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Related papers: Randomized Nonnegative Matrix Factorization

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This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…

Optimization and Control · Mathematics 2013-02-05 Victor Bittorf , Benjamin Recht , Christopher Re , Joel A. Tropp

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Machine Learning · Statistics 2014-01-10 Jason Gejie Liu , Shuchin Aeron

In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…

Optimization and Control · Mathematics 2015-04-24 Yat Tin Chow , Kazufumi Ito , Jun Zou

Nonnegative Matrix Factorization (NMF) models are widely used to recover 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…

Signal Processing · Electrical Eng. & Systems 2023-05-31 Cécile Hautecoeur , Lieven De Lathauwer , Nicolas Gillis , François Glineur

Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a…

Machine Learning · Computer Science 2021-04-14 Junjun Pan , Nicolas Gillis

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex…

Numerical Analysis · Computer Science 2020-01-14 Andersen Man Shun Ang , Nicolas Gillis

Collaborative filtering generates recommendations by exploiting user-item similarities based on rating data, which often contains numerous unrated items. To predict scores for unrated items, matrix factorization techniques such as…

Statistical Mechanics · Physics 2025-07-30 Yukino Terui , Yuka Inoue , Yohei Hamakawa , Kosuke Tatsumura , Kazue Kudo

Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image…

Machine Learning · Statistics 2020-12-08 Matthew Corsetti , Ernest Fokoué

Non-negative matrix factorization (NMF) has become a popular method for representing meaningful data by extracting a non-negative basis feature from an observed non-negative data matrix. Some of the unique features of this method in…

Optimization and Control · Mathematics 2022-11-15 Sajad Fathi Hafshejani , Zahra Moaberfard

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…

Optimization and Control · Mathematics 2012-08-13 Nicolas Gillis , François Glineur

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

Optimization and Control · Mathematics 2015-07-01 Duy-Khuong Nguyen , Tu-Bao Ho

Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction that has been widely used for text mining, computer vision, pattern discovery, and bioinformatics. In this paper, a framework called ARkNLS…

Numerical Analysis · Mathematics 2020-07-14 Delin Chu , Wenya Shi , Srinivas Eswar , Haesun Park

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…

Numerical Analysis · Mathematics 2013-05-27 Shu-Zhen Lai , Hou-Biao Li , Zu-Tao Zhang

Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$. SymNMF can be used for…

Numerical Analysis · Computer Science 2016-10-07 Arnaud Vandaele , Nicolas Gillis , Qi Lei , Kai Zhong , Inderjit Dhillon

In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ find, for assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and $H\in\R_+^{k\times n}$…

Optimization and Control · Mathematics 2014-07-08 Lorenzo Finesso , Peter Spreij

Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear…

Machine Learning · Computer Science 2012-04-12 Bin Shen , Luo Si , Rongrong Ji , Baodi Liu

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

We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…

Machine Learning · Computer Science 2011-12-19 Youngmin Cho , Lawrence K. Saul

Non-negative matrix factorization (NMF) is a dimensionality reduction technique that has shown promise for analyzing noisy data, especially astronomical data. For these datasets, the observed data may contain negative values due to noise…

Instrumentation and Methods for Astrophysics · Physics 2024-10-04 Dylan Green , Stephen Bailey

In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ find, for assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and $H\in\R_+^{k\times n}$…

Optimization and Control · Mathematics 2007-05-23 Lorenzo Finesso , Peter Spreij