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Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…

Machine Learning · Computer Science 2023-11-07 Mengyuan Zhang , Kai Liu

Nonnegative Matrix Factorization(NMF) is a common used technique in machine learning to extract features out of data such as text documents and images thanks to its natural clustering properties. In particular, it is popular in image…

Computer Vision and Pattern Recognition · Computer Science 2016-08-05 Giovanni Barbarino

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise)…

Machine Learning · Computer Science 2021-02-10 Nicolas Gillis , Le Thi Khanh Hien , Valentin Leplat , Vincent Y. F. Tan

Nonnegative matrix factorization (NMF) was popularized as a tool for data mining by Lee and Seung in 1999. NMF attempts to approximate a matrix with nonnegative entries by a product of two low-rank matrices, also with nonnegative entries.…

Information Retrieval · Computer Science 2008-05-02 Michael Biggs , Ali Ghodsi , Stephen Vavasis

Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…

Machine Learning · Computer Science 2018-11-15 Zhihui Zhu , Xiao Li , Kai Liu , Qiuwei Li

Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative…

Machine Learning · Statistics 2013-12-06 Jim Jing-Yan Wang

The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…

Machine Learning · Computer Science 2023-01-26 Xiao Li , Zhihui Zhu , Qiuwei Li , Kai Liu

Non-Negative Matrix Factorization (NMF) is a widely used dimension reduction method that factorizes a non-negative data matrix into two lower dimensional non-negative matrices: One is the basis or feature matrix which consists of the…

Applications · Statistics 2022-11-03 Yun Cai , Hong Gu , Toby Kenney

Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…

Machine Learning · Computer Science 2022-06-08 Tingting Shen , Junhang Li , Can Tong , Qiang He , Chen Li , Yudong Yao , Yueyang Teng

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…

Machine Learning · Computer Science 2024-05-07 Farid Saberi-Movahed , Kamal Berahman , Razieh Sheikhpour , Yuefeng Li , Shirui Pan

Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic…

Machine Learning · Computer Science 2019-07-02 Anthony Degleris , Ben Antin , Surya Ganguli , Alex H Williams

Nonnegative matrix factorization (NMF) is a popular dimension reduction technique that produces interpretable decomposition of the data into parts. However, this decompostion is not generally identifiable (even up to permutation and…

Machine Learning · Computer Science 2016-04-05 W. Pan , F. Doshi-Velez

Bayesian Poisson Non-Negative Matrix Factorization (NMF) is widely used to model count data, including in cancer mutational signature analysis. However, standard Gibbs samplers rely on computationally expensive Poisson augmentation, and…

Methodology · Statistics 2026-03-31 Jenna M. Landy , Nishanth Basava , Giovanni Parmigiani

Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…

Instrumentation and Methods for Astrophysics · Physics 2016-12-20 Guangtun Zhu

Nonnegative matrix factorization (NMF) is a widely used tool for learning parts-based, low-dimensional representations of nonnegative data, with applications in vision, text, and bioinformatics. In clustering applications, orthogonal NMF…

Machine Learning · Computer Science 2025-12-10 Manh Nguyen , Daniel Pimentel-Alarcón

Non-negative matrix factorization (NMF) is a popular unsupervised learning approach widely used in image clustering. However, in real-world clustering scenarios, most existing NMF methods are highly sensitive to noise corruption and are…

Computer Vision and Pattern Recognition · Computer Science 2025-05-01 Jingjing Liu , Nian Wu , Xianchao Xiu , Jianhua Zhang

Nonnegative matrix factorization (NMF) methods have proved to be powerful across a wide range of real-world clustering applications. Integrating multiple types of measurements for the same objects/subjects allows us to gain a deeper…

Machine Learning · Computer Science 2014-09-16 Daniel Hidru , Anna Goldenberg

Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…

Machine Learning · Statistics 2018-05-02 N. Benjamin Erichson , Ariana Mendible , Sophie Wihlborn , J. Nathan Kutz

Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different…

Machine Learning · Computer Science 2023-11-21 James Chapman , Yotam Yaniv , Deanna Needell

Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an…

Machine Learning · Computer Science 2020-02-12 Changlin Wan , Wennan Chang , Tong Zhao , Mengya Li , Sha Cao , Chi Zhang