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Robust graph regularized nonnegative matrix factorization for clustering

DATA MINING AND KNOWLEDGE DISCOVERY 2018年第2期32卷 483-503页

作者： Huang, Shudong Wang, Hongjun Li, Tao Li, Tianrui Xu, Zenglin Univ Elect Sci & Technol China Chengdu 611731 Sichuan Peoples R China Southwest Jiaotong Univ Chengdu 611756 Sichuan Peoples R China Florida Int Univ Miami FL 33199 USA

nonnegative matrix factorization and its graph regularized extensions have received significant attention in machine learning and data mining. However, existing approaches are sensitive to outliers and noise due to the utilization of the squared loss function in measuring the quality of graph regularization and data reconstruction. In this paper, we present a novel robust graph regularized NMF model (RGNMF) to approximate the data matrix for clustering. Our assumption is that there may exist some entries of the data corrupted arbitrarily, but the corruption is sparse. To address this problem, an error matrix is introduced to capture the sparse corruption. With this sparse outlier matrix, a robust factorization result could be obtained since a much cleaned data could be reconstructed. Moreover, the -norm function is used to alleviate the influence of unreliable regularization which is incurred by unexpected graphs. That is, the sparse error matrix alleviates the impact of noise and outliers, and the -norm function leads to a faithful regularization since the influence of the unreliable regularization errors can be reduced. Thus, RGNMF is robust to unreliable graphs and noisy data. In order to solve the optimization problem of our method, an iterative updating algorithm is proposed and its convergence is also guaranteed theoretically. Experimental results show that the proposed method consistently outperforms many state-of-the-art methods.

关键词： nonnegative matrix factorization Robust regularization l(1)-norm function Clustering

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Block kernel nonnegative matrix factorization for face recognition

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INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 2019年第1期17卷

作者： Chen, Wen-Sheng Liu, Jingmin Pan, Binbin Li, Yugao Shenzhen Univ Coll Math & Stat Shenzhen 518060 Peoples R China Guangdong Key Lab Intelligent Informat Proc Shenzhen 518060 Peoples R China

nonnegative matrix factorization (NMF) is a linear approach for extracting localized feature of facial image. However, NMF may fail to process the data points that are nonlinearly separable. The kernel extension of NMF, named kernel NMF (KNMF), can model the nonlinear relationship among data points and extract nonlinear features of facial images. KNMF is an unsupervised method, thus it does not utilize the supervision information. Moreover, the extracted features by KNMF are not sparse enough. To overcome these limitations, this paper proposes a supervised KNMF called block kernel NMF (BKNMF). A novel objective function is established by incorporating the intra-class information. The algorithm is derived by making use of the block strategy and kernel theory. Our BKNMF has some merits for face recognition, such as highly sparse features and orthogonal features from different classes. We theoretically analyze the convergence of the proposed BKNMF. Compared with some state-of-the-art methods, our BKNMF achieves superior performance in face recognition.

关键词： Kernel method face recognition nonnegative matrix factorization

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Content-based image retrieval using student's t-mixture model and constrained multiview nonnegative matrix factorization

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MULTIMEDIA TOOLS AND APPLICATIONS 2018年第11期77卷 14207-14239页

作者： Zhu, Hongqing Xie, Qunyi East China Univ Sci & Technol Sch Informat Sci & Engn 130 Mei Long Rd Shanghai 200237 Peoples R China

The expensive and time-consuming effort required for archiving images is the main motive for developing an effective retrieval system. This paper addresses a competitive scheme for Content-Based Image Retrieval (CBIR) based on a constrained multiview nonnegative matrix factorization (NMF) that has the ability to generate a sparse representation. The scheme blends multiple visual features, which can together reflect the content of images in terms of similarity metrics and the Frobenius norm. Then, the proposed method constructs a similarity-preserving matrix factorization via an improved NMF, where the structural constraint, L (1/2)-sparse constraint and farness-preserving constraint are integrated into the objective function of conventional NMF. In this way, the structure and content of high-dimensional feature data source can be preserved in low-dimensional space. Another critical part of the proposed system is to establish Student's t-Mixture Model (SMM) based on a Markov Random Field (MRF), which can best manipulate the clustering of sparse representations according to the statistical properties of the image features. With this method, the task of image retrieval of the whole dataset is reduced to a nearest-neighbour search in a specific category containing the query image. Convergence of the proposed update rule, investigated in this study, is also verified by numerical simulations. Lastly, we conduct experiments on public datasets to compare the performance of the proposed algorithm with existing works in terms of Precision and Recall Rates. The encouraging results indicate the effectiveness of the proposed technique.

关键词： Imageretrieval Student's t-mixture model nonnegative matrix factorization sparse constraint Markov random field multiview

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Co-regularized multiview nonnegative matrix factorization with correlation constraint for representation learning

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MULTIMEDIA TOOLS AND APPLICATIONS 2018年第10期77卷 12955-12978页

作者： Ou, Weihua Long, Fei Tan, Yi Yu, Shujian Wang, Pengpeng Guizhou Normal Univ Sch Big Data & Comp Sci Guiyang 550025 Guizhou Peoples R China Guizhou Inst Technol Sch Elect & Informat Engn Guiyang 550003 Guizhou Peoples R China Guizhou Univ Coll Big Data & Informat Engn Guiyang 550025 Guizhou Peoples R China Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

With the increasing availability of multiview nonnegative data in real applications, multiview representation learning based on nonnegative matrix factorization (NMF) has attracted more and more attentions. However, existing NMF-based methods are sensitive to noises and are difficult to generate discriminative features with noisy views. To address these problems, we propose a co-regularized multiview nonnegative matrix factorization method with correlation constraint for nonnegative representation learning, which jointly exploits consistent and complementary information across different views. Different from previous works, we aim at integrating information from multiple views efficiently and making it more robust to the presence of noisy views. More specifically, we exploit the complementary information of multiple views through the co-regularization to accommodate the presence of the noisy views. Meanwhile, correlation constraint is imposed on the low-dimensional space to learn a common latent representation shared by different views. For the induced objective function, we derive an alternative algorithm to solve the optimization problem. The experimental results on four real datasets demonstrate the effectiveness and robustness of the proposed algorithm.

关键词： nonnegative matrix factorization Co-regularization Correlation constraint Consistent Complementary

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Doubly Nonparametric Sparse nonnegative matrix factorization Based on Dependent Indian Buffet Processes

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018年第5期29卷 1835-1849页

作者： Xuan, Junyu Lu, Jie Zhang, Guangquan Xu, Richard Yi Da Luo, Xiangfeng Univ Technol Sydney Fac Engn & Informat Technol Ultimo NSW 2007 Australia Shanghai Univ Sch Comp Engn & Sci Shanghai 200444 Peoples R China

Sparse nonnegative matrix factorization (SNMF) aims to factorize a data matrix into two optimized nonnegative sparse factor matrices, which could benefit many tasks, such as document-word co-clustering. However, the traditional SNMF typically assumes the number of latent factors (i.e., dimensionality of the factor matrices) to be fixed. This assumption makes it inflexible in practice. In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian buffet processes (dIBP). We apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two factor matrices will be columnwise correlated. Under this framework, two classes of correlation function are proposed: 1) using bivariate Beta distribution and 2) using Copula function. Compared with the single IBP-based NMF, this paper jointly makes two factor matrices nonparametric and sparse, which could be applied to broader scenarios, such as co-clustering. This paper is seen to be much more flexible than Gaussian process-based and hierarchial Beta process-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries. Our experiments on synthetic data show the merits of this paper compared with the state-of-the-art models in respect of factorization efficiency, sparsity, and flexibility. Experiments on real-world data sets demonstrate the efficiency of this paper in document-word co-clustering tasks.

关键词： Co-clustering nonnegative matrix factorization probability graphical model text mining

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Combined Method of an Efficient Cuckoo Search Algorithm and nonnegative matrix factorization of Different Zernike Moment Features for Discrimination Between Oil Spills and Lookalikes in SAR Images

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 2018年第11期11卷 4193-4205页

作者： Raeisi, Asma Akbarizadeh, Gholamreza Mahmoudi, Alimorad Shahid Chamran Univ Ahvaz Fac Engn Dept Elect Engn Ahvaz *** Iran

Oil spill detection in synthetic aperture radar (SAR) images plays a crucial role in oil slick monitoring on the sea surface. In addition to oil spills, SAR images incorporate a large number of similar phenomena called "lookalikes". Choosing a method of discriminating between oil spills and lookalikes with high accuracy is a necessity. In this paper, a new algorithm is proposed for discrimination between oil spills and lookalikes, which consists of the following four main parts. 1) Dark spot detection in SAR images. 2) Shape-based feature extraction of oil spills and lookalikes selected from dark spots in the previous stage. 3) Feature transformation using the NMF algorithm. 4) Classification. To evaluate the performance of the proposed algorithm, it was tested on the several real SAR images. This algorithm was able to provide promising results for both dark spot detection and oil spill classification. The average error rate of dark spot detection for a typical image was 1.31% and it could discriminate between oil spills and lookalikes with an average accuracy of 96.31% using feature transformation modes after transforming the features and classifying them using the K-nearest neighbor classifier.

关键词： Classification efficient cuckoo search algorithm feature transformation nonnegative matrix factorization oil spill zernike moment descriptor

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Detecting evolving communities in dynamic networks using graph regularized evolutionary nonnegative matrix factorization

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 530卷

作者： Ma, Xiaoke Li, Dongyuan Tan, Shiyin Huang, Zhihao Xidian Univ Sch Comp Sci & Technol 2 South Taibai Rd Xian Shaanxi Peoples R China Xidian Univ Xidian Ningbo Informat Technol Inst 777 Zhongguanxi Rd Ningbo Zhejiang Peoples R China

Many networks in society and nature are dynamic, and identifying evolving communities in dynamic networks sheds light on revealing the structure and function of the overall systems. Evolutionary clustering is based on the temporal smoothness framework that simultaneously maximizes the clustering accuracy at the current time step and minimizes the clustering drift between two successive time steps. However, they are criticized for the linear combination of networks at two successive time steps because the relation between networks is unnecessary linear. To address this problem, we propose the Graph regularized Evolutionary nonnegative matrix factorization algorithm (GrENMF) for the dynamic community detection, where the network at the previous time step is transformed as a regularizer into the objective function. Moreover, the local topological structure in the network at the previous time step is preserved in communities at the current time step, which improves the performance of algorithm without increasing the time complexity. Furthermore, we prove the equivalence among evolutionary nonnegative matrix factorization (ENMF), spectral clustering, kernel K-means, modularity density and GrENMF, which serves as the theoretical foundation for the GrENMF algorithm. The experimental results over a number of artificial and real world dynamic networks illustrate that the proposed method is not only more accurate, but also more robust than state-of-the-art approaches. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Dynamic networks Community Evolutionary clustering nonnegative matrix factorization Graph regularization

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Informed nonnegative matrix factorization Methods for Mobile Sensor Network Calibration

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2018年第4期4卷 667-682页

作者： Dorffer, Clement Puigt, Matthieu Delmaire, Gilles Roussel, Gilles Univ Littoral Cote dOpale F-62228 Calais France Lab STICC UMR 6285 F-29238 Brest France CNRS F-75016 Paris France Ecole Natl Super Tech Avancees Bretagne F-29200 Brest France Univ Littoral Cote dOpale LISIC EA 4491 F-62228 Calais France

In this paper, we consider the problem of blindly calibrating a mobile sensor network-i.e., determining the gain and the offset of each sensor-fromheterogeneous observations on a defined spatial area over time. For that purpose, we propose to revisit blind sensor calibration as an informed nonnegative matrix factorization (NMF) problem with missing entries. In the considered framework, one matrix factor contains the calibration structure of the sensors-and especially the values of the sensed phenomenon-while the other one contains the calibration parameters of the whole sensor network. The available information is taken into account by using a specific parameterization of the NMF problem. Moreover, we also consider additional NMF constraints which can be independently taken into account, i.e., an approximate constraint over the mean calibration parameters and a sparse approximation of the sensed phenomenon over a known dictionary. The enhancement of our proposed approaches is investigated through more than 5000 simulations and is shown to be accurate for the considered application and to outperform a multihop micro-calibration technique as well as a method based on low-rank matrix completion and nonnegative least squares.

关键词： nonnegative matrix factorization mobile sensor calibration matrix completion wireless sensor network mobile crowdsensing

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Supervised and Constrained nonnegative matrix factorization with Sparseness for Image Representation

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WIRELESS PERSONAL COMMUNICATIONS 2018年第4期102卷 3055-3066页

作者： Cai, Xibiao Sun, Fuming Liaoning Univ Technol Sch Elect & Informat Engn Jinzhou Peoples R China

nonnegative matrix factorization (NMF) has been becoming an important method for feature dimension reduction in recent years since it can represent data with strong strength. In this paper, we present a novel image representation method by integrating prior information of known samples and a certain sparseness constraint into NMF framework simultaneously, called Supervised and Constrained nonnegative matrix factorization with Sparseness (SCNMFS). The proposed method can harvest the promising identification ability of the acquired coefficient matrix under the condition that the better sparsity of the factorized base matrix is ensured. From the perspective of theory, the proposed method can effectively reveal the intrinsic geometric characteristics of images. Extensive experimental results on common benchmarks demonstrate that SCNMFS has superiority compared with three state-of-the-art algorithms in image classification problem.

关键词： nonnegative matrix factorization Feature dimension reduction Local geometric characteristics Sparse constraint Image classification

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Modularized tri-factor nonnegative matrix factorization for community detection enhancement

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 533卷

作者： Yan, Chao Chang, Zhenhai Cent Univ Finance & Econ Sch Math & Stat Beijing 100081 Peoples R China Tianshui Normal Univ Sch Math & Stat Tianshui 741000 Peoples R China

Community structure detection is a fundamental problem for understanding the relationship between the topology structures and the functions of complex networks. NMF-based models are a promising method for identifying communities from networks, but most of them require the number of communities in advance, which is inconvenient for real applications. Also, the basic NMF model could not reflect the characteristics of networks more comprehensively under the sole nonnegative constraint. In this paper, we develop a novel modularized tri-factor nonnegative matrix factorization model which combines the modularized information as the regularization term, leading to improved performance in community detection. Besides, we utilize general modularity density to determine the number of communities. Finally, the effectiveness of our approach is demonstrated on both synthetic and real-world networks. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Community detection Modularized regularization nonnegative matrix factorization General modularity density

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