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Modified subspace Barzilai-Borwein gradient method for non-negative matrix factorization

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2013年第1期55卷 173-196页

作者： Liu, Hongwei Li, Xiangli Xidian Univ Dept Math Xian 710071 Peoples R China Guilin Univ Elect Technol Coll Math & Comp Sci Guilin 541004 Peoples R China

non-negative matrix factorization (NMF) is a problem to obtain a representation of data using non-negativity constraints. Since the NMF was first proposed by Lee, NMF has attracted much attention for over a decade and has been successfully applied to numerous data analysis problems. Recent years, many variants of NMF have been proposed. Common methods are: iterative multiplicative update algorithms, gradient descent methods, alternating least squares (ANLS). Since alternating least squares has nice optimization properties, various optimization methods can be used to solve ANLS's subproblems. In this paper, we propose a modified subspace Barzilai-Borwein for subproblems of ANLS. Moreover, we propose a modified strategy for ANLS. Global convergence results of our algorithm are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

关键词： non-negative matrix factorization Alternating least squares Active sets non-monotone technique

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Feature selection based dual-graph sparse non-negative matrix factorization for local discriminative clustering

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NEUROCOMPUTING 2018年 290卷 87-99页

作者： Meng, Yang Shang, Ronghua Jiao, Licheng Zhang, Wenya Yuan, Yijing Yang, Shuyuan Xidian Univ Key Lab Intelligent Percept & Image Understanding Minist Educ Xian 710071 Shaanxi Peoples R China Xidian Univ Sch Comp Sci Xian 710071 Shaanxi Peoples R China

non-negative matrix factorization (NMF) can map high-dimensional data into a low-dimensional data space. Feature selection can eliminate the redundant and irrelevant features from the alternative features. In this paper, we propose a feature selection based dual-graph sparse non-negative matrix factorization (DSNMF) which can find an appropriate low dimensional representation of data by NMF and then select more discriminative features to further reduce the dimension of the low dimensional space by feature selection rather than reduce the dimension by only NMF or feature selection in many previous methods. DSNMF combines dual-graph model with non-negative matrix factorization, which can not only simultaneously preserve the geometric structures in both the data space and the feature space, but also make the two non-negative matrix factors update iteratively and interactively. In addition, DSNMF exerts L-2,L-1-norm constraint on the non-negative matrix factor of the feature space to make full use of the sparse self-representation information. What's more, we propose a new local discriminative feature selection clustering called feature selection based dual-graph sparse non-negative matrix factorization for local discriminative clustering (DSNMF-LDC) whose clustering effects are better. We give the objective function, the iterative updating rules and the convergence proof. Our empirical study shows that DSNMF-LDC is robust and excellent in comparison to 9 feature selection algorithms and 7 clustering algorithms in clustering accuracy (ACC) and normalized mutual information (NMI). (c) 2018 Elsevier B.V. All rights reserved.

关键词： Dual-graph non-negative matrix factorization Local discriminative Feature selection Clustering

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Adaptive graph regularized non-negative matrix factorization with self-weighted learning for data clustering

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APPLIED INTELLIGENCE 2023年第23期53卷 28054-28073页

作者： Ma, Ziping Wang, Jingyu Li, Huirong Huang, Yulei North Minzu Univ Sch Math & Informat Sci Yinchuan 750000 Ningxia Peoples R China North Minzu Univ Key Lab Intelligent Informat & Big Data Proc Ning Yinchuan 750000 Ningxia Peoples R China Shangluo Univ Sch Math & Comp Applicat Shangluo 726000 Peoples R China

In general, fully exploiting the local structure of the original data space can effectively improve the clustering performance of nonnegative matrix factorization (NMF). Therefore, graph-based NMF algorithms have been widely studied and applied. However, traditional graph-based NMF methods generally employ predefined models to construct similarity graphs, so that the clustering results depend heavily on the quality of the similarity graph. Furthermore, most of these methods follow the ideal assumption that the importance of different features is equal in the process of learning the similarity matrix, which results in irrelevant features being valued. To alleviate the above issues, this paper develops an adaptive graph regularized nonnegative matrix factorization with self-weighted learning (SWAGNMF) method. Firstly, the proposed method learns the similarity matrix flexibly and adaptively to explore the local structure of samples based on the assumption that data points with smaller distances should have a higher probability of adjacency. Furthermore, the self-weight matrix assigns different weights automatically according to the importance of features in the process of constructing similarity graph, i.e., discriminative features are assigned more significant weights than redundant features, which can effectively suppress irrelevant features and enhance the robustness of our model. Finally, considering the duality between samples and features, the proposed method is capable of exploring the local structures of both the data space and the feature space. An effective alternative optimization algorithm is proposed, and convergence is theoretically guaranteed. Extensive experiments on benchmark and synthetic datasets show that the proposed method outperforms compared state-of-the-art clustering methods.

关键词： non-negative matrix factorization Adaptive local structure learning Self-weighted learning Data clustering

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Multichannel Extensions of non-negative matrix factorization With Complex-Valued Data

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IEEE TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2013年第5期21卷 971-982页

作者： Sawada, Hiroshi Kameoka, Hirokazu Araki, Shoko Ueda, Naonori NTT Corp NTT Commun Sci Labs Kyoto 6190237 Japan

This paper presents new formulations and algorithms for multichannel extensions of non-negative matrix factorization (NMF). The formulations employ Hermitian positive semidefinite matrices to represent a multichannel version of non-negative elements. Multichannel Euclidean distance and multichannel Itakura-Saito (IS) divergence are defined based on appropriate statistical models utilizing multivariate complex Gaussian distributions. To minimize this distance/divergence, efficient optimization algorithms in the form of multiplicative updates are derived by using properly designed auxiliary functions. Two methods are proposed for clustering NMF bases according to the estimated spatial property. Convolutive blind source separation (BSS) is performed by the multichannel extensions of NMF with the clustering mechanism. Experimental results show that 1) the derived multiplicative update rules exhibited good convergence behavior, and 2) BSS tasks for several music sources with two microphones and three instrumental parts were evaluated successfully.

关键词： Blind source separation clustering convolutive mixture multichannel non-negative matrix factorization

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Application of orthogonal sparse joint non-negative matrix factorization based on connectivity in Alzheimer?s disease research

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2023年第6期20卷 9923-9947页

作者： Kong, Wei Xu, Feifan Wang, Shuaiqun Wei, Kai Wen, Gen Yu, Yaling Shanghai Maritime Univ Coll Informat Engn Shanghai 201306 Peoples R China Chinese Acad Sci Univ Chinese Acad Sci Shanghai Inst Nutr & Hlth Biomed Big Data CtrCAS Key Lab Computat Biol Shanghai Peoples R China Shanghai Jiao Tong Univ Dept Orthoped Surg Affiliated Peoples Hosp 6 Shanghai 200233 Peoples R China Shanghai Jiao Tong Univ Inst Microsurg Extrem Affiliated Peoples Hosp 6 Shanghai 200233 Peoples R China

Based on the mining of micro-and macro-relationships of genetic variation and brain imaging data, imaging genetics has been widely applied in the early diagnosis of Alzheimer's disease (AD). However, effective integration of prior knowledge remains a barrier to determining the biological mechanism of AD. This paper proposes a new connectivity-based orthogonal sparse joint non-negative matrix factorization (OSJNMF-C) method based on integrating the structural magnetic resonance image, single nucleotide polymorphism and gene expression data of AD patients;the correlation information, sparseness, orthogonal constraint and brain connectivity information between the brain image data and genetic data are designed as constraints in the proposed algorithm, which efficiently improved the accuracy and convergence through multiple iterative experiments. Compared with the competitive algorithm, OSJNMF-C has significantly smaller related errors and objective function values than the competitive algorithm, showing its good anti-noise performance. From the biological point of view, we have identified some biomarkers and statistically significant relationship pairs of AD/mild cognitive impairment (MCI), such as rs75277622 and BCL7A, which may affect the function and structure of multiple brain regions. These findings will promote the prediction of AD/MCI.

关键词： image genetics Alzheimer?s disease structural magnetic resonance imaging non-negative matrix factorization

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Multi-view data clustering via non-negative matrix factorization with manifold regularization

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2022年第3期13卷 677-689页

作者： Khan, Ghufran Ahmad Hu, Jie Li, Tianrui Diallo, Bassoma Wang, Hongjun Southwest Jiaotong Univ Inst Artificial Intelligence Chengdu 611756 Peoples R China

Nowadays, non-negative matrix factorization (NMF) based cluster analysis for multi-view data shows impressive behavior in machine learning. Usually, multi-view data have complementary information from various views. The main concern behind the NMF is how to factorize the data to achieve a significant clustering solution from these complementary views. However, NMF does not focus to conserve the geometrical structures of the data space. In this article, we intensify on the above issue and evolve a new NMF clustering method with manifold regularization for multi-view data. The manifold regularization factor is exploited to retain the locally geometrical structure of the data space and gives extensively common clustering solution from multiple views. The weight control term is adopted to handle the distribution of each view weight. An iterative optimization strategy depended on multiplicative update rule is applied on the objective function to achieve optimization. Experimental analysis on the real-world datasets are exhibited that the proposed approach achieves better clustering performance than some state-of-the-art algorithms.

关键词： non-negative matrix factorization Multi-view clustering Manifold regularization Weighted view

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Data fusion by joint non-negative matrix factorization for hypothesizing pseudo-chemistry using Bayesian networks

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REACTION CHEMISTRY & ENGINEERING 2020年第9期5卷 1719-1737页

作者： Puliyanda, Anjana Sivaramakrishnan, Kaushik Li, Zukui de Klerk, Arno Prasad, Vinay Dept Chem & Mat Engn 9211 116 St NW Edmonton AB T6G 1H9 Canada

Inferring the reaction pathways underlying the processing of complex feeds, using noisy data from spectral sensors that may contain information regarding molecular mechanisms, is challenging. This is tackled by a two-step approach for the partial upgrading of Cold Lake bitumen: first, joint non-negative matrix factorization (JNMF) is used as a data fusion algorithm to extract pseudocomponent spectra by combining complementary information about the reacting environment from Fourier transform infrared (FTIR) and proton nuclear magnetic resonance (H-1-NMR) spectroscopic sensors. Second, a probabilistic inferential model that hypothesizes reaction mechanisms among the identified pseudocomponent spectra is constructed using Bayesian networks that encode directed acyclic causal pathways among the nodes of the random variables (pseudocomponent spectra). The JNMF algorithm has been developed to handle process data artefacts by imputing missing data, using a rotationally invariant norm for robustness to outliers and noise, and enforcing the non-negativity constraint to ensure physical interpretability in compliance with Beer's law for spectral data. The projected optimal gradient approach developed to solve the JNMF objective converges within fewer iterations at the specified tolerance as compared to the multiplicative update rules (MUR). Solution ambiguity in JNMF is limited by incorporating graph regularization terms: (a) inter-sensor co-regularization that penalizes redundancy in the pseudocomponent spectra across spectral sensors, and (b) intra-spectral manifold regularization that penalizes overfitting of the pseudocomponent spectra from each sensor by penalizing redundant peaks within a spectrum. Weighting the intra-spectral regularization term that minimizes similarly correlated peaks across spectral channels of a sensor to zero is seen to result in chemically meaningful pseudocomponent spectra, given that different organic compounds share similar properties with resp

关键词： non-negative matrix factorization

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An efficient manifold regularized sparse non-negative matrix factorization model for large-scale recommender systems on GPUs

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INFORMATION SCIENCES 2019年 496卷 464-484页

作者： Li, Hao Li, Keqin An, Jiyao Zheng, Weihua Li, Kenli Hunan Univ Natl Supercomp Ctr Changsha Sch Informat Sci & Engn Changsha 410082 Hunan Peoples R China SUNY Coll New Paltz Dept Comp Sci New Paltz NY 12561 USA Hunan Univ Technol Coll Elect & Informat Engn Changsha 412007 Hunan Peoples R China

non-negative matrix factorization (NMF) plays an important role in many data mining applications for low-rank representation and analysis. Due to the sparsity that is caused by missing information in many high-dimension scenes, e.g., social networks or recommender systems, NMF cannot mine a more accurate representation from the explicit information. Manifold learning can incorporate the intrinsic geometry of the data, which is combined with a neighborhood with implicit information. Thus, manifold-regularized NMF (MNMF) can realize a more compact representation for the sparse data. However, MNMF suffers from (a) the forming of large-scale Laplacian matrices, (b) frequent large-scale matrix manipulation, and (c) the involved K-nearest neighbor points, which will result in the over-writing problem in parallelization. To address these issues, a single-thread-based MNMF model is proposed on two types of divergence, i.e., Euclidean distance and Kullback-Leibler (KL) divergence, which depends only on the involved feature-tuples' multiplication and summation and can avoid large-scale matrix manipulation. Furthermore, this model can remove the dependence among the feature vectors with fine-grain parallelization inherence. On that basis, a CUDA parallelization MNMF (CUMNMF) is presented on GPU computing. From the experimental results, CUMNMF achieves a 20X speedup compared with MNMF, as well as a lower time complexity and space requirement. (C) 2018 Published by Elsevier Inc.

关键词： Collaborative filtering recommender systems Data mining Euclidean distance and KL-divergence GPU parallelization Manifold regularization non-negative matrix factorization

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Multimodal voice conversion based on non-negative matrix factorization

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EURASIP JOURNAL ON AUDIO SPEECH AND MUSIC PROCESSING 2015年第1期2015卷 1页

作者： Masaka, Kenta Aihara, Ryo Takiguchi, Tetsuya Ariki, Yasuo Kobe Univ Grad Sch Syst Informat Nada Ku Kobe Hyogo 6578501 Japan Kobe Univ Org Adv Sci & Technol Nada Ku Kobe Hyogo 6578501 Japan

A multimodal voice conversion (VC) method for noisy environments is proposed. In our previous non-negative matrix factorization (NMF)-based VC method, source and target exemplars are extracted from parallel training data, in which the same texts are uttered by the source and target speakers. The input source signal is then decomposed into source exemplars, noise exemplars, and their weights. Then, the converted speech is constructed from the target exemplars and the weights related to the source exemplars. In this study, we propose multimodal VC that improves the noise robustness of our NMF-based VC method. Furthermore, we introduce the combination weight between audio and visual features and formulate a new cost function to estimate audio-visual exemplars. Using the joint audio-visual features as source features, VC performance is improved compared with that of a previous audio-input exemplar-based VC method. The effectiveness of the proposed method is confirmed by comparing its effectiveness with that of a conventional audio-input NMF-based method and a Gaussian mixture model-based method.

关键词： Voice conversion Multimodal Image features non-negative matrix factorization Noise robustness

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Robust video identification approach based on local non-negative matrix factorization

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2015年第1期69卷 82-89页

作者： Lu, Zhe-Ming Li, Bo Ji, Qing-Ge Tan, Zhi-Feng Zhang, Yong Zhejiang Univ Sch Aeronaut & Astronaut Hangzhou 310027 Zhejiang Peoples R China Sun Yat Sen Univ Sch Informat Sci & Technol Guangzhou 510006 Guangdong Peoples R China Shenzhen Univ Coll Informat Engn ATR Natl Def Technol Key Lab Shenzhen 518060 Peoples R China

With the popularization of media-capture devices and the development of the Internet's basic facilities, video has become the most popular media information in recent years. The massive capacity of video imposes the demand of automatic video identification techniques which are very important to various applications such as content based video retrieval and copy detection. Therefore, as a challenging problem, video identification has drawn more and more attention in the past decade. The problem addressed here is to identify a given video clip in a given set of video sequences. In this paper, a robust video identification algorithm based on local non-negative matrix factorization (LNMF) is presented. First, some concepts about LNMF are described and the way of finding the factorized matrix is given. Then, its convergence is proven. In addition, a LNMF based shot detection method is proposed for constructing a video identification framework completely based on LNMF. Finally, a LNMF based identification approach using Hausdorff distance is introduced and a two-stage search process is proposed. Experimental results show the robustness of the proposed approach to many kinds of content-preserved distortions and its superiority to other algorithms. (C) 2014 Elsevier GmbH. All rights reserved.

关键词： Video identification non-negative matrix factorization Local non-negative matrix factorization Shot detection Content preserved distortion

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