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WSNMF: Weighted symmetric nonnegative matrix factorization for attributed graph clustering

NEUROCOMPUTING 2024年 566卷

作者： Berahmand, Kamal Mohammadi, Mehrnoush Sheikhpour, Razieh Li, Yuefeng Xu, Yue Queensland Univ Technol Fac Sci Sch Comp Sci Brisbane Australia Univ Kurdistan Dept Comp Engn Sanandaj Iran Ardakan Univ Fac Engn Dept Comp Engn POB 184 Ardakan Iran

In recent times, symmetric nonnegative matrix factorization (SNMF), a derivative of nonnegative matrix factorization (NMF), has surfaced as a promising technique for graph clustering. Nevertheless, when applied to attributed graph clustering, it confronts notable challenges. These include the disregard for attributed information, the oversight of geometric data point structures, and the inability to discriminate irrelevant features and data outliers. In response, we introduce an innovative extension of SNMF termed Weighted symmetric nonnegative matrix factorization (WSNMF). This method introduces node attribute similarity to compute a weight matrix, effectively bridging the gap for attributed graph clustering. Our approach incorporates graph regularization and sparsity constraints to uphold the geometric structure of data points and discern irrelevant features and data outliers. Additionally, we present an updating rule to address optimization complexities and validate algorithmic convergence. Rigorous experimentation on real-world and synthetic networks, employing well-established metrics including F-measure, RI, Modularity, Density, and entropy, substantiates the performance enhancement offered by WSNMF.

关键词： Attributed networks Attributed graph clustering nonnegative matrix factorization symmetric nonnegative matrix factorization

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A unified framework of community hiding using symmetric nonnegative matrix factorization

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INFORMATION SCIENCES 2024年 663卷

作者： Liu, Dong Jia, Ruoxue Liu, Xia Zhang, Wensheng Henan Normal Univ Coll Comp & Informat Engn Xinxiang 453007 Henan Peoples R China Key Lab Artificial Intelligence & Personalized Lea Xinxiang 453007 Henan Peoples R China Big Data Engn Lab Teaching Resources & Assessment Xinxiang Henan Peoples R China Chinese Acad Sci Inst Automat Beijing 100190 Peoples R China

Community detection can help us to deeply understand community structures and reveal potential social relationships among members. However, as people's concerns over the excessive mining of personal information have grown, the idea of community hiding has been proposed for privacy protection. Most existing community hiding methods based on heuristic approaches and genetic algorithms ignore the generative process of the network and cannot provide a better explanation of the rationality of the hiding mechanism. In addition, they are not simultaneously applicable to the global community, target community, or target nodes. In this study, we address the community hiding problem on three scales: global community hiding (macroscopic), target community hiding (mesoscopic), and target node hiding (microscopic). We propose a unified community hiding framework (CH-SNMF) that can be applied to all three scales. The basic idea is to use symmetric nonnegative matrix factorization to describe the network generative mechanism. It has a potential clustering capability that can mine key links and link sets during the network generation process. Therefore, they can be used to disrupt community structures with minimal perturbation budgets. The experimental results show that CH-SNMF outperforms many advanced baseline methods and effectively protects organizational and individual privacy.

关键词： Community detection Community hiding symmetric nonnegative matrix factorization Community structure Social network analysis

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Hypergraph based semi-supervised symmetric nonnegative matrix factorization for image clustering

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PATTERN RECOGNITION 2023年第1期137卷

作者： Yin, Jingxing Peng, Siyuan Yang, Zhijing Chen, Badong Lin, Zhiping Guangdong Univ Technol Sch Informat Engn GuangZhou 510006 Peoples R China Guangdong Prov Key Lab Intellectual Property & Big Guangzhou Peoples R China Xi An Jiao Tong Univ Inst Artificial Intelligence & Robot Xian 710049 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

Semi-supervised symmetric nonnegative matrix factorization (SNMF) has been shown to be a signifi-cant method for both linear and nonlinear data clustering applications. Nevertheless, existing SNMF-based methods only adopt a simple graph to construct the similarity matrix, and cannot fully use the limited supervised information for the construction of the similarity matrix. To overcome the drawbacks of pre-vious SNMF-based methods, a new semi-supervised SNMF-based method called hypergraph based semi -supervised SNMF (HSSNMF), is proposed in this paper for image clustering. Specifically, HSSNMF adopts a predefined hypergraph to build a similarity matrix for capturing the high-order relationships of samples. By exploiting a new hypergraph based pairwise constraints propagation (HPCP) algorithm, HSSNMF prop-agates the pairwise constraints of the limited data points to the entire data points, which can make full use of the limited supervised information and construct a more informative similarity matrix. Using the multiplicative updating algorithm, a discriminative assignment matrix can then be obtained by solving the optimization problem of HSSNMF. Moreover, analyses of the convergence, supervisory information, and computational complexity of HSSNMF are presented. Finally, extensive clustering experiments have been conducted on six real-world image datasets, and the experimental results have demonstrated the superiority of HSSNMF while compared with several state-of-the-art methods.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： symmetric nonnegative matrix factorization Hypergraph learning Semi -supervised learning Clustering

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An augmented Lagrangian alternating direction method for overlapping community detection based on symmetric nonnegative matrix factorization

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2020年第2期11卷 403-415页

作者： Hu, Liying Guo, Gongde Fujian Normal Univ Sch Math & Informat Fuzhou Peoples R China Fujian Normal Univ Digital Fujian Internet Of Things Lab Environm Mo Fuzhou Peoples R China

In this paper, we present an augmented Lagrangian alternating direction algorithm for symmetric nonnegative matrix factorization. The convergence of the algorithm is also proved in detail and strictly. Then we present a modified overlapping community detection method which is based on the presented symmetric nonnegative matrix factorization algorithm. We apply the modified community detection method to several real world networks. The obtained results show the capability of our method in detecting overlapping communities, hubs and outliers. We find that our experimental results have better quality than several competing methods for identifying communities.

关键词： Augmented Lagrangian function Alternating direction method symmetric nonnegative matrix factorization Overlapping community detection

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MHSNMF: multi-view hessian regularization based symmetric nonnegative matrix factorization for microbiome data analysis

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BMC BIOINFORMATICS 2020年第Sup6期21卷 234-234页

作者： Ma, Yuanyuan Zhao, Junmin Ma, Yingjun Anyang Normal Univ Sch Comp & Informat Engn Anyang Peoples R China Henan Univ Urban Construct Sch Comp & Data Sci Pingdingshan Peoples R China Cent China Normal Sch Comp Wuhan Peoples R China

BackgroundWith the rapid development of high-throughput technique, multiple heterogeneous omics data have been accumulated vastly (e.g., genomics, proteomics and metabolomics data). Integrating information from multiple sources or views is challenging to obtain a profound insight into the complicated relations among micro-organisms, nutrients and host environment. In this paper we propose a multi-view Hessian regularization based symmetric nonnegative matrix factorization algorithm (MHSNMF) for clustering heterogeneous microbiome data. Compared with many existing approaches, the advantages of MHSNMF lie in: (1) MHSNMF combines multiple Hessian regularization to leverage the high-order information from the same cohort of instances with multiple representations;(2) MHSNMF utilities the advantages of SNMF and naturally handles the complex relationship among microbiome samples;(3) uses the consensus matrix obtained by MHSNMF, we also design a novel approach to predict the classification of new microbiome *** conduct extensive experiments on two real-word datasets (Three-source dataset and Human Microbiome Plan dataset), the experimental results show that the proposed MHSNMF algorithm outperforms other baseline and state-of-the-art methods. Compared with other methods, MHSNMF achieves the best performance (accuracy: 95.28%, normalized mutual information: 91.79%) on microbiome data. It suggests the potential application of MHSNMF in microbiome data *** show that the proposed MHSNMF algorithm can effectively combine the phylogenetic, transporter, and metabolic profiles into a unified paradigm to analyze the relationships among different microbiome samples. Furthermore, the proposed prediction method based on MHSNMF has been shown to be effective in judging the types of new microbiome samples.

关键词： symmetric nonnegative matrix factorization Hessian regularization Multi-view clustering Human microbiome

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Clustering and Integrating of Heterogeneous Microbiome Data by Joint symmetric nonnegative matrix factorization with Laplacian Regularization

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020年第3期17卷 788-795页

作者： Ma, Yuanyuan Hu, Xiaohua He, Tingting Jiang, Xingpeng Cent China Normal Univ Sch Informat Management Wuhan 430079 Peoples R China Cent China Normal Univ Sch Comp Wuhan 430079 Peoples R China

Many datasets that exists in the real world are often comprised of different representations or views which provide complementary information to each other. To integrate information from multiple views, data integration approaches such as nonnegative matrix factorization (NMF) have been developed to combine multiple heterogeneous data simultaneously to obtain a comprehensive representation. In this paper, we proposed a novel variant of symmetric nonnegative matrix factorization (SNMF), called Laplacian regularization based joint symmetric nonnegative matrix factorization (LJ-SNMF) for clustering multi-view data. We conduct extensive experiments on several realistic datasets including Human Microbiome Project data. The experimental results show that the proposed method outperforms other variants of NMF, which suggests the potential application of LJ-SNMF in clustering multi-view datasets. Additionally, we also demonstrate the capability of LJ-SNMF in community finding.

关键词： symmetric matrices Laplace equations Kernel Linear programming Sequential analysis Feature extraction Phylogeny symmetric nonnegative matrix factorization multi-view clustering similarity network fusion laplacian regularization human microbiome

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Adaptive computation of the symmetric nonnegative matrix factorization (SymNMF)

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SeMA Journal 2020年第2期77卷 203-217页

作者： Favati, P. Lotti, G. Menchi, O. Romani, F. IIT-CNR Via G. Moruzzi 1 Pisa 56124 Italy Dip. di Scienze Matematiche Fisiche e Informatiche University of Parma Parco Area delle Scienze 53/A Parma 43124 Italy Dip. di Informatica University of Pisa Largo Pontecorvo 3 Pisa 56127 Italy

symmetric nonnegative matrix factorization (SymNMF) provides a symmetric nonnegative low rank decomposition of symmetric matrices. It has found application in several domains such as data mining, bioinformatics and graph clustering. In this paper SymNMF is obtained by solving a penalized nonsymmetric minimization problem. Instead of letting the penalizing parameter increase according to an a priori fixed rule, as suggested in literature, we propose a heuristic approach based on an adaptive technique. The factorization is performed by applying, as inner-outer procedure, the Alternating nonnegative Least Squares (ANLS). The inner problems are solved by two nonnegative quadratic optimization methods: an Active-Set-like method (BPP) and the Greedy Coordinate Descent method (GCD). Extensive experimentation shows that the proposed heuristic approach is effective with both the inner methods, GCD outperforming BPP in terms of computational time complexity. © 2020, Sociedad Española de Matemática Aplicada.

关键词： Graph Clustering symmetric nonnegative matrix factorization

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An Evolutionary Approach Based on symmetric nonnegative matrix factorization for Community Detection in Dynamic Networks

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2019年第12期E102D卷 2619-2623页

作者： Pan, Yu Hu, Guyu Pan, Zhisong Wang, Shuaihui Shao, Dongsheng Army Engn Univ Inst Command & Control Engn Nanjing 210007 Jiangsu Peoples R China

Detecting community structures and analyzing temporal evolution in dynamic networks are challenging tasks to explore the inherent characteristics of the complex networks. In this paper, we propose a semi-supervised evolutionary clustering model based on symmetric nonnegative matrix factorization to detect communities in dynamic networks, named sEC-SNMF. We use the results of community partition at the previous time step as the priori information to modify the current network topology, then smooth-out the evolution of the communities and reduce the impact of noise. Furthermore, we introduce a community transition probability matrix to track and analyze the temporal evolutions. Different from previous algorithms, our approach does not need to know the number of communities in advance and can deal with the situation in which the number of communities and nodes varies over time. Extensive experiments on synthetic datasets demonstrate that the proposed method is competitive and has a superior performance.

关键词： dynamic networks community detection symmetric nonnegative matrix factorization

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A Collaborative Neurodynamic Approach to symmetric nonnegative matrix factorization 25th

A Collaborative Neurodynamic Approach to Symmetric Nonnegati...

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25th International Conference on Neural Information Processing (ICONIP)

作者： Che, Hangjun Wang, Jun City Univ Hong Kong Dept Comp Sci Kowloon Tong Hong Kong Peoples R China City Univ Hong Kong Shenzhen Res Inst Shenzhen Peoples R China

ISBN: (纸本)9783030041793;9783030041786

This paper presents a collaborative neurodynamic approach to symmetric nonnegative matrix factorization (SNMF). First, a formulated nonconvex optimization problem of SNMF is described. To solve this problem, a neurodynamic model based on an augmented Lagrangian function is proposed and proven to be convergent to a strict local optimal solution under the second-order sufficiency condition. Next, a group of neurodynamic models are employed to search for an optimal factorized matrix by using particle swarm algorithm to update the initial neuronal states. The efficacy of the proposed approach is substantiated on two datasets.

关键词： symmetric nonnegative matrix factorization Collaborative neurodynamic approach Augmented Lagrangian function

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ESNMF: Evolutionary symmetric nonnegative matrix factorization for Dissecting Dynamic Microbial Networks 1

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14th International Conference on Intelligent Computing (ICIC)

作者： Ma, Yuanyuan Hu, Xiaohua He, Tingting Zhu, Xianchao Zhou, Meijun Jiang, Xingpeng Cent China Normal Univ Sch Informat Management Wuhan Hubei Peoples R China Cent China Normal Univ Sch Comp Wuhan Hubei Peoples R China

ISBN: (数字)9783319959573

ISBN: (纸本)9783319959573;9783319959566

Dynamic network is drawing more and more attention due to its potential in capturing time-dependent phenomena such as online public opinion and biological system. Microbial interaction networks that model the microbial system are often dynamic, static analysis methods are difficult to obtain reliable knowledge on evolving communities. To fulfill this gap, a dynamic clustering approach based on evolutionary symmetric nonnegative matrix factorization (ESNMF) is used to analyze the microbiome time-series data. To our knowledge, this is the first attempt to extract dynamic modules across time-series microbial interaction network. ESNMF systematically integrates temporal smoothness cost into the objective function by simultaneously refining the clustering structure in the current network and minimizing the clustering deviation in successive timestamps. We apply the proposed framework on a human microbiome datasets from infants delivered vaginally and ones born via C-section. The proposed method cannot only identify the evolving modules related to certain functions of microbial communities, but also discriminate differences in two kinds of networks obtained from infants delivered vaginally and via C-section.

关键词： Dynamic network Evolutionary module symmetric nonnegative matrix factorization Microbiome

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