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Novel Proximal Gradient Methods for nonnegative matrix factorization with Sparsity Constraints

SIAM JOURNAL ON IMAGING SCIENCES 2020年第1期13卷 381-421页

作者： Teboulle, Marc Vaisbourd, Yakov Tel Aviv Univ Sch Math Sci IL-69978 Ramat Aviv Israel

We consider the nonnegative matrix factorization (NMF) problem with sparsity constraints formulated as a nonconvex composite minimization problem. We introduce four novel proximal gradient based algorithms proven globally convergent to a critical point and which are applicable to sparsity constrained NMF models. Our approach builds on recent results allowing one to lift the classical global Lipschitz continuity requirement through the use of a non-Euclidean Bregman based distance. Since under the proposed framework we are not restricted by the gradient Lipschitz continuity assumption, we can consider new decomposition settings of the NMF problem. Two of the derived schemes are genuine non-Euclidean proximal methods that tackle nonstandard decompositions of the NMF problem. The two other schemes are novel extensions of the well-known state-of-the-art methods (the multiplicative and hierarchical alternating least squares), thus allowing one to significantly broaden the scope of these algorithms. Numerical experiments illustrate the performance of the proposed methods.

关键词： nonnegative matrix factorization sparsity constraints nonconvex nonsmooth composite minimization proximal gradient algorithms non-Euclidean Bregman distance Kurdyka-Losiajewicz property essentially cyclic block proximal gradient global convergence

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Community Detection in Complex Networks Using nonnegative matrix factorization and Density-Based Clustering Algorithm

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NEURAL PROCESSING LETTERS 2020年第2期51卷 1731-1748页

作者： Lu, Hong Zhao, Qinghua Sang, Xiaoshuang Lu, Jianfeng Nanjing Univ Sci & Technol Sch Comp Sci Xiaolingwei 200 Nanjing 210094 Peoples R China Nanjing Univ Finance & Econ Coll Informat Engn Nanjing 210023 Peoples R China

Community detection is a critical issue in the field of complex networks. Capable of extracting inherent patterns and structures in high dimensional data, the non-negative matrix factorization (NMF) method has become one of the hottest research topics in community detection recently. However, this method has a significant drawback;most community detection methods using NMF require the number of communities to be preassigned or determined by searching for the best community structure among all candidates. To address the problem, in this paper, we use an improved density peak clustering to obtain the number of cores as the pre-defined parameter of nonnegative matrix factorization. Then we adopt nonnegative double singular value decomposition initialization which can rapidly reduce the approximation error of nonnegative matrix factorization. Finally, we compare and analyze the performance of different algorithms on artificial networks and real-world networks. Experimental results indicate that the proposed method is superior to the state-of-the-art methods.

关键词： Community detection nonnegative matrix factorization Density peak clustering NNDSVD

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Safety Monitoring by a Graph-Regularized Semi-Supervised nonnegative matrix factorization With Applications to a Vision-Based Marking Process

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IEEE ACCESS 2020年 8卷 112278-112286页

作者： Fan, Song Jia, Qilong Cheng, Wan Sheng Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China Univ Sci & Technol Liaoning Sch Elect & Informat Engn Anshan 114051 Peoples R China

This paper proposes a brand-new method to perform safety monitoring using images for steel coil marking industrial processes. The new safety monitoring method is developed with the aid of a new graph-regularized semi-supervised nonnegative matrix factorization (GSNMF) algorithm. Compared with the existing nonnegative matrix factorization (NMF)-like algorithms, GSNMF is developed in an all-new manner so that it not only can take advantage of images with known labels and images with unknown labels to train a model for monitoring purpose, but also can take advantage of graph theory to improve the monitoring performance. Because any two different samples are connected by an edge in a graph, thus graph theory is beneficial for GSNMF to measure the similarity between any two different samples and to assign the same labels for the samples with close connections between them. As a result, GSNMF is more capable of analyzing the samples with a complicated distribution than the existing NMF-like algorithms, theoretically. Finally, an experiment on a steel coil marking process is adopted to evaluate the superiorities of our proposed method over the existing methods.

关键词： Fault detection nonnegative matrix factorization semi-supervised learning marking process

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nonnegative matrix factorization-based blind source separation for full-field and high-resolution modal identification from video

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JOURNAL OF SOUND AND VIBRATION 2020年 487卷

作者： Silva, Moises Martinez, Bridget Figueiredo, Eloi Costa, Joao C. W. A. Yang, Yongchao Mascarenas, David Fed Univ Para Appl Electromagnetism Lab Guama 01 BR-66075110 Belem Para Brazil Los Alamos Natl Lab Engn Inst POB 1663MS T001 Los Alamos NM 87545 USA Lusofona Univ Fac Engn Campo Grande 376 P-1749024 Lisbon Portugal Inst R&D Struct & Construct CONSTRUCT R Dr Roberto Frias S-N P-4200465 Porto Portugal Michigan Technol Univ Dept Mech Engn Houghton MI 49931 USA

Traditional modal analysis requires physically attached sensors for data acquisition and vibration-based monitoring. Although traditional modal analysis presents well-established techniques for dynamics analysis, they can impose mass-loading effects on lightweight structures and increase budgetary demands on the maintenance of such data acquisition systems. Recently video-based techniques have become of increasing interest in the identification of the dynamic properties of infrastructures with arbitrary complexity. However, most applications rely on frame by frame tracking of fixed speckle targets to derive time-varying physical parameters. This imposes serious limitations for real-world applications, especially in scenarios where the structure is out of reach. Therefore, to address these issues, we propose a novel output-only operational modal analysis method based on visionbased blind source separation scheme. The proposed algorithm makes use of each pixel as a potential measurement point. This enables an increase in the spatial density of sensors conventionally used on a structure by orders of magnitude. This simultaneous processing of all pixel time-series derives full-field high-resolution mode shapes instead of low spatial resolution mode shapes achieved when measuring a limited number of discrete locations with typical sensors. Compared to other approaches, we propose a blind source separation scheme simpler than the ones based on phase extraction and complex steerable pyramids that still capable of disentangling local structural vibration from video measurement only. Moreover, a simple method to magnify and visualize independent vibration modes is introduced using the extracted modal information only. We validate our method by laboratory experiments on a bench-scale building structure and a cantilever beam. The results demonstrate that the proposed technique can decompose high-resolution modal parameters, visualize and reconstruct even those weakly-excited v

关键词： Video-based dynamics monitoring Non-contact measurements Modal disentangling Blind source separation Output-only modal analysis nonnegative matrix factorization

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Semi-Supervised nonnegative matrix factorization of Wide-Field Fluorescence Microscopic Images for Tissue Diagnosis

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MICROSCOPY AND MICROANALYSIS 2020年第3期26卷 419-428页

作者： Soman, Shania M. Rekha, Charuvil Radhakrishna Pillai Santhakumar, Hema Narendrakumar, Uttamchand Jayasree, Ramapurath S. VIT Univ Sch Elect & Engn Vellore 632014 Tamil Nadu India Sree Chitra Tirunal Inst Med Sci & Technol Div Biophoton & Imaging Trivandrum 695012 Kerala India VIT Univ Sch Mech Engn Vellore 632014 Tamil Nadu India

This study tests the use of a constrained nonnegative matrix factorization (NMF) algorithm to explore the comparatively new field of chemometric microscopy to support tissue diagnosis. The algorithm can extract the spectral signature and the absolute concentration map of endogenous fluorophores from wide-field microscopic images. The resultant data distinguished normal and fibrous calvarial tissues, based on the changes in their spectral signatures. The absolute concentration map of endogenous fluorophores, nicotinamide adenine dinucleotide (NADH), flavin adenine dinucleotide (FAD), and lipofuscin were derived from microscopic images and compared with the fluorescence from pure fluorophores. While the absolute concentration of NADH increased, the same of FAD and lipofuscin decreased from a normal to fibrous calvarial condition. An increase in the optical redox ratio, possibly due to the metabolic changes during the development of fibrosis, was observed. Differentiating tissue types using the absolute concentration map was found to be considerably more precise than that achievable with relative concentration. The quantification of fluorophores with reference to the absolute concentration map can eliminate uncertainties due to system responses or measurement details, thereby generating more biologically apposite data. Wide-field microscopy augmented with a constrained NMF algorithm could emerge as an advanced diagnostic tool, potentially heralding the emergence of chemometric microscopy.

关键词： chemometric microscopy endogenous fluorescence nonnegative matrix factorization optical redox ratio spatial distribution spatial diversity

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Community detection method using improved density peak clustering and nonnegative matrix factorization

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NEUROCOMPUTING 2020年 415卷 247-257页

作者： Lu, Hong Shen, Zhu Sang, Xiaoshuang Zhao, Qinghua Lu, Jianfeng Nanjing Univ Sci & Technol Sch Comp Sci Xiaolingwei 200 Nanjing 210094 Peoples R China Stanford Univ Stat Dept Stanford CA 94305 USA Nanjing Univ Finance & Econ Coll Informat Engn Nanjing 210023 Peoples R China

Community detection in networks is valuable in analyzing, designing, and optimizing complex network. Recently, the nonnegative matrix factorization (NMF) method has successfully uncovered the community structure in the complex networks. However, most of community detection methods based on NMF require the number of the community as a prior information. To address this problem, in this paper, we use the improved density peak clustering (DPC) to obtain the number of centers as the preassigned parameter for nonnegative matrix factorization. The proposed algorithm first calculates the modified PageRank of nodes as the density indexes and then draws a decision graph to obtain the hubs of the network. By means of Markov chain model of a random walk, we execute NMF on one expansion feature matrix. Finally, we compare and analyze the performance of different algorithms on artificial networks and real-world networks. Experimental results indicate that the proposed method is superior to the state-of-the-art methods. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Community detection nonnegative matrix factorization Density peak clustering Random walk Amendatory PageRank

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Bayesian nonnegative matrix factorization With Dirichlet Process Mixtures

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年 68卷 3860-3870页

作者： Li, Caoyuan Xie, Hong-Bo Mengersen, Kerrie Fan, Xuhui Da Xu, Richard Yi Sisson, Scott A. Van Huffel, Sabine Beijing Inst Technol Sch Comp Sci & Technol Beijing 100081 Peoples R China Univ Technol Sydney Fac Engn & Informat Technol Ultimo NSW 2007 Australia Queensland Univ Technol ARC Ctr Excellence Math & Stat Frontiers Brisbane Qld 4001 Australia Univ New South Wales Sch Math & Stat Sydney NSW 2033 Australia Katholieke Univ Leuven ESAT Stadius Div Dept Elect Engn B-3001 Leuven Belgium

nonnegative matrix factorization (NMF) is valuable in many applications of blind source separation, signal processing and machine learning. A number of algorithms that can infer nonnegative latent factors have been developed, but most of these assume a specific noise kernel. This is insufficient to deal with complex noise in real scenarios. In this paper, we present a hierarchical Dirichlet process nonnegative matrix factorization (DPNMF) model in which the Gaussian mixture model is used to approximate the complex noise distribution. Moreover, the model is cast in the nonparametric Bayesian framework by using Dirichlet process mixture to infer the necessary number of Gaussian components. We derive a mean-field variational inference algorithm for the proposed nonparametric Bayesian model. We first test the model on synthetic data sets contaminated by Gaussian, sparse and mixed noise. We then apply it to extract muscle synergies from the electromyographic (EMG) signal and to select discriminative features for motor imagery single-trial electroencephalogram (EEG) classification. Experimental results demonstrate that DPNMF performs better in extracting the latent nonnegative factors in comparison with state-of-the-art methods.

关键词： Dirichlet process nonnegative matrix factorization nonparametric Bayesian methods Gaussian mixture model variational Bayes

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Progressive transduction nonnegative matrix factorization for dimensionality reduction

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NEUROCOMPUTING 2020年 414卷 76-89页

作者： Peng, Xinjun Xu, Dong Chen, De Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China

Dimensionality reduction is one important technique to find out meaningful representations of data by discovering the underlying structures of data. As one widely applied method, by learning parts-based representations, nonnegative matrix factorization (NMF) has been widely researched and used to various application fields. Compared with the previous methods, this paper presents a novel semi-supervised NMF learning framework, called progressive transduction NMF (PTNMF), that learns a robustly discriminative representation by introducing a progressive transduction structure. Specifically, a progressive transduction based scheme is employed to gradually update the representations of unlabeled points according to the similarity between the labeled and unlabeled data points. This is helpful to improve the effectiveness of NMF, especially for the case that labeled data is inadequate. The efficiency of the proposed method is discussed both theoretically and empirically. Extensive experiments on several real-world data sets are listed, and the experimental results demonstrate that the proposed algorithm obtains better discriminant ability in comparison to the state-of-the-art methods. (C) 2020 Elsevier B.V. All rights reserved.

关键词： nonnegative matrix factorization Representation learning Progressive transduction Data structure Semi-supervised learning

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Decision of the Optimal Rank of a nonnegative matrix factorization Model for Gene Expression Data Sets Utilizing the Unit Invariant Knee Method: Development and Evaluation of the Elbow Method for Rank Selection

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JMIR Bioinformatics and Biotechnology 2023年第1期4卷 e43665页

作者： Guven, Emine Department of Biomedical Engineering Düzce University Düzce Turkey

Background: There is a great need to develop a computational approach to analyze and exploit the information contained in gene expression data. The recent utilization of nonnegative matrix factorization (NMF) in computational biology has demonstrated the capability to derive essential details from a high amount of data in particular gene expression microarrays. A common problem in NMF is finding the proper number rank (r) of factors of the degraded demonstration, but no agreement exists on which technique is most appropriate to utilize for this purpose. Thus, various techniques have been suggested to select the optimal value of rank factorization (r). Objective: In this work, a new metric for rank selection is proposed based on the elbow method, which was methodically compared against the cophenetic metric. Methods: To decide the optimum number rank (r), this study focused on the unit invariant knee (UIK) method of the NMF on gene expression data sets. Since the UIK method requires an extremum distance estimator that is eventually employed for inflection and identification of a knee point, the proposed method finds the first inflection point of the curvature of the residual sum of squares of the proposed algorithms using the UIK method on gene expression data sets as a target matrix. Results: Computation was conducted for the UIK task using gene expression data of acute lymphoblastic leukemia and acute myeloid leukemia samples. Consequently, the distinct results of NMF were subjected to comparison on different algorithms. The proposed UIK method is easy to perform, fast, free of a priori rank value input, and does not require initial parameters that significantly influence the model’s functionality. Conclusions: This study demonstrates that the elbow method provides a credible prediction for both gene expression data and for precisely estimating simulated mutational processes data with known dimensions. The proposed UIK method is faster than conventional methods, in

关键词： consensus matrix elbow method gene expression data nonnegative matrix factorization optimal rank rank factorization unit invariant knee method

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Tight Semi-nonnegative matrix factorization

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PATTERN RECOGNITION AND IMAGE ANALYSIS 2020年第4期30卷 632-637页

作者： Dreisigmeyer, David W. US Census Bur Ctr Econ Studies 4600 Silver Hill Rd Suitland MD 20746 USA Colorado State Univ Dept Elect & Comp Engn Ft Collins CO 80523 USA

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far as possible only the initial data set can be represented this way. However, the templates are not required to be nonnegative nor convex combinations of the original data.

关键词： archetypal analysis nonnegative matrix factorization

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