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We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity…

Machine Learning · Computer Science 2020-06-16 Nicolas Nadisic , Arnaud Vandaele , Jeremy E. Cohen , Nicolas Gillis

Random projections became popular tools to process big data. In particular, when applied to Nonnegative Matrix Factorization (NMF), it was shown that structured random projections were far more efficient than classical strategies based on…

Signal Processing · Electrical Eng. & Systems 2020-11-13 Farouk Yahaya , Matthieu Puigt , Gilles Delmaire , Gilles Roussel

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

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

In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…

Machine Learning · Computer Science 2019-11-15 Anthony Degleris , Nicolas Gillis

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

Sequence model based NLP applications can be large. Yet, many applications that benefit from them run on small devices with very limited compute and storage capabilities, while still having run-time constraints. As a result, there is a need…

Computation and Language · Computer Science 2020-10-08 Urmish Thakker , Jesse Beu , Dibakar Gope , Ganesh Dasika , Matthew Mattina

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) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that…

Machine Learning · Statistics 2015-08-31 Ali Caner Türkmen

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…

Numerical Analysis · Mathematics 2025-11-11 Junjun Pan , Valentin Leplat , Michael Ng , Nicolas Gillis

Non-negative matrix factorization (NMF) is widely used as a feature extraction technique for matrices with non-negative entries, such as image data, purchase histories, and other types of count data. In NMF, a non-negative matrix is…

Computation · Statistics 2026-01-01 Ryo Ohashi , Hiroyasu Abe , Fumitake Sakaori

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 a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…

Computer Vision and Pattern Recognition · Computer Science 2017-07-27 Lihua Zhang , Shihua Zhang

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

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

Numerical Analysis · Computer Science 2016-05-09 Yuan Lu , Jie Yang

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

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In…

Machine Learning · Statistics 2012-10-04 Abhishek Kumar , Vikas Sindhwani , Prabhanjan Kambadur

Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale…

Machine Learning · Computer Science 2026-02-27 Jichao Zhang , Ran Miao , Limin Li

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

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