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Inexact Block Coordinate Descent Methods for symmetric nonnegative matrix factorization

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第22期65卷 5995-6008页

作者： Shi, Qingjiang Sun, Haoran Lu, Songtao Hong, Mingyi Razaviyayn, Meisam Iowa State Univ Dept Ind & Mfg Syst Engn Ames IA 50011 USA Nanjing Univ Aeronaut & Astronaut Coll Elect Informat Engn Nanjing 210016 Jiangsu Peoples R China Univ Southern Calif Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA

symmetric nonnegativematrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix factorization technique and has better ability of clustering nonlinearly separable data. In this paper, we focus on the algorithmic aspect of the SNMF problem and propose simple inexact block coordinate decentmethods to address the problem, leading to both serial and parallel algorithms. The proposed algorithms have guaranteed convergence to stationary solutions and can efficiently handle large-scale and/or sparse SNMF problems. Extensive simulations verify the effectiveness of the proposed algorithms compared to recent state-of-the-art algorithms.

关键词： symmetric nonnegative matrix factorization block coordinate decent block successive upper-bounding minimization parallel algorithm stationary solution

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A Nonconvex Splitting Method for symmetric nonnegative matrix factorization: Convergence Analysis and Optimality

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第12期65卷 3120-3135页

作者： Lu, Songtao Hong, Mingyi Wang, Zhengdao Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA Iowa State Univ Dept Ind & Mfg Syst Ames IA 50011 USA

symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection, and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem. Furthermore, it achieves a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in parallel. Further, sufficient conditions are provided that guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real datasets suggest that the proposed algorithm converges quickly to a local minimum solution.

关键词： symmetric nonnegative matrix factorization Karush-Kuhn-Tucker points variable splitting global and local optimality clustering

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Sparse symmetric nonnegative matrix factorization Applied to Face Recognition 9

Sparse Symmetric Nonnegative Matrix Factorization Applied to...

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9th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems - Technology and Applications (IDAACS)

作者： Dobrovolskyi, Hennadii Keberle, Nataliya Ternovyy, Yehor Zaporizhzhya Natl Univ Chair Comp Sci 66 Zhukovskogo Str Zaporizhzhya Ukraine

ISBN: (纸本)9781538606971

The task of Sparse symmetric nonnegative matrix factorization(SSNMF) is formulated as optimization problem and solved numerically with the method of projected gradients descent. The adjustable sparsity level allows to emphasize the most significant object features. Clustering of the Yale Faces data set shows that SSNMF provides the same level of quality as common clustering approaches.

关键词： face recognition symmetric nonnegative matrix factorization sparsity condition

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A NONCONVEX SPLITTING METHOD FOR symmetric nonnegative matrix factorization: CONVERGENCE ANALYSIS AND OPTIMALITY

A NONCONVEX SPLITTING METHOD FOR SYMMETRIC NONNEGATIVE MATRI...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Lu, Songtao Hong, Mingyi Wang, Zhengdao Iowa State Univ Dept Elect & Comp Engn Ames IA 50011 USA Iowa State Univ Ind & Mfg Syst Engn Ames IA 50011 USA

ISBN: (纸本)9781509041176

symmetric non-negative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. Different from the existing works, we prove that the algorithm converges to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem with a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in a distributed manner. Further, we provide sufficient conditions that guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real data sets suggest that the proposed algorithm yields high quality of the solutions and converges quickly to the set of local minimum solutions compared with other algorithms.

关键词： symmetric nonnegative matrix factorization Karush-Kuhn-Tucker points variable splitting global and local optimality clustering

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Efficient and Non-Convex Coordinate Descent for symmetric nonnegative matrix factorization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第21期64卷 5571-5584页

作者： Vandaele, Arnaud Gillis, Nicolas Lei, Qi Zhong, Kai Dhillon, Inderjit Univ Mons Dept Math & Operat Res B-7000 Mons Belgium Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA Univ Texas Austin Dept Comp Sci Austin TX 78712 USA

Given a symmetric nonnegative matrix A, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix H, usually with much fewer columns than A, such that A approximate to HHT. SymNMF can be used for data analysis and in particular for various clustering tasks. Unlike standard NMF, which is traditionally solved by a series of quadratic (convex) subproblems, we propose to solve symNMF by directly solving the nonconvex problem, namely, minimize parallel to A - HHT parallel to(2), which is a fourth-order nonconvex problem. In this paper, we propose simple and very efficient coordinate descent schemes, which solve a series of fourth-order univariate subproblems exactly. We also derive convergence guarantees for our methods and show that they perform favorably compared to recent state-of-the-art methods on synthetic and real-world datasets, especially on large and sparse input matrices.

关键词： symmetric nonnegative matrix factorization coordinate descent completely positive matrices

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A nonconvex splitting method for symmetric nonnegative matrix factorization: Convergence analysis and optimality

A nonconvex splitting method for symmetric nonnegative matri...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Songtao Lu Mingyi Hong Zhengdao Wang Department of Electrical and Computer Engineering Iowa State University Ames 50011 USA Industrial and Manufacturing Systems Engineering Iowa State University Ames 50011 USA

ISBN: (纸本)9781509041183

关键词： symmetric nonnegative matrix factorization Karush-Kuhn-Tucker points variable splitting global and local optimality clustering optimality matrix decomposition Cluster Analysis nonnegative CENTROsymmetric Solutions image segmentation Converge Dataset Sufficient conditions

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Hessian regularization based symmetric nonnegative matrix factorization for clustering gene expression and microbiome data

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METHODS 2016年 111卷 80-84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

nonnegative matrix factorization (NMF) has received considerable attention due to its interpretation of observed samples as combinations of different components, and has been successfully used as a clustering method. As an extension of NMF, symmetric NMF (SNMF) inherits the advantages of NMF. Unlike NMF, however, SNMF takes a nonnegative similarity matrix as an input, and two lower rank nonnegative matrices (H, H-T) are computed as an output to approximate the original similarity matrix. Laplacian regularization has improved the clustering performance of NMF and SNMF. However, Laplacian regularization (LR), as a classic manifold regularization method, suffers some problems because of its weak extrapolating ability. In this paper, we propose a novel variant of SNMF, called Hessian regularization based symmetric nonnegative matrix factorization (HSNMF), for this purpose. In contrast to Laplacian regularization, Hessian regularization fits the data perfectly and extrapolates nicely to unseen data. We conduct extensive experiments on several datasets including text data, gene expression data and HMP (Human Microbiome Project) data. The results show that the proposed method outperforms other methods, which suggests the potential application of HSNMF in biological data clustering. (C) 2016 Published by Elsevier Inc.

关键词： symmetric nonnegative matrix factorization Hessian regularization Data clustering Laplacian regularization

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Multi-View Clustering Microbiome Data by Joint symmetric nonnegative matrix factorization with Laplacian Regularization

Multi-View Clustering Microbiome Data by Joint Symmetric Non...

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IEEE International Conference on Bioinformatics and Biomedicine (IEEE BIBM)

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

ISBN: (纸本)9781509016105

Many datasets existed in the real world are often comprised of different representations or views which provide complementary information to each other. For example, microbiome datasets can be represented by metabolic paths, taxonomic assignment or gene families. To integrate information from multiple views, data integration approaches such as methods based on nonnegative matrix factorization (NMF) have been developed to combine multi-view information simultaneously to obtain a comprehensive view which reveals the underlying data structure shared by multiple views. In this paper, we proposed a novel variant of symmetric nonnegative matrix factorization (SNMF), called Laplacian regularized joint symmetric nonnegative matrix factorization (LJ-SNMF) for clustering multi-view data. We conduct extensive experiments on several realistic datasets including Human Microbiome Project (HMP) 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.

关键词： symmetric nonnegative matrix factorization Multi-view Clustering Laplacian Regularization Human Microbiome

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Robust Community Detection in Graphs

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IEEE ACCESS 2021年 9卷 118757-118770页

作者： Al-Sharoa, Esraa M. Ababneh, Bara' M. Alkhassaweneh, Mahmood A. Jordan Univ Sci & Technol Elect Engn Dept Irbid 22110 Jordan Yarmouk Univ Comp Engn Dept Irbid 21163 Jordan Lewis Univ Dept Engn Comp & Math Sci Romeoville IL 60446 USA

Community detection in network-type data provides a powerful tool in analyzing and understanding real-world systems. In fact, community detection approaches aim to reduce the network's dimensionality and partition it into a set of disjoint clusters or communities. However, real networks are usually corrupted with noise or outliers which affect the detected community structure quality. In this paper, a new robust community detection algorithm that is capable of recovering a clean or a smoothed version of the corrupted graph and detecting the correct community structure is introduced. The proposed approach combines robust principal component analysis (RPCA) and symmetric nonnegative matrix factorization (SymNMF) in a single optimization problem. The proposed problem is solved under the framework of alternating direction methods of multipliers (ADMM). In particular, the corrupted adjacency matrix is decomposed into a low-rank and sparse components using RPCA and the community structure is detected by applying SymNMF to the extracted low-rank component. Extensive experiments that have been conducted on real and simulated binary and weighted networks show that the proposed approach significantly outperforms existing algorithms in detecting the correct community structure even in grossly corrupted networks.

关键词： Clustering algorithms Sparse matrices symmetric matrices Principal component analysis matrix decomposition Tools STEM Community detection graph theory robust principal component analysis symmetric nonnegative matrix factorization

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symmetric nonnegative matrix factorization: Algorithms and Applications to Probabilistic Clustering

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2011年第12期22卷 2117-2131页

作者： He, Zhaoshui Xie, Shengli Zdunek, Rafal Zhou, Guoxu Cichocki, Andrzej Guangdong Univ Technol Fac Automat Guangzhou 510641 Guangdong Peoples R China RIKEN Brain Sci Inst Lab Adv Brain Signal Proc Wako Saitama 3510198 Japan Wroclaw Univ Technol Inst Telecommun Teleinformat & Acoust PL-50370 Wroclaw Poland Polish Acad Sci Syst Res Inst PL-00901 Warsaw Poland

nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: alpha-SNMF and beta-SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.

关键词： Basic linear algebra subprograms completely positive coordinate update multiplicative update nonnegative matrix factorization parallel update probabilistic clustering symmetric nonnegative matrix factorization

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