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Boosting nonnegative matrix factorization Based Community Detection With Graph Attention Auto-Encoder

IEEE TRANSACTIONS ON BIG DATA 2021年第4期8卷 968-981页

作者： He, Chaobo Zheng, Yulong Fei, Xiang Li, Hanchao Hu, Zeng Tang, Yong Zhongkai Univ Agr & Engn Sch Informat Sci & Technol Guangzhou 510225 Peoples R China South China Normal Univ Sch Comp Sci Guangzhou 510631 Peoples R China Coventry Univ Dept Comp Coventry CV1 5FB W Midlands England

Community detection is of great help to understand the structures and functions of complex networks. It has become one of popular research topics in the field of complex networks analysis. Due to the simplicity, flexibility, effectiveness and better interpretability, nonnegative matrix factorization (NMF)-based methods have been widely employed for community detection. However, most existing NMF-based community detection methods are linear and their performance is limited when facing networks with diversified structure information. In view of this, we propose a nonlinear NMF-based method named NMFGAAE, which is composed of two main modules: NMF and Graph Attention Auto-Encoder (GAAE). This approach can boost the performance of NMF-based community detection methods by the aid of graph neural networks and deep clustering. More specifically, GAAE introduces an attention mechanism directed by NMF-based community detection to learn the node representations, while NMF can simultaneously factor these representations to uncover the community structure. We design a unified framework to jointly optimize GAAE and NMF modules, which is very beneficial to obtain better community detection results. We conduct extensive experiments on synthetic and real-world networks. The results show that our NMFGAAE not only performs better than state-of-the-art NMF-based community detection methods, but also outperforms some network representation based baselines. More importantly, NMFGAAE indeed can boost the performance of NMF-based community detection methods.

关键词： Complex networks Convolution Task analysis Data models Graph neural networks Feature extraction Big Data Community detection nonnegative matrix factorization graph attention auto-encoder graph neural networks deep clustering complex networks

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An improved nonnegative matrix factorization with the imputation method model for pollution source apportionment during rainstorm events

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2023年第1期328卷 116888页

作者： Feng, Jiashen Duan, Tingting Zhou, Yanqing Chang, Xuan Li, Yingxia Beijing Normal Univ Sch Environm State Key Joint Lab Environm Simulat & Pollut Cont Beijing Peoples R China 19th Xinjiekouwai St Beijing 100875 Peoples R China

Data scarcity caused by extreme conditions during storms adds difficulties in performing pollution source apportionment. This study integrated nonnegative matrix factorization with the imputation method (NMF-IM) to fill in missing data (NAs) and conduct source apportionment. A total of 367 river samples and 35 runoff samples were taken from the Banqiao and Nanfei River basins located in Hefei, China, during four rainfall events from June to August 2020. Sixteen indicators were quantified and used for source diagnostics using NMF-IM. The results showed that total phosphorus (TP) had higher concentrations and more violent fluctuations than total nitrogen (TN) in river samples taken from rain. NMF-IM was shown to recover the value distribution of NAs approximately. The source profiles and contribution rates calculated by NMF-IM with NAs were close to the original results calculated by NMF without NAs, with root mean square error of less than 2.3% and differences less than 9.5%. Multiple forms of nitrogen and phosphorus indicators benefit reaching reasonable source diagnostics results. At least four indicators were needed to reach the same contribution rates as 16 indicator diagnostics. The two good indicator combination groups are nitrate (NO3-N), nitrite (NO2-N), ammonia nitrogen (NH3-N), and total suspended solids (TSS) and NO3-N, NO2-N, phosphorus (PO4-P), and TSS. The pollution source contributions changed with the Antecedent dry period (ADPs) of rain events. Treated tailwater and untreated sewage were major sources, contributing more than 80% of the total pollution of the rainstorm events with short ADPs. Dust wash became the dominant contributor after 60 min and contributed 36% of the total pollution of rainstorm events with long ADPs. The average source contribution rates for rainfall events in the Banqiao River were treated tailwater (41%) > untreated sewage (27%) > dust wash (19%) > other sources (16%). The pollution source diagnostics results were verified to

关键词： nonnegative matrix factorization Pollution source analysis Rainstorm event Receptor model Rivers

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Robust latent nonnegative matrix factorization with automatic sparse reconstruction for unsupervised feature extraction

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INFORMATION SCIENCES 2023年第1期648卷

作者： Wan, Minghua Cai, Mingxiu Yang, Zhangjing Tan, Hai Yang, Guowei Tang, Mingwei Nanjing Audit Univ Sch Comp Sci Sch Intelligent Auditing Nanjing 211815 Peoples R China Nanjing Univ Sci & Technol Jiangsu Key Lab Image & Video Understanding Social Nanjing 210094 Peoples R China Nanjing Univ Sci & Technol Key Lab Intelligent Percept & Syst High Dimens Inf Minist Educ Nanjing 210094 Peoples R China Nanjing Xiaozhuang Univ Key Lab Intelligent Informat Proc Nanjing 211171 Peoples R China Qingdao Univ Sch Elect & Informat Qingdao 266071 Peoples R China

In recent years, the combination of nonnegative matrix factorization (NMF) and manifold learning has been widely confirmed. Although these methods are successful, there are some shortcomings: 1) The traditional manifold learning methods require predefined manifold geometry, which cannot reasonably reflect intrinsic geometric properties;2) Most previous methods only consider the robustness of models to noise and outliers, but not occlusion;3) Many models only contain the local neighborhood structure, but not the global geometric structure. To address these issues, we propose a novel model robust latent nonnegative matrix factorization with sparse reconstruction (RLNMF-SR) to conduct complex classification tasks. Our method utilizes sparse nodes to automatically reconstruct a global-based affinity graph without manually defining the graph structure, which guarantees that our model more accurately grasps the underlying distribution of the data. In addition, by decomposing the principal component with a low-rank structure, we can not only remove redundant features and reduce the computational cost but also obtain a more compact, discriminative and interpretable low-rank representation. At the same time, low-rank restriction can also recover the row and column information of the matrix to decrease the negative effects of noise and occlusion. On the other hand, applying the L2,1-norm to perform part-based nonnegative factorization can also attain the local attribute information of the data and suppress the model's sensitivity to destruction, greatly enhancing the robustness of the RLNMF-SR. Extensive experiments indicate that our method outperforms other state-of-the-art methods, especially on low-quality image datasets.

关键词： nonnegative matrix factorization Low-rank learning Sparse reconstruction Global geometric structure Local neighborhood structure

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Community detection in networks through a deep robust auto-encoder nonnegative matrix factorization

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2023年 118卷

作者： Al-sharoa, Esraa Rahahleh, Baraa Jordan Univ Sci & Technol Irbid 22110 Jordan

Community detection is a field of research with increasing influence due to its importance in dimensionality reduction and revealing the organizational patterns in networks. A community or cluster in a network reflects the interactions among the objects that are strongly connected and distinguish them from the ones in other clusters. Over the past decades, various algorithms have been developed to detect the community structure in networks. However, the performance of these algorithm is affected by the existence of noise or nonlinear information in the network. Consequently, deep learning algorithms arise to tackle this issue. In this paper, we propose a novel deep robust auto-encoder nonnegative matrix factorization (DRANMF) approach to detect the community structure in networks. In particular, DRANMF consists of a deep structured decoder and encoder components to transform the high-order proximity matrix of the network to and from the cluster membership space, respectively. Moreover, we enhance the robustness of the proposed approach against noise and outliers by adopting the I-2,I-1-norm to formulate the objective function. The experiments on multiple synthetic and real-world networks demonstrate that the proposed DRANMF has a better performance and robustness than other existing methods.

关键词： Networks Auto-encoder Deep learning Community detection nonnegative matrix factorization

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Bi-level algorithm for optimizing hyperparameters in penalized nonnegative matrix factorization

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APPLIED MATHEMATICS AND COMPUTATION 2023年第1期457卷

作者： Del Buono, Nicoletta Esposito, Flavia Selicato, Laura Zdunek, Rafal Univ Bari Aldo Moro Dept Math Via Orabona 4 I-70125 Bari Italy Wroclaw Univ Sci & Technol Fac Elect Photon & Microsyst 27 Wybrzeze Wyspianskiego St Wroclaw PL-50370 Poland

Learning approaches rely on hyperparameters that impact the algorithm's performance and affect the knowledge extraction process from data. Recently, nonnegative matrix Factoriza-tion (NMF) has attracted a growing interest as a learning algorithm. This technique cap-tures the latent information embedded in large datasets while preserving feature proper-ties. NMF can be formalized as a penalized optimization task in which tuning the penalty hyperparameters is an open issue. The current literature does not provide any general framework addressing this task. This study proposes to express the penalty hyperparam-eters problem in NMF in terms of a bi-level optimization. We design a novel algorithm, named Alternating Bi-level (AltBi), which incorporates the hyperparameters tuning proce-dure into the updates of NMF factors. Results of the existence and convergence of numer-ical solutions, under appropriate assumptions, are studied, and numerical experiments are provided.& COPY;2023 Elsevier Inc. All rights reserved.

关键词： nonnegative matrix factorization Hyperparameter optimization Penalty coefficient Low -rank approximation

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Global and local similarity learning in multi-kernel space for nonnegative matrix factorization

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KNOWLEDGE-BASED SYSTEMS 2023年 279卷 110946页

作者： Peng, Chong Hou, Xingrong Chen, Yongyong Kang, Zhao Chen, Chenglizhao Cheng, Qiang Qingdao Univ Coll Comp Sci & Technol Qingdao Peoples R China Harbin Inst Technol Sch Comp Sci & Technol Shenzhen Peoples R China Univ Elect Sci & Technol China Sch Comp Sci & Engn Chnegdu Peoples R China Univ Kentucky Dept Comp Sci Lexington KY USA Univ Kentucky Inst Biomed Informat Lexington KY USA

Most of existing nonnegative matrix factorization (NMF) methods do not fully exploit global and local similarity information from data. In this paper, we propose a novel local similarity learning approach in the convex NMF framework, which encourages inter-class separability that is desired for clustering. Thus, the new model is capable of enhancing intra-class similarity and inter-class separability with simultaneous global and local learning. Moreover, the model learns the factor matrices in an augmented kernel space, which is a convex combination of pre-defined kernels with auto-learned weights. Thus, the learnings of cluster structure, representation factor matrix, and the optimal kernel mutually enhance each other in a seamlessly integrated model, which leads to informative representation. Multiplicative updating rules are developed with theoretical convergence guarantee. Extensive experimental results have confirmed the effectiveness of the proposed model.(c) 2023 Elsevier B.V. All rights reserved.

关键词： nonnegative matrix factorization Clustering Local similarity Multiple kernels

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Link prediction by adversarial nonnegative matrix factorization

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KNOWLEDGE-BASED SYSTEMS 2023年 280卷

作者： Mahmoodi, Reza Seyedi, Seyed Amjad Tab, Fardin Akhlaghian Abdollahpouri, Alireza Univ Kurdistan Dept Comp Engn Sanandaj Iran

Networks are now more crucial than ever for modeling complex systems with interconnected components. Many methods have been developed to infer unobserved links or predict latent links based on observed network topology. However, the effectiveness of current methods is often limited due to the nature of sparseness in large-scale networks. nonnegative matrix factorization (NMF) is one of the most popular low -rank approximation methods which has been successfully applied to large-scale data. However, maintaining generalization from limited observations is still an open challenge. To overcome these challenges, we propose a novel link prediction method based on adversarial NMF, which reconstructs a sparse network by an efficient adversarial training algorithm. Unlike the conventional NMF methods, our model considers potential test adversaries beyond the pre-defined bounds and provides a robust reconstruction with good generalization power. Besides, to preserve the local structure of a network, we use the common neighbor algorithm to extract the node similarity and apply it to low-dimensional latent representation. Simultaneously, we use Frobenius-norm regularization to prevent the factorization from overfitting. We provide an effective Majorization-Minimization method to learn the model parameters. Our method outperforms the state-of-the-art methods, as shown by extensive experiment results on twelve real-world datasets.

关键词： Link prediction Adversarial training Robustness Generalization nonnegative matrix factorization

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Auto weighted robust dual graph nonnegative matrix factorization for multiview clustering

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APPLIED SOFT COMPUTING 2023年 146卷

作者： Jia, Mengxue Liu, Sanyang Bai, Yiguang Xidian Univ Sch Math & Stat Xian 710126 Peoples R China

Recent multi-data fusion techniques have inspired multi-view clustering study, which has become a popular topic in machine learning. One successful way of solving multi-view clustering is nonnegative matrix factorization. This paper proposes an auto weighted robust dual graph nonnegative matrix factorization (ARDNMF), where l2,1 norm is adopted to make ARDNMF robust as data contain noise and outliers. Through dual graphs, structure information in data space and feature space is considered. Moreover, an auto weighted assignment method is introduced in ARDNMF to assign appropriate weights to views. Effective updating rules are given. Experiments on real datasets show ARDNMF superiors to state-of-the-art algorithms in terms of clustering results.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Multiview clustering nonnegative matrix factorization l21 norm Dual graph

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Self-supervise d semi-supervise d nonnegative matrix factorization for data clustering

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PATTERN RECOGNITION 2023年第1期137卷

作者： Chavoshinejad, Jovan Seyedi, Seyed Amjad Tab, Fardin Akhlaghian Salahian, Navid Univ Kurdistan Dept Comp Engn Sanandaj Iran

Semi-supervised nonnegative matrix factorization exploits the strengths of matrix factorization in suc-cessfully learning part-based representation and is also able to achieve high learning performance when facing a scarcity of labeled data and a large amount of unlabeled data. Its major challenge lies in how to learn more discriminative representations from limited labeled data. Furthermore, self-supervised learn-ing has been proven very effective at learning representations from unlabeled data in various learning tasks. Recent research works focus on utilizing the capacity of self-supervised learning to enhance semi-supervised learning. In this paper, we design an effective Self-Supervised Semi-Supervised nonnegative matrix factorization (S4NMF) in a semi-supervised clustering setting. The S4NMF directly extracts a con-sensus result from ensembled NMFs with similarity and dissimilarity regularizations. In an iterative pro-cess, this self-supervisory information will be fed back to the proposed model to boost semi-supervised learning and form more distinct clusters. The proposed iterative algorithm is used to solve the given problem, which is defined as an optimization problem with a well-formulated objective function. In ad-dition, the theoretical and empirical analyses investigate the convergence of the proposed optimization algorithm. To demonstrate the effectiveness of the proposed model in semi-supervised clustering, we con-duct extensive experiments on standard benchmark datasets. The source code for reproducing our results can be found at https://***/ChavoshiNejad/S4NMF .(c) 2022 Elsevier Ltd. All rights reserved.

关键词： nonnegative matrix factorization Semi-supervised learning Self-supervised learning Ensemble clustering

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A majorization-minimization based solution to penalized nonnegative matrix factorization with orthogonal regularization

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2023年 421卷

作者： Tong, Can Wei, Jiao Qi, Shouliang Yao, Yudong Zhang, Tie Teng, Yueyang Northeastern Univ Coll Med & Biol Informat Engn Shenyang 110169 Peoples R China Northeastern Univ Coll Sci Shenyang 110819 Peoples R China Minist Educ Key Lab Intelligent Comp Med Image Shenyang 110169 Peoples R China Stevens Inst Technol Dept Elect & Comp Engn Hoboken NJ USA

nonnegative matrix factorization (NMF) is a dimension reduction and clustering tech-nique for data analysis which has been widely used in image processing, text analysis and hyperspectral decomposition because of its stronger practical significance and better interpretability. Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal NMF (ONMF), have been shown to work remarkably better for clustering tasks than NMF. At present, a large number of algorithms have been used to solve the ONMF problems, but these methods usually cannot take into account the classification accuracy and calculation speed. In this paper, we propose a new form of penalized NMF with orthogonal regularization that combines the decomposition residual minimization based on the Euclidean distance and the orthogonality maximization based on the Kullback-Leibler divergence. This paper uses Majorization-Minimization (MM) method by minimizing a majorization function of the original problem and obtains a new iterative scheme (MM-ONMF). Comparing with several traditional ONMF methods on eight datasets, experimental results show that the proposed method has better clustering results and less computing time. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Kullback-Leibler divergence Majorization-Minimization method nonnegative matrix factorization Orthogonal regularization

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