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Identification of key nodes in complex networks by using a joint technique of nonnegative matrix factorization and regularization

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PHYSICAL COMMUNICATION 2024年 65卷

作者： Lu, Pengli Yang, Junxia Liu, Wenzhi Lanzhou Univ Technol Sch Comp & Commun Lanzhou 730050 Peoples R China

Identifying key nodes in complex networks is essential to deeply understand and fully utilize the properties and functions of complex systems. Currently, existing traditional methods perform critical nodes identification by manually selecting important attribute features of nodes, but there are limitations in this approach. Manual selection of attribute features may overlook non -obvious features related to nodes criticality and correlations between attribute features. To compensate for the shortcomings of traditional methods, a Joint Technique for identifying critical nodes, called JTNMFR, is presented based on nonnegative matrix factorization and Regularization. factorization of weighted adjacency matrix is performed to obtain potential attribute features of nodes, and communicability network matrix and similarity matrix are introduced as regularization terms to control sparsity of the decomposition results. Ultimately, the importance of nodes is assessed by constructing an objective function that integrates these two aspects and utilizing alternative iteration to obtain the attribute matrix. To validate the accuracy and reliability of JTNMFR, we compare it with nine other identification approaches on eight real networks. Experimental results show that JTNMFR not only significantly outperforms the other algorithms in terms of accuracy of node importance, monotonicity, and node spreading ability but also provides a more accurate means of assessing node importance.

关键词： Complex networks Node centrality nonnegative matrix factorization Regularization

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Entropy regularized fuzzy nonnegative matrix factorization for data clustering

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2024年第2期15卷 459-476页

作者： Chen, Kun Liang, Junchen Liu, Junmin Shen, Weilin Xu, Zongben Yao, Zhengjian Xi An Jiao Tong Univ Sch Math & Stat West Xianning Rd Xian 710049 Shaanxi Peoples R China

Clustering high-dimensional data is very challenging due to the curse of dimensionality. To address this problem, low-rank matrix approximations are widely used to identify the underlying low-dimensional structure of a dataset. Among these, nonnegative matrix factorization (NMF) is the most popular because its decomposed factors are nonnegative and meaningful. However, the NMF problem has been proved to be nonconvex and NP-hard, thus resulting in many local minima. To obtain high-quality local minima, we propose an entropy regularized fuzzy nonnegative matrix factorization (ERF-NMF) model for high-dimensional data fuzzy clustering. First, probability simplex constraints on the decomposed weight components are added to achieve dimension reduction and fuzzy clustering of a dataset simultaneously. Based on the constraints, we also introduce entropy regularization to further reduce the search space for optimal solutions. Finally, we present multiplicative update rules for solving the ERF-NMF model and provide a complexity and convergence analysis. Comprehensive experiments show that the proposed ERF-NMF performs remarkably well with promising results, and its decomposition will be sparser because of entropy regularization and have a clearer physical meaning because of probability simplex constraints.

关键词： High-dimensional data clustering nonnegative matrix factorization Entropy regularization Fuzzy modeling

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Deep asymmetric nonnegative matrix factorization for graph clustering

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PATTERN RECOGNITION 2024年 148卷

作者： Hajiveiseh, Akram Seyedi, Seyed Amjad Tab, Fardin Akhlaghian Univ Kurdistan Dept Comp Engn Sanandaj Iran

Graph clustering is a fundamental technique in machine learning that has widespread applications in various fields. Deep nonnegative matrix factorization (DNMF) was recently emerged to cope with the extraction of several layers of features, and it has been demonstrated to achieve remarkable results on unsupervised tasks. While DNMF has been applied for analyzing graphs, the effectiveness of the current DNMF approaches for graph clustering is generally unsatisfactory: these methods are intrinsically data representation models, and their objective functions do not capture cluster structures, also ignores direction which is crucial in the directed graph clustering problems. To overcome these downsides, this paper proposes a graph-specific DNMF model based on the Asymmetric NMF which can handle undirected and directed graphs. Inspired by hierarchical graph clustering and graph summarization approaches, the Deep Asymmetric nonnegative matrix factorization (DAsNMF) is introduced for the directed graph clustering problem. In a pseudo-hierarchical clustering setting, DAsNMF decomposes the input graph to extract low-level to high-level node representations and graph representations (summarized graphs). In addition, the asymmetric cosine and PageRank-based similarities are imposed on the proposed model to preserve the local and global graph structures. The learning process is formulated as a unified optimization problem to jointly train representation learning model and clustering model. The extensive experimental studies validate the effectiveness of the proposed method on directed graphs.

关键词： nonnegative matrix factorization Deep learning Graph clustering Directed graph

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Alternating block linearized Bregman iterations for regularized nonnegative matrix factorization

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2024年第12期47卷 9858-9873页

作者： Chen, Beier Zhang, Hui Natl Univ Def Technol Dept Math Changsha 410073 Hunan Peoples R China

In this paper, we propose an alternating block variant of the linearized Bregman iterations for a class of regularized nonnegative matrix factorization (NMF) problems. The proposed method exploits the block structure of NMF, utilizes the smooth adaptable property of the loss function based on the Bregman distance, and at the same time follows the iterative regularization idea of the linearized Bregman iterations method. Theoretically, we show that the proposed method is a descent method by adjusting the involved parameters. Finally, we end with several illustrative numerical experiments.

关键词： alternating block Bregman distance linearized Bregman iterations nonnegative matrix factorization sparse regularization sufficient descent

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A Framework for Compressed Weighted nonnegative matrix factorization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2024年 72卷 4798-4811页

作者： Yahaya, Farouk Puigt, Matthieu Delmaire, Gilles Roussel, Gilles Univ Littoral Cote dOpale LISIC UR 4491 F-62228 Calais France Expleo Grp F-33700 Meerignac France

In this paper we propose a novel framework that successfully combines random projection or compression to weighted nonnegative matrix factorization (NMF). Indeed a large body of NMF research has focused on the unweighted case-i.e., a complete data matrix to factorize-with a few extensions to handle incomplete data. Also most of these works are typically not efficient enough when the size of the data is arbitrarily large. Random projections belong to the major techniques used to process big data and although have been successfully applied to NMF, there was no investigation with weighted NMF. For this reason we propose to combine random projection with weighted NMF, where the weight models the confidence in the data (or the absence of confidence in the case of missing data). We experimentally show the proposed framework to significantly speed-up state-of-the-art NMF methods under some mild conditions when applied on various data.

关键词： Cost function Convergence Symmetric matrices Standards Signal processing algorithms Iterative methods Image processing Calibration Time complexity Symbols nonnegative matrix factorization random projections matrix sketching missing entries matrix completion

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Multitarget scattering imaging based on nonnegative matrix factorization beyond the optical memory effect

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OPTICS COMMUNICATIONS 2024年 558卷

作者： Xi, Teli Zhou, Lei Cheng, Huachao Lv, Pei Liu, Fei Xiang, Meng Liu, Jinpeng Shao, Xiaopeng Xidian Univ Sch Optoelect Engn Xian Key Lab Computat Imaging Xian 710071 Peoples R China Xidian Univ Hangzhou Inst Technol Adv Optoelect Imaging & Device Lab Hangzhou 311200 Peoples R China

Speckle correlation technique is limited by the optical memory effect (OME) range, and aliasing phenomenon occurs in multitarget information beyond the range. Here, we propose a multitarget scattering imaging method based on nonnegative matrix factorization (NMF) beyond the OME, which can separate and interpret the single target information from the aliasing information. Based on the study of the multitarget aliasing speckle autocorrelation model, we apply NMF to unmix the multitarget speckle autocorrelation beyond the OME, and combine with phase retrieval (PR) technology to recover the target. Our approach requires only single-shot speckle information without prior information to realize wide-field multitarget imaging. This work provides potential value for biomedical imaging and astronomical observation, and helps to broaden the application scope of speckle correlation technique.

关键词： Scattering imaging Optical memory effect nonnegative matrix factorization Speckle

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The rise of nonnegative matrix factorization: Algorithms and applications

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INFORMATION SYSTEMS 2024年 123卷

作者： Guo, Yi-Ting Li, Qin-Qin Liang, Chun-Sheng Lanzhou Univ Collaborat Innovat Ctr West Ecol Safety Lanzhou Peoples R China Lanzhou Univ Coll Atmospher Sci Key Lab Semiarid Climate Change Minist Educ Lanzhou Peoples R China Guizhou Inst Technol Sch Transportat Engn Guiyang Peoples R China First Peoples Hosp Xiushui Cty Jiujiang Peoples R China

Although nonnegative matrix factorization (NMF) is widely used, some matrix factorization methods result in misleading results and waste of computing resources due to lack of timely optimization and case-by-case consideration. Therefore, an up -to -date and comprehensive review on its algorithms and applications is needed to promote improvement and applications for NMF. Here, we start with introducing background and gathering the principles and formulae of NMF algorithms. There have been dozens of new algorithms since its birth in the 1990s. Generally, several or even more algorithms are adopted in a single software package written in R, Python, C/C ++, etc. Besides, the applications of NMF are analyzed. NMF is not only most widely used in modern subjects or techniques such as computer science, telecommunications, imaging science, and remote sensing but also increasingly used in traditional subjects such as physics, chemistry, biology, medicine, and psychology, being accepted by around 130 fields (disciplines) in about 20 years. Finally, the features and performance of different categories of NMF are summarized and evaluated. The summarized advantages and disadvantages and proposed suggestions for improvements are expected to enlighten the future efforts to polish the mathematical principles and procedures of NMF to realize higher accuracy and productivity in practical use.

关键词： nonnegative matrix factorization Algorithms Applications Programming languages Supervised learning Reinforcement learning NMF features NMF performance NMF mathematical principles NMF computing procedures Dynamic NMF Case-by-case NMF Self-correction NMF

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Convergence of a Fast Hierarchical Alternating Least Squares Algorithm for nonnegative matrix factorization

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2024年第1期36卷 77-89页

作者： Hou, Liangshao Chu, Delin Liao, Li-Zhi Hong Kong Baptist Univ Dept Math Kowloon Tong Hong Kong Peoples R China Natl Univ Singapore Dept Math Singapore 119076 Singapore

The hierarchical alternating least squares (HALS) algorithms are powerful tools for nonnegative matrix factorization (NMF), among which the Fast-HALS, proposed in [A. Cichocki and A.-H. Phan, 2009], is one of the most efficient. This paper investigates the convergence of Fast-HALS. First, a more general weak convergence (converged subsequences exist and converge to the stationary point set) is established without any assumption, while most existing results assume all the columns of iterates are strictly away from the origin. Then, a simplified strong convergence (the entire sequence converges to a stationary point) proof is provided. The existing strong convergence is attributed to the block prox-linear (BPL) method, which is a more general framework including Fast-HALS as a special case. So, the convergence proof under BPL is quite complex. Our simplified proof explores the structure of Fast-HALS and can be regarded as a complement to the results under BPL. In addition, some numerical verifications are presented.

关键词： Convergence Power line communications Signal processing algorithms Linear programming Approximation algorithms Roads Postal services Kurdyka-Lojasiewicz property nonnegative matrix factorization the fast hierarchical alternating least squares algorithm

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nonnegative matrix factorization Framework for Disease-Related CircRNA Prediction 21st

Nonnegative Matrix Factorization Framework for Disease-Relat...

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21st International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP)

作者： Yang, Cheng Peng, Li Liu, Wei Fu, Xiangzheng Li, Ni Hunan Univ Sci & Technol Coll Comp Sci & Engn Xiangtan Hunan Peoples R China Xiangtan Univ Coll Informat Engn Xiangtan Hunan Peoples R China Hunan Univ Coll Informat Sci & Engn Changsha Hunan Peoples R China

ISBN: (纸本)9783030953911;9783030953904

Nowadays, more and more scholars and related studies have shown that circular RNA (circRNA) is related to the occurrence and development of human diseases. It is necessary to use computational approach to predict potential and unknown associations between circRNA and disease, which will save time and money in developing drugs for treating disease. In this paper, we propose a new computational model called robust nonnegative matrix factorization framework (RNMF), which learns a robust association discriminative representation by using the similarity information structure of network space and l(2,1)-norm loss function. Specifically, we use integrated circRNA similarity network and integrated disease similarity network to update known association matrix from the perspective of matrix multiplication at first. Then, the problems of noise and outliers of elements in the updated association matrix are well addressed by the l(2,1)-norm loss function. Finally, the computational model is expressed as an optimization problem of objective function solved by iterative algorithm. Experimental results show that our model can achieve better performance than state-of-the-art methods in several aspects.

关键词： CircRNA-disease associations nonnegative matrix factorization Computational prediction model

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Smoothed separable nonnegative matrix factorization

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LINEAR ALGEBRA AND ITS APPLICATIONS 2023年第1期676卷 174-204页

作者： Nadisic, Nicolas Gillis, Nicolas Kervazo, Christophe Univ Mons Fac Polytech Dept Math & Operat Res Rue Houdain 9 B-7000 Mons Belgium Inst Polytech Paris LTCI Telecom Paris 19 Pl Marguer Perey F-91120 Palaiseau France

Given a set of data points belonging to the convex hull of a set of vertices, a key problem in linear algebra, signal processing, data analysis and machine learning is to estimate these vertices in the presence of noise. Many algorithms have been developed under the assumption that there is at least one nearby data point to each vertex;two of the most widely used ones are vertex component analysis (VCA) and the successive projection algorithm (SPA). This assumption is known as the pure-pixel assumption in blind hyperspectral unmixing, and as the separability assumption in nonnegative matrix factorization. More recently, Bhattacharyya and Kannan (ACM-SIAM Symposium on Discrete Algorithms, 2020) proposed an algorithm for learning a latent simplex (ALLS) that relies on the assumption that there is more than one nearby data point to each vertex. In that scenario, ALLS is probabilistically more robust to noise than algorithms based on the separability assumption. In this paper, inspired by ALLS, we propose smoothed VCA (SVCA) and smoothed SPA (SSPA) that generalize VCA and SPA by assuming the presence of several nearby data points to each vertex. We illustrate the effectiveness of SVCA and SSPA over VCA, SPA and ALLS on synthetic data sets, on the unmixing of hyperspectral images, and on feature extraction on facial images data sets. In addition, our study highlights new theoretical results for VCA.& COPY;2023 Elsevier Inc. All rights reserved.

关键词： nonnegative matrix factorization Separability Blind hyperspectral unmixing Pure-pixel search algorithms Latent simplex Simplex-structured matrix factorization

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