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nonnegative matrix factorization with local similarity learning

INFORMATION SCIENCES 2021年 562卷 325-346页

作者： Peng, Chong Zhang, Zhilu Kang, Zhao Chen, Chenglizhao Cheng, Qiang Qingdao Univ Coll Comp Sci & Technol Qingdao Peoples R China Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu Peoples R China Univ Kentucky Dept Comp Sci Lexington KY 40506 USA Univ Kentucky Inst Biomed Informat Lexington KY 40506 USA

High-dimensional data are ubiquitous in the learning community and it has become increasingly challenging to learn from such data [1]. For example, as one of the most important tasks in multimedia and data mining, information retrieval has drawn considerable attentions in recent years [2-4], where there is often a need to handle high-dimensional data. Often times, it is desirable and demanding to seek a data representation to reveal latent data structures of high-dimensional data, which is usually helpful for further data processing. It is thus a critical problem to find a suitable representation of the data in many learning tasks, such as image clustering and classification [5,1], foreground-background separation in surveillance video [6,7], matrix completion [8], community detection [9], link prediction [10], etc. To this end, a number of methods have been developed to seek proper representations of data, among which matrix factorization technique has been widely used to handle high-dimensional data. matrix factorization seeks two or more low-dimensional matrices to approximate the original data such that the high-dimensional data can be represented with reduced dimensions [11,12]. For some types of data, such as images and documents, the entries are naturally nonnegative. For such data, nonnegative Existing nonnegative matrix factorization methods usually focus on learning global struc-ture of the data to construct basis and coefficient matrices, which ignores the local struc-ture that commonly exists among data. To overcome this drawback, in this paper, we propose a new type of nonnegative matrix factorization method, which learns local simi-larity and clustering in a mutually enhanced way. The learned new representation is more representative in that it better reveals inherent geometric property of the data. Moreover, the new representation is performed in the kernel space, which enhances the capability of the proposed model in discovering nonlinear structures

关键词： nonnegative matrix factorization Clustering Local similarity

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Adaptive graph nonnegative matrix factorization with the self-paced regularization

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APPLIED INTELLIGENCE 2023年第12期53卷 15818-15835页

作者： Yang, Xuanhao Che, Hangjun Leung, Man-Fai Liu, Cheng Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China Chongqing Key Lab Nonlinear Circuits & Intelligen Chongqing 400715 Peoples R China Anglia Ruskin Univ Fac Sci & Engn Sch Comp & Information Sci Cambridge England Shantou Univ Dept Comp Sci Shantou Peoples R China

nonnegative matrix factorization (NMF) is a popular approach to extract intrinsic features from the original data. As the nonconvexity of NMF formulation, it always leads to degrade the performance. To alleviate the defect, in this paper, the self-paced regularization is introduced to find a better factorized matrices by sequentially selecteing data in the learning process. Additionally, to find the low-dimensional manifold embeded in the high-dimensional space, adaptive graph is introduced by using dynamic neighbors assignment. An alternating iterative algorithm is designed to sovle the proposed mathematical factorization formulation. The experimental results are given to show the effectiveness of the proposed approach in comparison with state-of-the-art algorithms on six public datasets.

关键词： Clustering nonnegative matrix factorization Self-paced learning Adaptive neighbors

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Network-Based Structural Learning nonnegative matrix factorization Algorithm for Clustering of scRNA-Seq Data

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2023年第1期20卷 566-575页

作者： Wu, Wenming Ma, Xiaoke Xidian Univ Sch Comp Sci & Technol Xian 710071 Shaanxi Peoples R China

Single-cell RNA sequencing (scRNA-seq) measures expression profiles at the single-cell level, which sheds light on revealing the heterogeneity and functional diversity among cell populations. The vast majority of current algorithms identify cell types by directly clustering transcriptional profiles, which ignore indirect relations among cells, resulting in an undesirable performance on cell type discovery and trajectory inference. Therefore, there is a critical need for inferring cell types and trajectories by exploiting the interactions among cells. In this study, we propose a network-based structural learning nonnegative matrix factorization algorithm (aka SLNMF) for the identification of cell types in scRNA-seq, which is transformed into a constrained optimization problem. SLNMF first constructs the similarity network for cells and then extracts latent features of the cells by exploiting the topological structure of the cell-cell network. To improve the clustering performance, the structural constraint is imposed on the model to learn the latent features of cells by preserving the structural information of the networks, thereby significantly improving the performance of algorithms. Finally, we track the trajectory of cells by exploring the relationships among cell types. Fourteen scRNA-seq datasets are adopted to validate the performance of algorithms with the number of single cells varying from 49 to 26,484. The experimental results demonstrate that SLNMF significantly outperforms fifteen state-of-the-art methods with 15.32% improvement in terms of accuracy, and it accurately identifies the trajectories of cells. The proposed model and methods provide an effective strategy to analyze scRNA-seq data. (The software is coded using matlab, and is freely available for academic https://***/xkmaxidian/SLNMF).

关键词： Single-cell RNA-seq cell-cell network nonnegative matrix factorization structural learning cell clustering

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Community Detection in Multilayer Networks Via Semi-Supervised Joint Symmetric nonnegative matrix factorization

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2023年第3期10卷 1623-1635页

作者： Lv, Laishui Hu, Peng Bardou, Dalal Zheng, Zijun Zhang, Ting China Jiliang Univ Coll informat Engn Hangzhou 310018 Peoples R China Anhui Normal Univ Sch Comp & informat Wuhu 241002 Peoples R China Univ Abbes Laghrour Dept Comp Sci & Math Khenchela 4004 Algeria China Jiliang Univ Coll Sci Hangzhou 310018 Peoples R China Nanjing Normal Univ Sch Comp & Elect informat Nanjing 210023 Peoples R China

Community detection plays an important role in network analysis and has attracted considerable interest from researchers. In the past few decades, various community detection algorithms have been developed for single networks. However, in the real world, relationships between nodes are often of multiple natures, such as friendship, kinship and common interests among people in social networks. These relationships can be modeled by a multilayer network. Thus, identifying communities in multilayer networks has become a challenging problem. The existing algorithms for multilayer networks only utilize the topological structure and ignore the prior information, thereby resulting in low accuracy. In this article, by combining the graph regularization with the prior information, we propose a semi-supervised joint symmetric nonnegative matrix factorization(SSJSNMF) algorithm for community detection in multilayer networks. We use graph regularization term to penalize the latent space dissimilarity of some nodes when prior information shows that these nodes belong to same community. Then, by fusing graph regularization into a joint symmetric nonnegative matrix factorization(NMF) model, the proposed model can utilize the topological structure information and prior information simultaneously. Furthermore, we develop effective multiplicative updating rules to solve the proposed model. Finally, numerical experiments demonstrate that SSSNMF outperforms some existing algorithms.

关键词： Nonhomogeneous media Detection algorithms Clustering algorithms Symmetric matrices Feature extraction Multiplexing Tensors Multilayer networks community detection nonnegative matrix factorization semi-supervised learning graph regularization

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PARTIAL IDENTIFIABILITY FOR nonnegative matrix factorization\ast

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SIAM JOURNAL ON matrix ANALYSIS AND APPLICATIONS 2023年第1期44卷 27-52页

作者： Gillis, Nicolas Rajko, Robert Univ Mons Dept Math & Operat Res B-7000 Mons Belgium Univ Pecs Inst Math & Informat Fac Sci Ifjusag U 6 H-7624 Pecs Hungary

Given a nonnegative matrix factorization, R, and a factorization rank, r, exact nonnegative matrix factorization (exact NMF) decomposes R as the product of two nonnegative matrices, C and S with r columns, such as R = CS\top. A central research topic in the literature is the conditions under which such a decomposition is unique/identifiable up to trivial ambiguities. In this paper, we focus on partial identifiability, that is, the uniqueness of a subset of columns of C and S. We start our investigations with the data-based uniqueness (DBU) theorem from the chemometrics literature. The DBU theorem analyzes all feasible solutions of exact NMF and relies on sparsity conditions on C and S. We provide a mathematically rigorous theorem of a recently published restricted version of the DBU theorem, relying only on simple sparsity and algebraic conditions: it applies to a particular solution of exact NMF (as opposed to all feasible solutions) and allows us to guarantee the partial uniqueness of a single column of C or S. Second, based on a geometric interpretation of the restricted DBU theorem, we obtain a new partial identifiability result. This geometric interpretation also leads us to another partial identifiability result in the case r = 3. Third, we show how partial identifiability results can be used sequentially to guarantee the identifiability of more columns of C and S. We illustrate these results on several examples, including one from the chemometrics literature.

关键词： nonnegative matrix factorization uniqueness identifiability multivariate curve resolution window factor analysis self-modeling curve resolution

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nonnegative matrix factorization constrained by multiple labelled spanning trees for label propagation

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INFORMATION SCIENCES 2023年第1期648卷

作者： Deng, Furong Zhao, Yang Pei, Jihong Wang, Shiqi Yang, Xuan Shenzhen Univ Coll Elect & Informat Engn Shenzhen 518160 Peoples R China City Univ Hong Kong Dept Comp Sci Kwoloon Hong Kong Peoples R China Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518160 Peoples R China

Label propagation is an important semi-supervised learning method that generalizes the attributes of labelled samples to unlabelled samples based on the correlation of the data distribution. However, handling data containing imbalanced labels, multiple subclasses, bridging points, and nonlinear distributions is challenging. These challenges often make it difficult for existing methods to learn accurate relationships between labelled and unlabelled samples. In this paper, we propose multiple labelled spanning trees (MLSTs). Each labelled sample is initialized as the root node of a tree, and all trees are grown asynchronously according to the manifold structure of their neighbours such that all of the unlabelled samples can establish a connection with the labelled samples. The MLST construction method can better adapt to different disturbances. In addition, MLSTs-constrained nonnegative matrix factorization (MLSTs-NMF) is proposed for label propagation;it constructs a global relationship by using nonlinear representation with labelled samples and combines the manifold structure information from multiple labelled spanning trees to comprehensively estimate the labels of unlabelled samples. The results of the experiments demonstrate that the prediction accuracy of the proposed method is higher than that of the existing methods, and it exhibits better robustness to various interferences.

关键词： Label propagation Multiple labelled spanning trees nonnegative matrix factorization Graph construction

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Unknown fault diagnosis of planetary gearbox based on optimal rank nonnegative matrix factorization and improved stochastic resonance of bistable system

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NONLINEAR DYNAMICS 2023年第1期111卷 217-242页

作者： Yang, Chen Li, Hongkun Cao, Shunxin Dalian Univ Technol Sch Mech Engn Dalian 116024 Peoples R China

Planetary gearboxes are widely used in modern industrial fields due to the characteristics of large transmission ratio and high transmission efficiency, etc. A new diagnosis method is proposed in this work to identify the unknown fault of planetary gearbox under the strong noise background. Firstly, an optimal rank estimation strategy based on signal spectrum clustering results, a prerequisite for using the nonnegative matrix factorization (NMF) method, is proposed to guide the NMF process of original signal spectrum matrix. Secondly, consider the interpretability of decomposition results, the basis matrix generated by NMF is interpreted as the spectrum feature selection library of the original signal. Meanwhile, the basis vector with the largest kurtosis value in the basis matrix is selected to participate in the filtering of the original signal, and the envelope of filtered signal is obtained. Then, the excellent ability of stochastic resonance to amplify weak signals is utilized. A quantitative index independent of the prior fault knowledge is constructed to evaluate the stochastic resonance response of envelope signal. Finally, the fault mode of planetary gearbox is determined by the structural characteristics of resonance response spectrum. Simulation and experimental results confirm the effectiveness and robustness of the proposed method. It has good performance in pattern recognition of the unknown faults of planetary gearbox.

关键词： Planetary gearbox nonnegative matrix factorization Optimal rank estimation Stochastic resonance New evaluation index Unknown fault

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Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks

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MULTIMEDIA TOOLS AND APPLICATIONS 2023年第3期82卷 3745-3768页

作者： Nasiri, Elahe Berahmand, Kamal Li, Yuefeng Azarbaijan Shahid Madani Univ Dept Informat Technol & Commun Tabriz Iran Queensland Univ Technol QUT Fac Sci Sch Comp Sci Brisbane Qld Australia

Link prediction is one of the most widely studied problems in the area of complex network analysis, in which machine learning techniques can be applied to deal with it. The biggest drawback of the existing methods, however, is that in most cases they only consider the topological structure of the network, and therefore completely miss out on the great potential that stems from the nodal attributes. Both topological structure and nodes' attributes are essential in predicting the evolution of attributed networks and can act as complements to each other. To bring out their full potential in solving the link prediction problem, a novel Robust Graph Regularization nonnegative matrix factorization for Attributed Networks (RGNMF-AN) was proposed, which models not only the topology structure of networks but also their node attributes for direct link prediction. This model, in particular, combines two types of information, namely network topology, and nodal attributes information, and calculates high-order proximities between nodes using the Structure-Attribute Random Walk Similarity (SARWS) method. The SARWS score matrix is an indicator structural and attributed matrix that collects more useful attributed information in high-order proximities, whereas graph regularization technology combines the SARWS score matrix with topological and attribute information to collect more valuable attributed information in high-order proximities. Furthermore, the RGNMF-AN employs the l(2,1)-norm to constrain the loss function and regularization terms, effectively removing random noise and spurious links. According to empirical findings on nine real-world complex network datasets, the use of a combination of attributed and topological information in tandem enhances the prediction performance significantly compared to the baseline and other NMF-based algorithms.

关键词： Complex network Link prediction nonnegative matrix factorization Attributed network

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Conic optimization-based algorithms for nonnegative matrix factorization

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OPTIMIZATION METHODS & SOFTWARE 2023年第4期38卷 837-859页

作者： Leplat, Valentin Nesterov, Yurii Gillis, Nicolas Glineur, Francois Skoltech Ctr Artificial Intelligence Technol Moscow Russia UCLouvain CORE & ICTEAM Math Engn INMA Ottignies Louvain La Neuv Belgium Univ Mons Fac Polytech Dept Math & Operat Res Mons Belgium Univ Mons Fac Polytech Dept Math & Operat Res Rue Houdain 9 B-7000 Mons Belgium

nonnegative matrix factorization is the following problem: given a nonnegative input matrix V and a factorization rank K, compute two nonnegative matrices, W with K columns and H with K rows, such that WH approximates V as well as possible. In this paper, we propose two new approaches for computing high-quality NMF solutions using conic optimization. These approaches rely on the same two steps. First, we reformulate NMF as minimizing a concave function over a product of convex cones - one approach is based on the exponential cone and the other on the second-order cone. Then, we solve these reformulations iteratively: at each step, we minimize exactly, over the feasible set, a majorization of the objective functions obtained via linearization at the current iterate. Hence these subproblems are convex conic programs and can be solved efficiently using dedicated algorithms. We prove that our approaches reach a stationary point with an accuracy decreasing as O(1/i), where i denotes the iteration number. To the best of our knowledge, our analysis is the first to provide a convergence rate to stationary points for NMF. Furthermore, in the particular cases of rank-1 factorizations (i.e. K = 1), we show that one of our formulations can be expressed as a convex optimization problem, implying that optimal rank-1 approximations can be computed efficiently. Finally, we show on several numerical examples that our approaches are able to frequently compute exact NMFs (i.e. with V = WH) and compete favourably with the state of the art.

关键词： nonnegative matrix factorization nonnegative rank exponential cone second-order cone concave minimization conic optimization Frank-Wolfe gap convergence to stationary points

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A High-Order Proximity-Incorporated nonnegative matrix factorization-Based Community Detector

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2023年第3期7卷 700-714页

作者： Liu, Zhigang Yi, Yugen Luo, Xin Chongqing Univ Posts & Telecommun Sch Comp Sci & Technol Chongqing 400065 Peoples R China Chinese Acad Sci Chongqing Inst Green & Intelligent Technol Chongqing 330022 Peoples R China Jiangxi Normal Univ Sch Software Nanchang 400715 Peoples R China Southwest Univ Coll Comp & Informat Sci Chongqing 400715 Peoples R China

Community describes the functional mechanism of an undirected network, making community detection a fundamental tool for graph representation learning-related applications like social circle discovery. To date, a Symmetric and nonnegative matrix factorization (SNMF) model has been frequently adopted to address this issue owing to its high interpretability and scalability. However, most existing SNMF-based community detectors neglect the high-order proximity in an undirected network, thus suffering from accuracy loss caused by incomplete information. Motivated by this discovery, this paper proposes a High-Order Proximity-incorporated nonnegative matrix factorization (HOP-NMF)-based community detector with the following three-fold ideas: a) adopting a weighted pointwise mutual information-based approach to measure the high-order proximity among nodes in a network;b) leveraging an iterative network enhancement scheme to encode the captured high-order proximity into the network to effectively enhance the its information;and c) implementing a capacity-enlarged and graph-regularized factorization algorithm for highly-accurate representation to the enhanced network. With the above design, an HOP-NMF model is able to achieve highly-accurate community detection results. Theoretical proof is rigorously conducted to validate its convergence ability. Extensively empirical studies on eight real networks from industrial applications demonstrate that an HOP-NMF-based community detector significantly outperforms sophisticated and state-of-the-art community detectors in detection accuracy.

关键词： Detectors Symmetric matrices Indexes Training Probability Network analyzers Frequency measurement Learning system network representation learning community detection nonnegative matrix factorization symmetric model capacity graph regularization

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