, Kai Lanzhou Univ Technol Sch Comp & Commun Lanzhou 730050 Peoples R China Guangxi Univ Sci & Technol Sch Comp Sci & Technol Liuzhou 545006 Peoples R China

Link prediction aims to infer missing links or predict future links based on observed topology or attribute information in the network. Many link prediction methods based on non-negative matrix factorization (NMF) have been proposed to solve prediction problem. However, due to the sparsity of real networks, the observed topology information is probably very limited, which affects the performance of existing link prediction methods. In this paper, we utilize deep non-negative matrix factorization (DNMF) models with Edge Generator to address the network sparsity problem and propose link prediction methods EG-DNMF and EG-FDNMF. Under the framework of DNMF, several representative potential edges are incorporated so as to reconstruct the original network for link prediction. Specifically, in order to explore the potential structural features of the network in a more fine-grained manner, we first divide the original network into three sub-networks. Then, the DNMF models are employed to mine complex and nonlinear interaction relationships in sub-networks, thereby guiding the network reconstruction process. Finally, the NMF algorithm is applied on the reconstructed original network for link prediction. Experiment results on 12 different networks show that our methods have comparable performance with respect to 13 representative link prediction methods which include 6 NMF/DNMF-based approaches and 7 heuristic-based approaches. In addition, experiments also show that the sub-networks after partitioning are beneficial for capturing the underlying features of the network. Codes are available at https://***/yabingyao/EGDNMF4LinkPrediction

关键词： Link prediction Network reconstruction Sub-network deep non-negative matrix factorization

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Multi-layer manifold learning for deep non-negative matrix factorization-based multi-view clustering

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PATTERN RECOGNITION 2022年 131卷

作者： Luong, Khanh Nayak, Richi Balasubramaniam, Thirunavukarasu Bashar, Md Abul Queensland Univ Technol QUT Ctr Data Sci Sch Comp Sci Brisbane Qld Australia

Multi-view data clustering based on non-negative matrix factorization (NMF) has been commonly used for pattern recognition by grouping multi-view high-dimensional data by projecting it to a lower-order dimensional space. However, the NMF framework fails to learn the accurate lower-order representation of the input data if it exhibits complex and non-linear relationships. This paper proposes a deep non-negative matrix factorization-based framework for effective multi-view data clustering by uncovering both the non-linear relationships and the intrinsic components of the data. Both the consensus and complementary information present in multiple views are sufficiently learned in the proposed framework with the effective use of constraints such as normalized cut-type and orthogonal. The optimal manifold of multi-view data is effectively incorporated in all layers of the framework. Extensive experimental results show the proposed method outperforms state-of-the-art multi-view matrix factorization-based methods. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Multi-view data clustering Manifold learning non-negative matrix factorization (NMF) deep matrix factorization (DMF) deep non-negative matrix factorization (deep-NMF)

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Link prediction by deep non-negative matrix factorization

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期188卷 115991-115991页

作者： Chen, Guangfu Wang, Haibo Fang, Yili Jiang, Ling Wuyi Univ Coll Math & Comp Wuyishan 354399 Peoples R China Shenzhen Univ Coll Elect & Informat Engn Shenzhen 518060 Peoples R China Hunan Univ Sci & Engn Coll Elect & Informat Engn Yongzhou 425199 Peoples R China Zhejiang Gongshang Univ Coll Comp & Informat Engn Hangzhou 310018 Peoples R China

Link prediction aims to predict missing links or eliminate spurious links and new links in future network by known network structure information. Most existing link prediction methods are shallow models and did not consider network noise. To address these issues, in this paper, we propose a novel link prediction model based on deep non-negative matrix factorization, which elegantly fuses topology and sparsity-constrained to perform link prediction tasks. Specifically, our model fully exploits the observed link information for each hidden layer by deep non-negative matrix factorization. Then, we utilize the common neighbor method to calculate the similarity scores and map it to multi-layer low-dimensional latent space to obtain the topological information of each hidden layer. Simultaneously, we employ the l(2,1)-norm constrained factor matrix at each hidden layer to remove the random noise. Besides, we provide an effective the multiplicative updating rules to learn the parameter of this model with the convergence guarantees. Extensive experiments results on eight real-world datasets demonstrate that our proposed model significantly outperforms the state-of-the-art methods.

关键词： Link prediction deep non-negative matrix factorization Structural information Sparsity-constrained

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deep multiple non-negative matrix factorization for multi-view clustering

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INTELLIGENT DATA ANALYSIS 2021年第2期25卷 339-357页

作者： Du, Guowang Zhou, Lihua Lu, Kevin Ding, Haiyan Yunnan Univ Sch Informat Kunming 650091 Yunnan Peoples R China Brunel Univ Uxbridge Middx England

Multi-view clustering aims to group similar samples into the same clusters and dissimilar samples into different clusters by integrating heterogeneous information from multi-view data. non-negative matrix factorization (NMF) has been widely applied to multi-view clustering owing to its interpretability. However, most NMF-based algorithms only factorize multi-view data based on the shallow structure, neglecting complex hierarchical and heterogeneous information in multi-view data. In this paper, we propose a deep multiple non-negative matrix factorization (DMNMF) framework based on AutoEncoder for multi-view clustering. DMNMF consists of multiple Encoder Components and Decoder Components with deep structures. Each pair of Encoder Component and Decoder Component are used to hierarchically factorize the input data from a view for capturing the hierarchical information, and all Encoder and Decoder Components are integrated into an abstract level to learn a common low-dimensional representation for combining the heterogeneous information across multi-view data. Furthermore, graph regularizers are also introduced to preserve the local geometric information of each view. To optimize the proposed framework, an iterative updating scheme is developed. Besides, the corresponding algorithm called MVC-DMNMF is also proposed and implemented. Extensive experiments on six benchmark datasets have been conducted, and the experimental results demonstrate the superior performance of our proposed MVC-DMNMF for multi-view clustering compared to other baseline algorithms.

关键词： deep non-negative matrix factorization multi-view clustering deep AutoEncoder graph regularization constraints

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deep GROUPED non-negative matrix factorization METHOD FOR IMAGE DATA REPRESENTATION 20

DEEP GROUPED NON-NEGATIVE MATRIX FACTORIZATION METHOD FOR IM...

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20th International Conference on Machine Learning and Cybernetics (ICMLC)

作者： Zhan, Zihao Chen, Wen-Sheng Pan, Binbin Chen, Bo Shenzhen Univ Coll Math & Stat Shenzhen Peoples R China Shenzhen Univ Guangdong Key Lab Media Secur Shenzhen Peoples R China Shenzhen Univ Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen Peoples R China

ISBN: (纸本)9781665466080

non-negative matrix factorization (NMF) is an unsupervised learning method that can be exploited for parts-based image representation due to non-negativity constraints. However, singer-layer NMF cannot capture the latent hierarchical structure features from images, while deep features play more important roles in the image representation and recognition tasks. To overcome the limitation of NMF, this paper proposes a novel deep grouped NMF (DGNMF) approach to learn different level attributes of the data. It is interesting that DGNMF approach automatically makes the data from distinct classes share different basis images and the feature vectors among different classes are mutually orthogonal at the same layer. Meanwhile, to preserve the local information, our DGNMF model establishes the objective function with graph regularization, and its optimization problem is solved using gradient descent method. The developed DGNMF algorithm is proved to be convergent and is finally evaluated on face datasets for classification. Compared with some state-of-the-art deep NMF variants, the results demonstrate the proposed DGNMF algorithm achieves surpassing performances using different layer features.

关键词： deep non-negative matrix factorization Supervised Learning Method Image Data Representation

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Community detection in multiplex networks by deep structure-preserving non-negative matrix factorization

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APPLIED INTELLIGENCE 2025年第1期55卷 1-16页

作者： Zhou, Qinli Zhu, Wenjie Chen, Hao Peng, Bo China Jiliang Univ Coll Informat Engn Key Lab Electromagnet Wave Informat Technol & Metr Hangzhou 310018 Zhejiang Peoples R China China Jiliang Univ Coll Sci Hangzhou 310018 Zhejiang Peoples R China Univ Queensland Brisbane 4072 Australia

Multiplex networks convey more valuable information than single-layer networks;thus, performing the community detection task involving these networks has become a subject of extensive research on the exploration of latent community structures. The non-negative matrix factorization (NMF) algorithm has proven successful in community detection scenarios by offering good interpretations of community structures. However, directly obtaining consensus community assignments using the traditional NMF algorithm poses a challenge due to the presence of complex structures spanning across different layers in the multiplex network. In this paper, we propose a novel algorithm called deep Structure-Preserving non-negative matrix factorization (DSP-NMF) to perform community detection in multiplex networks. Specifically, DSP-NMF constructs a deep autoencoder-like NMF model to generate meaningful network embeddings that are represented by multiple basis matrices and reconstructed by corresponding transposed basis matrices. By integrating the similarity relationships of nodes into the proposed DSP-NMF algorithm, the corresponding Laplacian matrices in each network layer are regularized to preserve the community structure during the learning process. Simultaneously, a consensus network embedding can be learned to obtain the final community partition. In this manner, the proposed DSP-NMF algorithm not only uncovers robust community structures in multiplex networks but also maintains the coherence between layers without losing complementary features. The experimental results obtained on five multiplex network datasets show that our proposed DSP-NMF algorithm outperforms other competitive methods in community detection tasks involving multiplex networks.

关键词： Community detection Multiplex networks deep non-negative matrix factorization Laplacian regularization

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deep graph regularized non-negative matrix factorization for multi-view clustering

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NEUROCOMPUTING 2020年 390卷 108-116页

作者： Li, Jianqiang Zhou, Guoxu Qiu, Yuning Wang, Yanjiao Zhang, Yu Xie, Shengli Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Minist Educ Key Lab Intelligent Detect & Internet Things Mfg Guangzhou 510006 Peoples R China Guangdong Hong Kong Macao Joint Lab Smart Discret Guangzhou 510006 Peoples R China Stanford Univ Dept Psychiat & Behav Sci Stanford CA 94305 USA

Multi-view clustering is an unsupervised method which aims to enhance the clustering performance by combining the knowledge from multiple view data. non-negative matrix factorization (NMF) is one of the most favourable multi-view clustering methods due to its strong representation ability of non-negative data. However, NMF only factorizes the data matrix into two non-negative factor matrices, which may limit its ability to learn higher level and more complex hierarchical information. To overcome this shortcoming, in this paper, we propose a multi-view clustering method based on deep graph regularized non-negative matrix factorization (MvDGNMF). MvDGNMF is able to extract more abstract representation by constructing a multilayer NMF model with graph Laplacian regularization and drive the last layer representation from each view to a common consensus representation. Meanwhile, an efficient algorithm using alternating multiplicative update rules is developed. Furthermore, in order to demonstrate the effectiveness of this proposed method, we employ several open datasets including image and text datasets to evaluate the clustering performance of MvDGNMF and the state-of-art methods. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Multi-view clustering deep non-negative matrix factorization Graph regularization

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A deep joint sparse non-negative matrix factorization framework for identifying the common and subject-specific functional units of tongue motion during speech

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MEDICAL IMAGE ANALYSIS 2021年 72卷 1页

作者： Woo, Jonghye Xing, Fangxu Prince, Jerry L. Stone, Maureen Gomez, Arnold D. Reese, Timothy G. Wedeen, Van J. El Fakhri, Georges Massachusetts Gen Hosp Dept Radiol Gordon Ctr Med Imaging Boston MA 02114 USA Harvard Med Sch Boston MA 02114 USA Johns Hopkins Univ Dept Elect & Comp Engn Baltimore MD 21218 USA Univ Maryland Sch Dent Dept Neural & Pain Sci Baltimore MD 21201 USA Johns Hopkins Univ Sch Med Dept Neurol Baltimore MD 21218 USA Massachusetts Gen Hosp Dept Radiol Athinoula A Martinos Ctr Biomed Imaging Boston MA 02129 USA

Intelligible speech is produced by creating varying internal local muscle groupings-i.e., functional units- that are generated in a systematic and coordinated manner. There are two major challenges in characterizing and analyzing functional units. First, due to the complex and convoluted nature of tongue structure and function, it is of great importance to develop a method that can accurately decode complex muscle coordination patterns during speech. Second, it is challenging to keep identified functional units across subjects comparable due to their substantial variability. In this work, to address these challenges, we develop a new deep learning framework to identify common and subject-specific functional units of tongue motion during speech. Our framework hinges on joint deep graph-regularized sparse non-negative matrix factorization (NMF) using motion quantities derived from displacements by tagged Magnetic Resonance Imaging. More specifically, we transform NMF with sparse and graph regularizations into modular architectures akin to deep neural networks by means of unfolding the Iterative ShrinkageThresholding Algorithm to learn interpretable building blocks and associated weighting map. We then apply spectral clustering to common and subject-specific weighting maps from which we jointly determine the common and subject-specific functional units. Experiments carried out with simulated datasets show that the proposed method achieved on par or better clustering performance over the comparison *** carried out with in vivo tongue motion data show that the proposed method can determine the common and subject-specific functional units with increased interpretability and decreased size variability. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Tagged-MRI deep non-negative matrix factorization Functional units Tongue motion

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A Feature-Aware Approach to Acupoint Compatibility Prediction Using Residual Graph Attention Networks and matrix factorization

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS 2025年第5期29卷 3750-3761页

作者： Li, Ruiling Pan, Ying Wu, Song Ma, Li Peng, Limei Hubei Univ Chinese Med Sch Informat Engn Wuhan 430065 Peoples R China Hubei Univ Chinese Med Sch Acupuncture Moxibust & Orthoped Wuhan 430065 Peoples R China Kyungpook Natl Univ Sch Comp Sci & Engn Daegu 41566 South Korea

Compatibility among acupoints is a fundamental principle in acupuncture treatment within traditional Chinese medicine, playing a vital role in enhancing the effectiveness and scope of therapeutic interventions. With the increasing availability of acupuncture-related data, link prediction offers a data-driven approach that facilitates the evidence-based exploration and validation of acupoint compatibilities. However, existing link prediction methods often focus on mapping acupoints and their compatibility relationships into lower-dimensional spaces. These approaches can overlook essential acupoint features and make the predictions susceptible to noise interference. To address these challenges, we propose a novel acupoint compatibility prediction model based on a Feature-Aware Residual Graph Attention Network and matrix factorization (FRGATMF). Our model introduces a feature-aware connectivity fusion strategy that integrates acupoint attributes with structural information to enrich acupoint representations. Following this, a deep non-negative matrix factorization approach is employed to construct a denoised feature matrix. This matrix is processed through a residual graph attention network to derive comprehensive and effective node embeddings, which are crucial for accurate link prediction. Experimental results on the acupuncture dataset, along with three public datasets, demonstrate that FRGATMF significantly outperforms seven existing comparison models across various evaluation metrics. Additionally, link prediction can identify previously unconsidered or undocumented acupoint combinations that may offer better therapeutic results, thus expanding the range of treatment options and highlighting its potential in improving the prediction of acupoint compatibility relationships.

关键词： Predictive models Acupuncture Noise Drugs Autoencoders Adaptation models Semantics Prediction algorithms Diseases Biological system modeling Acupoint compatibility deep non-negative matrix factorization residual graph attention network link prediction

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