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A Label-Embedding Online nonnegative matrix factorization Algorithm

IEEE ACCESS 2019年 7卷 105882-105891页

作者： Guo, Zhibo Zhang, Ying Yangzhou Univ Coll Informat Engn Yangzhou 225009 Jiangsu Peoples R China

nonnegative matrix factorization is a widely used data processing method, which has been applied in many fields, such as data dimension reduction and feature extraction. Considering the label information of training samples is helpful to improve the performance of data dimension reduction and classification, and how to apply the subspace calculated by training samples to testing samples to improve the computation efficiency is also a problem worth considering. In this paper, an algorithm called label-embedding online nonnegative matrix factorization (LEONMF) is proposed for image dimensionality reduction and classification. First, the label is embedded in the training matrix, by which the base matrix and the weight matrix can be calculated. The data amount of the base matrix is greatly small than that of the input matrix data. Next, the base matrix is adjusted and connected with the testing matrix to get the new connection matrix. The new connection matrix can be expressed as the product of the new base matrix and the new weight matrix. The new weight matrix can be used for classification after adjustment. The experimental results demonstrated that the proposed LEONMF outperforms the state-of-the-art algorithms in classification accuracy and calculation speed.

关键词： Feature extraction label embedding nonnegative matrix factorization online learning

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Novel method of informative frequency band selection for vibration signal using nonnegative matrix factorization of spectrogram matrix

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2019年第0期130卷 585-596页

作者： Wodecki, Jacek Kruczek, Piotr Bartkowiak, Anna Zimroz, Radoslaw Wylomanska, Agnieszka KGHM Cuprum Ltd Res & Dev Ctr Sikorskiego 2-8 PL-53659 Wroclaw Poland Wroclaw Univ Inst Comp Sci PL-50383 Wroclaw Poland Wroclaw Univ Sci & Technol Diagnost & Vibroacoust Sci Lab Fac Geoengn Min & Geol Na Grobli 15 PL-50421 Wroclaw Poland Wroclaw Univ Sci & Technol Fac Pure & Appl Math Hugo Steinhaus Ctr Janiszewskiego 14a PL-50370 Wroclaw Poland

The problem of local damage detection in rotating machines is currently the highly important subject of interest in the field of condition monitoring. In the literature one can find many different strategies. One of the most common approaches is the vibration signal analysis aiming at informative frequency band selection. In case of simply structured signals classic methods (e.g. spectral kurtosis) are sufficient and return clear information about the damage. However, in real-world cases the signal is usually much more complicated. Indeed, such signals consist of many different components, for instance: damage-related cyclic impulses, heavy-tailed background noise etc. Hence, there is a growing need for robust damage detection methods. In this paper a novel method of informative frequency band selection is proposed. It utilizes the approach of Non-negative matrix factorization applied to time-frequency signal representation. The described algorithm is evaluated using simulated signal containing several different components, that resembles real-life vibration signal from copper ore crusher, as well as real-life signal measured on the crusher. Using the obtained structure of informative frequency band it is possible to filter particular components out of the original signal. (C) 2019 Published by Elsevier Ltd.

关键词： nonnegative matrix factorization Filtration Vibration measurement Time-frequency representation Spectrogram

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Adaptive nonnegative matrix factorization and measure comparisons for recommender systems

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APPLIED MATHEMATICS AND COMPUTATION 2019年 354卷 164-179页

作者： del Corso, Gianna M. Romani, Francesco Univ Pisa Dipartimento Informat Pisa Italy

The nonnegative matrix factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem. In this paper we propose new methods based on the NMF of the rating matrix and we compare them with some classical algorithms such as the SVD and the regularized and unregularized non-negative matrix factorization approach. In particular a new algorithm is obtained changing adaptively the function to be minimized at each step, realizing a sort of dynamic prior strategy. Another algorithm is obtained modifying the function to be minimized in the NMF formulation by enforcing the reconstruction of the unknown ratings toward a prior term. We then combine different methods obtaining two mixed strategies which turn out to be very effective in the reconstruction of missing observations. We perform a thoughtful comparison of different methods on the basis of several evaluation measures. We consider in particular rating, classification and ranking measures showing that the algorithm obtaining the best score for a given measure is in general the best also when different measures are considered, lowering the interest in designing specific evaluation measures. The algorithms have been tested on different datasets, in particular the 1M, and 10M MovieLens datasets containing ratings on movies, the Jester dataset with ranting on jokes and Amazon Fine Foods dataset with ratings on foods. The comparison of the different algorithms, shows the good performance of methods employing both an explicit and an implicit regularization scheme. Moreover we can get a boost by mixed strategies combining a fast method with a more accurate one. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Recommender systems nonnegative matrix factorization ANLS Regularization Analysis of measures

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nonnegative matrix factorization WITH BAND CONSTRAINT

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Journal of Computational Mathematics 2018年第6期36卷 761-775页

作者： Xiangxiang Zhu Jicheng Li Zhuosheng Zhang School of Mathematics and Statistics Xi'an Jiaotong University Xi'an 710049 China

In this paper, we study a band constrained nonnegative matrix factorization （band NMF） problem： for a given nonnegative matrix Y, decompose it as Y ≈ AX with A a nonnegative matrix and X a nonnegative block band matrix. This factorization model extends a single low rank subspace model to a mixture of several overlapping low rank subspaces, which not only can provide sparse representation, but also can capture signifi- cant grouping structure from a dataset. Based on overlapping subspace clustering and the capture of the level of overlap between neighbouring subspaces, two simple and practical algorithms are presented to solve the band NMF problem. Numerical experiments on both synthetic data and real images data show that band NMF enhances the performance of NMF in data representation and processing.

关键词： nonnegative matrix factorization Band structure Subspace clustering Sparserepresentation Image compression

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A hybrid algorithm for low-rank approximation of nonnegative matrix factorization

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NEUROCOMPUTING 2019年 364卷 129-137页

作者： Wang, Peitao He, Zhaoshui Xie, Kan Gao, Junbin Antolovich, Michael Tan, Beihai Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China Guangdong Key Lab IoT Informat Technol Guangzhou 510006 Guangdong Peoples R China Univ Sydney Business Sch Discipline Business Analyt Camperdown NSW 2006 Australia Charles Sturt Univ Sch Comp & Math Bathurst NSW 2795 Australia

nonnegative matrix factorization (NMF) is a recently developed method for data analysis. So far, most of known algorithms for NMF are based on alternating nonnegative least squares (ANLS) minimization of the squared Euclidean distance between the original data matrix and its low-rank approximation. In this paper, we first develop a new NMF algorithm, in which a Procrustes rotation and a nonnegative projection are alternately performed. The new algorithm converges very rapidly. Then, we propose a hybrid NMF (HNMF) algorithm that combines the new algorithm with the low-rank approximation based NMF (lraNMF) algorithm. Furthermore, we extend the HNMF algorithm to nonnegative Tucker decomposition (NTD), which leads to a hybrid NTD (HNTD) algorithm. The simulations verify that the HNMF algorithm performs well under various noise conditions, and HNTD has a comparable performance to the low-rank approximation based sequential NTD (lraSNTD) algorithm for sparse representation of tensor objects. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Alternately updating Low-rank approximation nonnegative matrix factorization nonnegative Tucker decomposition

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Adaptive local learning regularized nonnegative matrix factorization for data clustering

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APPLIED INTELLIGENCE 2019年第6期49卷 2151-2168页

作者： Sheng, Yongpan Wang, Meng Wu, Tianxing Xu, Han Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu Sichuan Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing Jiangsu Peoples R China Nanyang Technol Univ Sch Comp Sci & Engn Singapore Singapore

Data clustering aims to group the input data instances into certain clusters according to the high similarity to each other, and it could be regarded as a fundamental and essential immediate or intermediate task that appears in areas of machine learning, pattern recognition, and information retrieval. Clustering algorithms based on graph regularized extensions have accumulated much interest for a couple of decades, and the performance of this category of approaches is largely determined by the data similarity matrix, which is usually calculated by the predefined model with carefully tuned parameters combination. However, they may lack a more flexible ability and not be optimal in practice. In this paper, we consider both discriminative information as well as the data manifold in a matrix factorization point of view, and propose an adaptive local learning regularized nonnegative matrix factorization (ALLRNMF) approach for data clustering, which assumes that similar instance pairs with a smaller distance should have a larger probability to be assigned to the probabilistic neighbors. ALLRNMF simultaneously learns the data similarity matrix under the assumption and performs the nonnegative matrix factorization. The constraint of the similarity matrix encodes both the discriminative information as well as the learned adaptive local structure and benefits the data clustering on manifold. In order to solve the optimization problem of our approach, an effective alternative optimization algorithm is proposed such that our objective function could be decomposed into several subproblems that each has an optimal solution, and its convergence is theoretically guaranteed. Experiments on real-world benchmark datasets demonstrate the superior performance of our approach against the existing clustering approaches.

关键词： Adaptive local structure learning Manifold regularization nonnegative matrix factorization Data clustering

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Impulsive source separation using combination of nonnegative matrix factorization of bi-frequency map, spatial denoising and Monte Carlo simulation

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2019年 127卷 89-101页

作者： Wodecki, Jacek Michalak, Anna Zimroz, Radoslaw Barszcz, Tomasz Wylomanska, Agnieszka Wroclaw Univ Sci & Technol Fac Geoengn Min & Geol Na Grobli 15 PL-50421 Wroclaw Poland AGH Univ Sci & Technol Krakow Poland Wroclaw Univ Sci & Technol Fac Pure & Appl Math Wyb Wyspianskiego 27 PL-50370 Wroclaw Poland

In this paper, authors present the original procedure for local damage detection in rolling bearings based on vibration data. The aim is to obtain envelope spectrum (ES) of the signal component related to damage, that is clear and easy to interpret. The method is especially aimed at cases, when multiple cyclic impulsive components are present and interfere with each other, which makes ES of such signal very difficult to evaluate. In order to deal with such situation properly, authors propose to choose Cyclic Spectral Coherence (CSC) map as a two-dimensional data representation that will be the basis for the analysis. nonnegative matrix factorization (NMF) is used to analyze such map in two ways: first, it helps to initially separate cyclic components by producing a set of filters for input vibration data, and second, to identify proper damage-related frequency components in envelope spectrum. In addition, an intermediate step of spatial denoising allows enhancing the properties of CSC map. Finally, Monte Carlo simulation improves statistical significance of the result and increases robustness by reducing the impact of random initialization effects. The method has been evaluated using real-life vibration data measured on rolling bearing operating in the industrial gas compressor. (C) 2019 Published by Elsevier Ltd.

关键词： Vibration Damage detection Bearings Cyclostationarity nonnegative matrix factorization Spatial denoising Monte Carlo simulation Separation

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nonnegative matrix factorization by joint locality-constrained and a"" _2,1-norm regularization

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MULTIMEDIA TOOLS AND APPLICATIONS 2018年第3期77卷 3029-3048页

作者： Xing, Ling Dong, Hao Jiang, Wei Tang, Kewei Henan Univ Sci & Technol Sch Informat Engn Luoyang 471023 Peoples R China Liaoning Normal Univ Sch Math Dalian 116029 Peoples R China

nonnegative matrix factorization has been widely applied recently. The nonnegativity constraints result in parts-based, sparse representations which can be more robust than global, non-sparse features. However, existing techniques could not accurately dominate the sparseness. To address this issue, we present a unified criterion, called nonnegative matrix factorization by Joint Locality-constrained and a"" (2,1)-norm Regularization(NMF2L), which is designed to simultaneously perform nonnegative matrix factorization and locality constraint as well as to obtain the row sparsity. We reformulate the nonnegative local coordinate factorization problem and use a"" (2,1)-norm on the coefficient matrix to obtain row sparsity, which results in selecting relevant features. An efficient updating rule is proposed, and its convergence is theoretically guaranteed. Experiments on benchmark face datasets demonstrate the effectiveness of our presented method in comparison to the state-of-the-art methods.

关键词： nonnegative matrix factorization Local constraint Clustering

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nonnegative matrix factorization with mixed hypergraph regularization for community detection

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INFORMATION SCIENCES 2018年 435卷 263-281页

作者： Wu, Wenhui Kwong, Sam Zhou, Yu Jia, Yuheng Gao, Wei City Univ Hong Kong Dept Comp Sci Kowloon Hong Kong Peoples R China City Univ Hong Kong Shenzhen Res Inst Shenzhen 51800 Peoples R China Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518060 Peoples R China

Community structure is the most significant attribute of networks, which is often identified to help discover the underlying organization of networks. Currently, nonnegative matrix factorization (NMF) based community detection method makes use of the related topology information and assumes that networks are able to be projected onto a latent low-dimensional space, in which the nodes can be efficiently clustered. In this paper, we propose a novel framework named mixed hypergraph regularized nonnegative matrix factorization (MHGNMF), which takes higher-order information among the nodes into consideration to enhance the clustering performance. The hypergraph regularization term forces the nodes within the identical hyperedge to be projected onto the same latent subspace, so that a more discriminative representation is achieved. In the proposed framework, we generate a set of hyperedges by mixing two kinds of neighbors for each centroid, which makes full use of topological connection information and structural similarity information. By testing on two artificial benchmarks and eight real-world networks, the proposed framework demonstrates better detection results than the other state-of-the-art methods. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Community detection nonnegative matrix factorization Hypergraph regularization

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Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2019年第6期10卷 1259-1268页

作者： Zhang, Xiaoxia Chen, Degang Wu, Kesheng North China Elect Power Univ Sch Control & Comp Engn Beijing 102206 Peoples R China North China Elect Power Univ Dept Math & Phys Beijing 102206 Peoples R China Lawrance Berkeley Natl Lab Computat Res Div Berkeley CA 94720 USA

matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.

关键词： nonnegative matrix factorization Graph regularized nonnegative matrix factorization Incremental nonnegative matrix factorization Incremental graph regularized nonnegative matrix factorization Correlation

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