检索结果-内蒙古大学图书馆

丛书名： Data Science

2020年

作者： Nicolas Gillis

ISBN: (数字)9781611976410

ISBN: (纸本)9781611976403

nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully.

nonnegative matrix factorization

is accessible to a wide audience and is ideal for anyone interested in the workings of NMF,
discusses some new results on the nonnegative rank and the identifiability of NMF, and
makes available MATLAB codes for readers to run the numerical examples presented in the book.

Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.

关键词： nonnegative matrix factorization low-rank matrix approximations nonnegative rank multiplicative updates extended formulations linear dimensionality reduction matrix factorization non-linear optimization blind source separation dictionary learning nested polytope problem identifiability recommender systems topic modeling feature extraction hyperspectral imaging extended formulations audio source separation communication complexity sparsity principal component analysis singular value decomposition computational complexity beta-divergences separability block coordinate descent methods self-modeling curve resolution gene expression analysis matrix factorization

来源：评论

学校读者我要写书评

暂无评论

nonnegative matrix factorization for analyzing state dependent neuronal network dynamics in calcium recordings

引用

SCIENTIFIC REPORTS 2024年第1期14卷 1-17页

作者： Carbonero, Daniel Noueihed, Jad Kramer, Mark A. White, John A. Boston Univ Dept Biomed Engn Boston MA 02215 USA Boston Univ Dept Math & Stat Boston MA USA Boston Univ Ctr Syst Neurosci Boston MA 02215 USA Boston Univ Neurophoton Ctr Boston MA 02215 USA

Calcium imaging allows recording from hundreds of neurons in vivo with the ability to resolve single cell activity. Evaluating and analyzing neuronal responses, while also considering all dimensions of the data set to make specific conclusions, is extremely difficult. Often, descriptive statistics are used to analyze these forms of data. These analyses, however, remove variance by averaging the responses of single neurons across recording sessions, or across combinations of neurons, to create single quantitative metrics, losing the temporal dynamics of neuronal activity, and their responses relative to each other. Dimensionally Reduction (DR) methods serve as a good foundation for these analyses because they reduce the dimensions of the data into components, while still maintaining the variance. nonnegative matrix factorization (NMF) is an especially promising DR analysis method for analyzing activity recorded in calcium imaging because of its mathematical constraints, which include positivity and linearity. We adapt NMF for our analyses and compare its performance to alternative dimensionality reduction methods on both artificial and in vivo data. We find that NMF is well-suited for analyzing calcium imaging recordings, accurately capturing the underlying dynamics of the data, and outperforming alternative methods in common use.

关键词： Dimensionality reduction nonnegative matrix factorization Calcium imaging Neuronal network dynamics Neuronal network analysis

来源：评论

学校读者我要写书评

暂无评论

nonnegative matrix factorization Based on Node Centrality for Community Detection

引用

ACM TRANSACTIONS ON KNOWLEDGE DISCOVERY FROM DATA 2023年第6期17卷 1-21页

作者： Su, Sixing Guan, Jiewen Chen, Bilian Huang, Xin Xiamen Univ Dept Automat Xiamen 361005 Peoples R China Xiamen Key Lab Big Data Intelligent Anal & Decis Xiamen 361005 Peoples R China Hong Kong Baptist Univ Dept Comp Sci Hong Kong Peoples R China

Community detection is an important topic in network analysis, and recently many community detection methods have been developed on top of the nonnegative matrix factorization (NMF) technique. Most NMFbased community detection methods only utilize the first-order proximity information in the adjacency matrix, which has some limitations. Besides, many NMF-based community detection methods involve sparse regularizations to promote clearer community memberships. However, in most of these regularizations, different nodes are treated equally, which seems unreasonable. To dismiss the above limitations, this article proposes a community detection method based on node centrality under the framework of NMF. Specifically, we design a new similarity measure which considers the proximity of higher-order neighbors to form a more informative graph regularization mechanism, so as to better refine the detected communities. Besides, we introduce the node centrality and Gini impurity to measure the importance of nodes and sparseness of the community memberships, respectively. Then, we propose a novel sparse regularization mechanism which forces nodes with higher node centrality to have smaller Gini impurity. Extensive experimental results on a variety of real-world networks show the superior performance of the proposed method over thirteen stateof-the-art methods.

关键词： Community detection nonnegative matrix factorization similarity measure sparse regularization optimization

来源：评论

学校读者我要写书评

暂无评论

nonnegative matrix factorization Based Heterogeneous Graph Embedding Method for Trigger-Action Programming in IoT

引用

IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2022年第2期18卷 1231-1239页

作者： Xing, Yongheng Hu, Liang Zhang, Xiaolu Wu, Gang Wang, Feng Jilin Univ Coll Comp Sci & Technol Engn Res Ctr Network Technol & Applcat Software Minist Educ Changchun 130012 Peoples R China Univ Texas San Antonio Dept Informat Syst & Cyber Secur San Antonio TX 78249 USA

Nowadays, users can personalize Internet of Things (IoT) devices/web services via trigger-action programming (TAP). As the number of connected entities grows, the relations of triggers and actions become progressively complex (i.e., the heterogeneity of TAP), which becomes a challenge for existing models to completely preserve the heterogeneous data and semantic information in trigger and action. To address this issue, in this article, we propose IoT nonnegative matrix factorization (IoT-NMF), a NMF-based heterogeneous graph embedding method for TAP. Prior to using IoT-NMF, we map triggers and actions to an IoT heterogeneous information network, from which we can extract three structures that preserve heterogeneous relations in triggers and actions. IoT-NMF can factorize the structures simultaneously for getting low-dimensional representation vectors of the triggers and actions, which can be further utilized in Artificial Intelligence of Things applications (e.g., TAP rule recommendation). Finally, we demonstrate the proposed approach using an if this then that (IFTTT) dataset. The result shows that IoT-NMF outperforms the state-of-the-art approaches.

关键词： Internet of Things Semantics Programming Feature extraction Cameras Data mining Machine learning Graph embedding heterogeneous information networks Internet of Things (IoT) nonnegative matrix factorization trigger-action programming (TAP)

来源：评论

学校读者我要写书评

暂无评论

nonnegative matrix factorization with Group and Basis Restrictions

引用

STATISTICS IN BIOSCIENCES 2023年第3期15卷 608-632页

作者： Shreeves, Phillip Andrews, Jeffrey L. Deng, Xinchen Ali-Adeeb, Ramie Jirasek, Andrew Univ British Columbia Okanagan Dept Stat Kelowna BC Canada Univ British Columbia Okanagan Dept Phys Kelowna BC Canada Simon Fraser Univ Dept Stat & Actuarial Sci Burnaby BC Canada

nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, X, into two lower rank nonnegative matrices multiplied together. These two matrices can be described as the latent factors, represented in the rows of H, and the scores of the observations on these factors that are found in the rows of W. This paper provides an extension of this method which allows one to specify prior knowledge of the data, including both group information and possible underlying factors. This is done by further decomposing the matrix, H, into matrices A and S multiplied together. These matrices represent an 'auxiliary' matrix and a semi-constrained factor matrix, respectively. This method and its updating criterion are proposed, followed by its application on both simulated and real-world examples displaying different uses of the algorithm.

关键词： nonnegative matrix factorization Semi-supervised learning Raman spectroscopy Dimensionality reduction

来源：评论

学校读者我要写书评

暂无评论

Graph regularized discriminative nonnegative matrix factorization

引用

ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 139卷

作者： Liu, Zhonghua Zhu, Fa Xiong, Hao Chen, Xingchi Pelusi, Danilo Vasilakos, Athanasios V. Zhejiang Ocean Univ Sch Informat Engn Zhoushan Peoples R China Nanjing Forestry Univ Coll Informat Sci & Technol Nanjing Peoples R China Nanjing Forestry Univ Coll Artificial Intelligence Nanjing Peoples R China Macquarie Univ Ctr Hlth Informat Sydney Australia Peng Cheng Lab Shenzhen Peoples R China IAU Coll Comp Sci & Informat Technol Dept Networks & Commun POB 1982 Dammam 31441 Saudi Arabia Univ Teramo Dept Commun Sci Teramo Italy Univ Agder UiA Ctr AI Res CAIR Grimstad Norway

It is well known that both the label information and the local geometry structure information are very important for image data clustering and classification. However, nonnegative matrix factorization (NMF) and its variants do not fully utilize the information or only use one of them. This paper presents a graph regularized discriminative nonnegative matrix factorization (GDNMF) for image data clustering, in which the local geometrical structure and label information of the observed samples are thoroughly considered. In the objective function of NMF, two constraint terms are added to preserve the above information. One is a sparse graph, which is adaptively constructed to obtain the local geometrical structure information. The other is data label information, which is used to capture discriminative information of the original data. By using local and label information, the proposed regularized discriminative nonnegative matrix factorization indeed improves the discrimination power of matrix decomposition. In addition, the F-norm formulation based cost function of regularized discriminative nonnegative matrix factorization is given, and the update rules for the optimization function of regularized discriminative nonnegative matrix factorization are proved. The experiment results on several public image datasets demonstrate the effectiveness of GDNMF algorithm. The innovation of this paper lies in extending unsupervised NMF to semi-supervised case and adaptively capturing the local structure of data based on sparse graph. However, the proposed method does not take into account the challenges of multiview data processing.

关键词： nonnegative matrix factorization Label information Graph regularized discriminative nonnegative matrix factorization Image clustering

来源：评论

学校读者我要写书评

暂无评论

RANDOMIZED ALGORITHMS FOR SYMMETRIC nonnegative matrix factorization

引用

SIAM JOURNAL ON matrix ANALYSIS AND APPLICATIONS 2025年第1期46卷 584-625页

作者： Hayashi, Koby Aksoy, Sinan g. Ballard, Grey Park, Haesun Georgia Inst Technol Sch Computat Sci & Engn Atlanta GA 30332 USA Pacific Northwest Natl Lab Seattle WA 98109 USA Wake Forest Univ Dept Comp Sci Winston Salem NC 27109 USA

Symmetric nonnegative matrix factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more scalable algorithms for SymNMF, we develop two randomized algorithms for its computation. The first algorithm uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to rapidly compute a SymNMF of the approximation. The second algorithm uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. We prove theoretically that leverage score sampling can approximately solve nonnegative least squares problems to a chosen accuracy with high probability. Additionally, we prove sampling complexity results for previously proposed hybrid sampling techniques which deterministically include high leverage score rows. This hybrid scheme is crucial for obtaining speedups in practice. Finally, we demonstrate that both methods work well in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speedups for both large dense and large sparse problems.

关键词： nonnegative matrix factorization symmetric nonnegative matrix factorization leverage scores matrix sketching randomized numerical linear algebra (RandNLA)

来源：评论

学校读者我要写书评

暂无评论

An efficient network clustering approach using graph-boosting and nonnegative matrix factorization

引用

ARTIFICIAL INTELLIGENCE REVIEW 2024年第11期57卷 292-292页

作者： Tang, Ji Xu, Xiaoru Wang, Teng Rezaeipanah, Amin South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Jiangsu Vocat Coll Finance & Econ Sch Law & Humanities & Arts Huaian 223003 Jiangsu Peoples R China Univ Rahjuyan Danesh Borazjan Dept Comp Engn Bushehr Iran

Network clustering is a critical task in data analysis, aimed at uncovering the underlying structure and patterns within complex networks. Traditional clustering methods often struggle with large-scale and noisy data, leading to suboptimal results. Also, the efficiency of positive samples in network clustering depends on the carefully constructed data augmentation, and the pre-training process of the model deals with large-scale data. To address these issues, in this paper, we introduce an efficient network clustering approach that leverages Graph-Boosting and nonnegative matrix factorization to enhance clustering performance (GBNMF). Our algorithm addresses the limitations of traditional clustering techniques by incorporating the strengths of graph-boosting, which iteratively improves the quality of clusters, and nonnegative matrix factorization (NMF), which effectively captures latent structures within the data. We validate our algorithm through extensive experiments on various benchmark network datasets, demonstrating significant improvements in clustering accuracy and robustness. The proposed algorithm not only achieves superior clustering results but also exhibits remarkable computational efficiency, making it a valuable tool for large-scale network analysis applications.

关键词： Network clustering Graph-boosting nonnegative matrix factorization

来源：评论

学校读者我要写书评

暂无评论

An ordered subsets orthogonal nonnegative matrix factorization framework with application to image clustering

引用

INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2025年第3期16卷 1531-1543页

作者： Ma, Limin Tong, Can Qi, Shouliang Yao, Yudong Teng, Yueyang Northeastern Univ Coll Med & Biol Informat Engn Shenyang 110169 Peoples R China Changshu Inst Technol Sch Comp Sci & Engn Suzhou 215500 Peoples R China Stevens Inst Technol Dept Elect & Comp Engn Hoboken NJ 07030 USA Minist Educ Key Lab Intelligent Comp Med Image Shenyang 110169 Peoples R China

nonnegative matrix factorization (NMF) for image clustering attains impressive machine learning performances. However, the current iterative methods for optimizing NMF problems involve numerous matrix calculations and suffer from high computational costs in large-scale images. To address this issue, this paper presents an ordered subsets orthogonal NMF framework (OS-ONMF) that divides the data matrix in an orderly manner into several subsets and performs NMF on each subset. It balances clustering performance and computational efficiency. After decomposition, each ordered subset still contains the core information of the original data. That is, blocking does not reduce image resolutions but can greatly shorten running time. This framework is a general model that can be applied to various existing iterative update algorithms. We also provide a subset selection method and a convergence analysis of the algorithm. Finally, we conducted clustering experiments on seven real-world image datasets. The experimental results showed that the proposed method can greatly shorten the running time without reducing clustering accuracy.

关键词： Acceleration Clustering nonnegative matrix factorization Ordered subsets

来源：评论

学校读者我要写书评

暂无评论

Motif-based mix-order nonnegative matrix factorization for community detection

引用

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2025年 661卷

作者： Bu, Xiaotong Wang, Gaoxia Hou, Ximei China Three Gorges Univ Coll Math & Phys Yichang 443002 Hubei Peoples R China Anhui Inst Informat Technol Coll Gen Educ & Foreign Languages Wuhu 241000 Anhui Peoples R China Huaibei Normal Univ Expt Middle Sch Huaibei 235000 Anhui Peoples R China

Community structure is one of the important characteristics of complex networks, so it is of great application value to correctly detect community structure in the study of network structure. nonnegative matrix factorization (NMF) has been proved to be an ideal model of the community detection. Traditional NMF only focuses on the first-order structure (such as adjacency matrix), but does not consider the higher-order structure (such as motif adjacency matrix). However, only considering one of them cannot well represent the global structural characteristics of complex networks. In this paper, we propose a new Mixed-Order nonnegative matrix factorization (MONMF) framework, which can model both first-order and higher-order structures. Previous nonnegative matrix factorization is mostly used in undirected networks, but we will study based on a variety of motif types in directed networks, use motifs to capture higher-order structures in networks, and introduce linear and nonlinear methods to combine the adjacency matrix representing the first-order structure with the motif adjacency matrix representing the higher-order structure to construct a new feature matrix of NMF. At the same time, we introduce the missing edge matrix that characterizes the edgeless connection structure of the network, and gives the expression of the motif adjacency matrix of the three-node open simple motif and the three-node open anchor motif. The MONMF operation is mainly performed on different real networks for open simple motifs and open anchor motifs. Compared with the comparison methods, MONMF can significantly improve the performance of community detection in complex networks.

关键词： Community detection nonnegative matrix factorization Motif adjacency matrix Open motif Directed network

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：