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Endmembers compression based nonnegative matrix factorization for hyperspectral unmixing

INTERNATIONAL JOURNAL OF REMOTE SENSING 2023年第6期44卷 2064-2092页

作者： Shu, Sheng Huang, Ting-Zhu Huang, Jie Wang, Jin-Ju Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Sichuan Peoples R China

Hyperspectral unmixing (HU) has grown more important in hyperspectral images (HSIs) research in recent years. Many models based on nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) have been extensively used to tackle the HU problem. Most of these models allow a large and extensive exploration of abundance and provide promising unmixing results. However, the exploration of each endmember information is insufficient. In this article, we propose an unmixing model called endmembers compressionbased NMF (EC-NMF) for HU. Specifically, by an orthogonal projection, the EC-NMF enables distinct endmembers to be differentiated from each other. In this space, each compressed endmember represents the distinct characteristics of the corresponding endmember, which makes it easier for the endmembers separated. Furthermore, the EC-NMF model incorporates the reweighted nuclear norm on the abundance map to fully account for spatial information and to constrain its low-rank properties. The EC-NMF model is solved by an augmented multiplicative algorithm. In particular, we achieve the proposed model based on the matrix representation, which reduces the computational complexity compared with NTF-based methods. Extensive experiments on synthetic and real data give concrete evidence that the proposed method outperforms other known methods in both the unmixing performance and running time.

关键词： hyperspectral unmixing endmembers compression nonnegative matrix factorization hyperspectral images

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Least-Squares Methods for nonnegative matrix factorization Over Rational Functions

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2023年 71卷 1712-1724页

作者： Hautecoeur, Cecile De Lathauwer, Lieven Gillis, Nicolas Glineur, Francois UCLouvain ICTEAM B-1348 Louvain La Neuve Belgium Katholieke Univ Leuven Dept Elektrotech Elect Engn B-8500 Kortrijk Belgium Univ Mons Math & Operat Res B-7000 Mons Belgium

nonnegative matrix factorization (NMF) models are widely used to analyze linearly mixed nonnegative data. When the data is made of samplings of continuous signals, the factors in NMF can be constrained to be samples of nonnegative rational functions. This leads to a fairly general model referred to as NMF using rational functions (R-NMF). We first show that, unlike NMF, R-NMF possesses an essentially unique factorization under mild assumptions, which is crucial in applications where the ground-truth factors need to be recovered, as in blind source separation problems. Then we present different approaches to solve R-NMF: the R-HANLS, R-ANLS and R-NLS methods. In our tests, no method significantly outperforms the others in all cases, and all three methods offer a different trade-off between solution accuracy and computational requirements. Indeed, while R-HANLS is fast and accurate for large problems, R-ANLS is more accurate, but also more resources demanding, both in time and memory and R-NLS is even more accurate but only for small problems. Then, crucially we show that R-NMF models outperforms NMF in various tasks including the recovery of semi-synthetic continuous signals, and a classification problem of real hyperspectral signals.

关键词： Splines (mathematics) Standards matrix decomposition Shape Poles and zeros Blind source separation Text mining nonnegative matrix factorization block-coordinate-descent sampled signals nonlinear least squares nonnegative rational functions projection

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Potential circRNA-Disease Association Prediction Using DeepWalk and nonnegative matrix factorization

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2023年第5期20卷 3154-3162页

作者： Qiao, Li-Juan Gao, Zhen Ji, Cun-Mei Liu, Zhi-Hao Zheng, Chun-Hou Wang, Yu-Tian Qufu Normal Univ Sch Cyber Sci & Engn Qufu 273165 Peoples R China Anhui Univ Sch Artifial Intelligence Hefei 230601 Peoples R China

Circular RNAs (circRNAs) are a category of noncoding RNAs that exist in great numbers in eukaryotes. They have recently been discovered to be crucial in the growth of tumors. Therefore, it is important to explore the association of circRNAs with disease. This paper proposes a new method based on DeepWalk and nonnegative matrix factorization (DWNMF) to predict circRNA-disease association. Based on the known circRNA-disease association, we calculate the topological similarity of circRNA and disease via the DeepWalk-based method to learn the node features on the association network. Next, the functional similarity of the circRNAs and the semantic similarity of the diseases are fused with their respective topological similarities at different scales. Then, we use the improved weighted K-nearest neighbor (IWKNN) method to preprocess the circRNA-disease association network and correct nonnegative associations by setting different parameters K-1 and K-2 in the circRNA and disease matrices. Finally, the L-2,L-1-norm, dual-graph regularization term and Frobenius norm regularization term are introduced into the nonnegative matrix factorization model to predict the circRNA-disease correlation. We perform cross-validation on circR2Disease, circRNADisease, and MNDR. The numerical results show that DWNMF is an efficient tool for forecasting potential circRNA-disease relationships, outperforming other state-of-the-art approaches in terms of predictive performance.

关键词： CircRNA-disease association circular RNAs DeepWalk disease nonnegative matrix factorization

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Explainable recommendations with nonnegative matrix factorization

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ARTIFICIAL INTELLIGENCE REVIEW 2023年第SUPPL3期56卷 S3927-S3955页

作者： Zhang, Xiaoxia Zhou, Xianjun Chen, Lu Liu, Yanjun Chongqing Univ Posts & Telecommun Chongqing Key Lab Computat Intelligence Chongqing 400065 Peoples R China Chongqing Univ Posts & Telecommun Key Lab Big Data Intelligent Comp Chongqing 400065 Peoples R China Chongqing Normal Univ Sch Math Sci Chongqing 401331 Peoples R China

Explicable recommendation system is proved to be conducive to improving the persuasiveness of the recommendation system, enabling users to trust the system more and make more intelligent decisions. nonnegative matrix factorization (NMF) produces interpretable solutions for many applications including collaborative filtering as it's nonnegativity. However, the latent features make it difficult to interpret recommendation results to users because we don't know the specific meaning of features that users are interested in and the extent to which the items or users belong to these features. To overcome this difficulty, we develop a novel method called Partially Explainable nonnegative matrix factorization (PE-NMF) by employing explicit data to replace part latent variables of item-feature matrix, by which users can learn more about the features of the items and then to make ideal decisions and recommendations. The objective function of PE-NMF is composed of two parts: one part corresponding to explicit features and the other part is about implicit features. We develop an iterative method to minimize the objective function and derive the iterative update rules, with which the objective function can be proved to be decreasing. Finally, the experiments are executed on Yelp, Amazon and Dianping datasets, and the experimental results demonstrate PE-NMF keeps a high prediction performance on both rating prediction and top-N recommendation that compare to fully explainable nonnegative matrix factorization (FE-NMF), which is obtained by using explicit opinions instead of item-feature matrix. Also PE-NMF holds almost the same recommendation ability as NMF.

关键词： nonnegative matrix factorization Partially explainable nonnegative matrix factorization Fully explainable nonnegative matrix factorization Recommendation explnation

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Constraint-Induced Symmetric nonnegative matrix factorization for Accurate Community Detection

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INFORMATION FUSION 2023年 89卷 588-602页

作者： Liu, Zhigang Luo, Xin Wang, Zidong Liu, Xiaohui Chongqing Univ Posts & Telecommun Sch Comp Sci & Technol Chongqing 400065 Peoples R China Chinese Acad Sci Chongqing Inst Green & Intelligent Technol Chongqing Key Lab Big Data & Intelligent Comp Chongqing 400714 Peoples R China Southwest Univ Coll Comp & Informat Sci Chongqing 400715 Peoples R China Brunel Univ London Dept Comp Sci Uxbridge UB8 3PH Middlesex England

As a fundamental characteristic of an undirected network, community reveals its networking organization and functional mechanisms, making community detection be a highly-interesting issue in network representation learning. With great interpretability, a symmetric and nonnegative matrix factorization (SNMF)-based approach is frequently adopted to tackle this issue. However, it only adopts a unique feature matrix for describing the symmetry of an undirected network, which unfortunately results in a reduced feature space that evidently impairs its representation learning ability. Motivated by this discovery, this paper proposes a novel Constraintinduced Symmetric nonnegative matrix factorization (C-SNMF) model that adopts three-fold ideas: a) Representing a target undirected network with multiple latent feature matrices, thus preserving its representation learning capacity;b) Incorporating a symmetry-regularizer into its objective function, which preserves the symmetry of the learnt low-rank approximation to the adjacency matrix, thereby making the resultant detector precisely illustrate the target network's symmetry;and c) Introducing a graph-regularizer that preserves local invariance of the network's intrinsic geometry into its learning objective, thus making the achieved detector well-aware of community structure within the target network. Note that the regularization coefficients are selected according to the modularity of the learnt community structure on the training data only, thereby greatly improving the achieved model's practical significance for real applications. Experimental results on six realworld networks demonstrate that the proposed C-SNMF model significantly outperforms the benchmarks and state-of-the-art models in achieving highly-accurate community detection results.

关键词： Undirected Network Social Network Information Fusion Network Representation Learning Community Detection nonnegative matrix factorization Symmetry -regularization Multiple Constraints

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Combining K Nearest Neighbor With nonnegative matrix factorization for Predicting Circrna-Disease Associations

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2023年第5期20卷 2610-2618页

作者： Wang, Mei-Neng Xie, Xue-Jun You, Zhu-Hong Wong, Leon Li, Li-Ping Chen, Zhan-Heng Yichun Univ Sch Math & Comp Sci Yichun 336000 Jiangxi Peoples R China Northwestern Polytech Univ Sch Comp Sci & Engn Xian 710072 Shaanxi Peoples R China Chinese Acad Sci Xinjiang Tech Inst Phys & Chem Urumqi 830011 Peoples R China

Accumulating evidences show that circular RNAs (circRNAs) play an important role in regulating gene expression, and involve in many complex human diseases. Identifying associations of circRNA with disease helps to understand the pathogenesis, treatment and diagnosis of complex diseases. Since inferring circRNA-disease associations by biological experiments is costly and time-consuming, there is an urgently need to develop a computational model to identify the association between them. In this paper, we proposed a novel method named KNN-NMF, which combines K nearest neighbors with nonnegative matrix factorization to infer associations between circRNA and disease (KNN-NMF). Frist, we compute the Gaussian Interaction Profile (GIP) kernel similarity of circRNA and disease, the semantic similarity of disease, respectively. Then, the circRNA-disease new interaction profiles are established using weight K nearest neighbors to reduce the false negative association impact on prediction performance. Finally, nonnegative matrix factorization is implemented to predict associations of circRNA with disease. The experiment results indicate that the prediction performance of KNN-NMF outperforms the competing methods under five-fold cross-validation. Moreover, case studies of two common diseases further show that KNN-NMF can identify potential circRNA-disease associations effectively.

关键词： Gaussian kernel similarity semantic similarity K nearest neighbor circRNA-disease association nonnegative matrix factorization

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Community Detection in Fully-Connected Multi-layer Networks Through Joint nonnegative matrix factorization

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IEEE ACCESS 2022年 10卷 43022-43043页

作者： Al-Sharoa, Esraa M. Aviyente, Selin Jordan Univ Sci & Technol Dept Elect Engn Irbid 22110 Jordan Michigan State Univ Dept Elect & Comp Engn E Lansing MI 48824 USA

Modern data analysis and processing tasks typically involve large sets of structured data. Graphs provide a powerful tool to describe the structure of such data, where the entities and the relationships between them are modeled as the nodes and edges of the graph. Traditional single layer network models are insufficient for describing the multiple entity types and modes of interaction encountered in real-world applications. Recently, multi-layer network models, which consider the different types of interactions both within and across layers, have emerged to model these systems. One of the important tools in understanding the topology of these high-dimensional networks is community detection. In this paper, a joint nonnegative matrix factorization approach is proposed to detect the community structure in multi-layer networks. The proposed approach models the multi-layer network as the union of a multiplex and bipartite network and formulates community detection as a regularized optimization problem. This optimization problem simultaneously finds the nonnegative low-rank embedding of the intra- and inter-layer adjacency matrices while minimizing the distance between the two to guarantee pair-wise similarity across embeddings. The proposed approach can detect the community structure for both homogeneous and heterogeneous multi-layer networks and is robust to noise and sparsity. The performance of the proposed approach is evaluated for both simulated and real networks and compared to state-of-the-art methods.

关键词： Multiplexing matrix decomposition Image edge detection Laplace equations Symmetric matrices Sparse matrices Optimization Multi-layer networks community detection intra-layer community inter-layer community nonnegative matrix factorization

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Evaluation of the default mode network using nonnegative matrix factorization in patients with cognitive impairment induced by occupational aluminum exposure

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CEREBRAL CORTEX 2023年第17期33卷 9815-9821页

作者： Zhang, Feifei Liu, Bo Shao, Yinbo Tan, Yan Niu, Qiao Wang, Xiaochun Zhang, Hui Shanxi Med Univ Dept Radiol Hosp 1 85 Jiefang South Rd Taiyuan 030001 Shanxi Peoples R China Shanxi Med Univ Dept Shanxi Key Lab Intelligent Imaging & Nanomed Hosp 1 Taiyuan 030001 Shanxi Peoples R China Shanxi Med Univ Dept Coll Med Imaging Taiyuan 030001 Shanxi Peoples R China Shanxi Med Univ Dept Occupat Hlth Taiyuan 030001 Shanxi Peoples R China

Aluminum (Al) is an important environmental pathogenic factor for neurodegenerative diseases, especially mild cognitive impairment (MCI). The aim of this study was to evaluate the gray matter volume of structural covariance network alterations in patients with Al-induced MCI. Male subjects who had been exposed to Al for >10 years were included in the present study. The plasma Al concentration, Montreal cognitive assessment (MoCA) score, and verbal memory assessed by the Rey auditory verbal learning test (AVLT) score were collected from each participant. nonnegative matrix factorization was used to identify the structural covariance network. The neural structural basis for patients with Al-induced MCI was investigated using correlation analysis and group comparison. Plasma Al concentration was inversely related to MoCA scores, particularly AVLT scores. In patients with Al-induced MCI, the gray matter volume of the default mode network (DMN) was considerably lower than that in controls. Positive correlations were discovered between the DMN and MoCA scores as well as between the DMN and AVLT scores. In sum, long-term occupational Al exposure has a negative impact on cognition, primarily by affecting delayed recognition. The reduced gray matter volume of the DMN may be the neural mechanism of Al-induced MCI.

关键词： cognitive impairment default mode network nonnegative matrix factorization magnetic resonance imaging occupational aluminum exposure

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Learning a Subspace and Clustering Simultaneously with Manifold Regularized nonnegative matrix factorization

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Guidance, Navigation and Control 2024年第3期4卷 147-165页

作者： Feiping Nie Huimin Chen Heng Huang Chris H.Q.Ding Xuelong Li School of Computer Science Northwestern Polytechnical University Xi'an 710072 P.R.China School of Artificial Intelligence Optics and Electronics(iOPEN)Northwestern Polytechnical University Xi'an 710072 P.R.China Key Laboratory of Intelligent Interaction and Applications(Northwestern Polytechnical University)Ministry of Industry and Information Technology Xi'an 710072 P.R.China Department of Electrical and Computer Engineering University of Pittsburgh PittsburghPA 15260USA Department of Computer Science and Engineering The Chinese University of Hong Kong Shenzhen 518172 P.R.China Institute of Artificial Intelligence(TeleAI)China Telecom Corporation Limited 31 Jinrong Street Beijing 100033P.R.China

With the incredible growth of high-dimensional data such as microarray gene expression data and web blogs from internet, the researchers are desirable to develop new clustering techniques to address the critical problem created by irrelevant dimensions. Properties of nonnegative matrix factorization(NMF) as a clustering method were studied by relating its formulation to other methods such as K-means clustering. In this paper, by introducing clustering indicator constraints on NMF and incorporating manifold regularization to preserve geometric structures,we propose a novel manifold regularized NMF method that can simultaneously learn subspace and do clustering. As a result, our clustering results can directly assign cluster label to data points. Extensive experimental results show that our method outperforms related other methods.

关键词： Subspace learning clustering nonnegative matrix factorization manifold learning

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Generalized Fast Multichannel nonnegative matrix factorization Based on Gaussian Scale Mixtures for Blind Source Separation

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2022年 30卷 1734-1748页

作者： Fontaine, Mathieu Sekiguchi, Kouhei Nugraha, Aditya Arie Bando, Yoshiaki Yoshii, Kazuyoshi Telecom Paris LTCI Inst Polytech Paris Palaiseau France Ctr Adv Intelligence Project AIP RIKEN Tokyo 1030027 Japan Kyoto Univ Grad Sch Informat Sakyo Ku Kyoto 6068501 Japan Natl Inst Adv Ind Sci & Technol Koto Ku Tokyo 1350064 Japan

This paper describes heavy-tailed extensions of a state of the art versatile blind source separation method called fast multichannel nonnegative matrix factorization (FastMNMF) from a unified point of view. The common way of deriving such an extension is to replace the multivariate complex Gaussian distribution in the likelihood function with its heavy-tailed generalization, e.g., the multivariate complex Student's t and leptokurtic generalized Gaussian distributions, and tailor-make the corresponding parameter optimization algorithm. Using a wider class of heavy-tailed distributions called a Gaussian scale mixture (GSM), i.e., a mixture of Gaussian distributions whose variances are perturbed by positive random scalars called impulse variables, we propose GSM-FastMNMF and develop an expectation-maximization algorithm that works even when the probability density function of the impulse variables have no analytical expressions. We show that existing heavy-tailed FastMNMF extensions are instances of GSM-FastMNMF and derive a new instance based on the generalized hyperbolic distribution that include the normal-inverse Gaussian, Student's t, and Gaussian distributions as the special cases. Our experiments show that the normal-inverse Gaussian FastMNMF outperforms the state-of-the-art FastMNMF extensions and ILRMA model in speech enhancement and separation in terms of the signal-to-distortion ratio.

关键词： nonnegative matrix factorization blind source separation probabilistic framework expectation-maximization

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