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Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals…

Machine Learning · Computer Science 2015-05-05 Nirav Bhatt , Arun Ayyar

Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…

Numerical Analysis · Computer Science 2017-12-07 Gabriele Torre , Michael Graber

Learning approaches rely on hyperparameters that impact the algorithm's performance and affect the knowledge extraction process from data. Recently, Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a learning…

Numerical Analysis · Mathematics 2023-06-29 Nicoletta Del Buono , Flavia Esposito , Laura Selicato , Rafal Zdunek

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

A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve…

Machine Learning · Computer Science 2018-11-16 Andri Mirzal

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, $\mathbf{X}$, into two lower rank nonnegative matrices…

Methodology · Statistics 2021-07-05 Phillip Shreeves , Jeffrey L. Andrews , Xinchen Deng , Ramie Ali-Adeeb , Andrew Jirasek

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-09-30 Ramakrishnan Kannan , Grey Ballard , Haesun Park

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

Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between the input data and the low-rank approximation, the Kullback-Leibler (KL)…

Optimization and Control · Mathematics 2021-05-12 Le Thi Khanh Hien , Nicolas Gillis

Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value…

Machine Learning · Computer Science 2024-10-30 Youdong Guo , Timothy E. Holy

Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…

Machine Learning · Computer Science 2017-11-21 Yuning Qiu , Guoxu Zhou , Kan Xie

This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean…

Machine Learning · Computer Science 2011-03-09 Cédric Févotte , Jérôme Idier

Matrix factorization learned by implicit alternating least squares (iALS) is a popular baseline in recommender system research publications. iALS is known to be one of the most computationally efficient and scalable collaborative filtering…

Information Retrieval · Computer Science 2021-10-28 Steffen Rendle , Walid Krichene , Li Zhang , Yehuda Koren

Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…

Machine Learning · Computer Science 2019-01-21 Prasad G Bhavana , Vineet C Nair

In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions,…

Numerical Analysis · Computer Science 2017-03-03 Nicolas Gillis

Nonnegative matrix factorization (NMF) seeks a low-rank approximation $X \approx UV^T$ with nonnegative factors and is commonly solved using interior methods that enforce feasibility throughout optimization. We show that such…

Machine Learning · Computer Science 2026-05-20 Qiujing Lu , Tonmoy Monsoor , Ehsan Ebrahimzadeh , Kartik Sharma , Vwani Roychowdhury

Non-negative matrix factorization (NMF) approximates a given matrix as a product of two non-negative matrices. Multiplicative algorithms deliver reliable results, but they show slow convergence for high-dimensional data and may be stuck…

Machine Learning · Computer Science 2014-12-05 Felipe Yanez , Francis Bach

Non-Negative Matrix Factorization (NMF) is an unsupervised learning method offering low-rank representations across various domains such as audio processing, biomedical signal analysis, and image recognition. The incorporation of…

Machine Learning · Computer Science 2025-10-09 Yasaman Torabi , Shahram Shirani , James P. Reilly

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

Nonnegative Matrix Factorization (NMF) is an unsupervised learning algorithm that produces a linear, parts-based approximation of a data matrix. NMF constructs a nonnegative low rank basis matrix and a nonnegative low rank matrix of weights…

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