English
Related papers

Related papers: Nonnegative Factorization of a Data Matrix as a Mo…

200 papers

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

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

Machine Learning · Statistics 2017-11-15 Arthur Mensch , Julien Mairal , Bertrand Thirion , Gaël Varoquaux

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

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), first proposed in 1994 for data analysis, has received successively much attention in a great variety of contexts such as data mining, text clustering, computer vision, bioinformatics, etc. In this…

Numerical Analysis · Mathematics 2019-03-05 Paola Favati , Grazia Lotti , Ornella Menchi , Francesco Romani

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…

Disordered Systems and Neural Networks · Physics 2023-07-12 Francesco Camilli , Marc Mézard

Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major…

Signal Processing · Electrical Eng. & Systems 2019-03-27 Xiao Fu , Kejun Huang , Nicholas D. Sidiropoulos , Wing-Kin Ma

Non-negative matrix factorization (NMF) is a prob- lem with many applications, ranging from facial recognition to document clustering. However, due to the variety of algorithms that solve NMF, the randomness involved in these algorithms,…

Numerical Analysis · Mathematics 2018-12-17 Connor Sell , Jeremy Kepner

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

Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix…

Machine Learning · Computer Science 2015-12-16 Gintare Karolina Dziugaite , Daniel M. Roy

Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…

Computer Vision and Pattern Recognition · Computer Science 2017-07-31 Zhenxing Guo , Shihua Zhang

By combining related objects, unsupervised machine learning techniques aim to reveal the underlying patterns in a data set. Non-negative Matrix Factorization (NMF) is a data mining technique that splits data matrices by imposing…

Artificial Intelligence · Computer Science 2023-08-10 Yasser Khalafaoui , Nistor Grozavu , Basarab Matei , Laurent-Walter Goix

The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve…

Machine Learning · Computer Science 2022-09-23 Rachid Hedjam , Abdelhamid Abdesselam , Abderrahmane Rahiche , Mohamed Cheriet

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

We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…

Optimization and Control · Mathematics 2026-02-17 Abraar Chaudhry , Elizaveta Rebrova

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…

Machine Learning · Computer Science 2025-02-04 Matej Mihelčić , Pauli Miettinen

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

Lee and Seung (2000) introduced numerical solutions for non-negative matrix factorization (NMF) using iterative multiplicative update algorithms. These algorithms have been actively utilized as dimensionality reduction tools for…

Numerical Analysis · Mathematics 2025-01-23 Sungjae Cho

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…

Machine Learning · Statistics 2015-01-26 Paul Honeine , Fei Zhu

Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…

Machine Learning · Computer Science 2019-07-10 Chong Peng , Zhao Kang , Chenglizhao Chen , Qiang Cheng