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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

Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have primarily centered…

Machine Learning · Computer Science 2025-01-10 Valentin Leplat , Le Thi Khanh Hien , Akwum Onwunta , Nicolas Gillis

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

Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role in…

Computer Vision and Pattern Recognition · Computer Science 2022-05-23 Xin-Ru Feng , Heng-Chao Li , Rui Wang , Qian Du , Xiuping Jia , Antonio Plaza

Semi-Non-negative Matrix Factorization is a technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our…

Computer Vision and Pattern Recognition · Computer Science 2015-09-11 George Trigeorgis , Konstantinos Bousmalis , Stefanos Zafeiriou , Bjoern W. Schuller

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices and has been widely used for unsupervised learning tasks such as product recommendation based on a rating matrix. However, although…

Social and Information Networks · Computer Science 2015-04-03 Junyu Xuan , Jie Lu , Xiangfeng Luo , Guangquan Zhang

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF…

Machine Learning · Statistics 2023-09-26 Duc Toan Nguyen , Eric C. Chi

Referring back to the original text in the course of hierarchical learning is a common human trait that ensures the right direction of learning. The models developed based on the concept of Non-negative Matrix Factorization (NMF), in this…

Machine Learning · Computer Science 2024-05-24 Prasun Dutta , Rajat K. De

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

Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank…

Machine Learning · Computer Science 2021-12-20 Pierre De Handschutter , Nicolas Gillis , Xavier Siebert

The establishment of robust target appearance model over time is an overriding concern in visual tracking. In this paper, we propose an inverse nonnegative matrix factorization (NMF) method for robust appearance modeling. Rather than using…

Computer Vision and Pattern Recognition · Computer Science 2016-01-13 Fanghui Liu , Tao Zhou , Keren Fu , Irene Y. H. Gu , Jie Yang

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

Symmetric nonnegative matrix factorization (symNMF) is a variant of nonnegative matrix factorization (NMF) that allows to handle symmetric input matrices and has been shown to be particularly well suited for clustering tasks. In this paper,…

Numerical Analysis · Mathematics 2020-03-11 François Moutier , Arnaud Vandaele , Nicolas Gillis

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

Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then…

Numerical Analysis · Computer Science 2007-09-27 Stephen A. Vavasis

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

Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute.…

Quantum Physics · Physics 2023-11-03 Hinako Asaoka , Kazue Kudo

Nonnegative matrix factorization (NMF) is a popular data embedding technique. Given a nonnegative data matrix $X$, it aims at finding two lower dimensional matrices, $W$ and $H$, such that $X\approx WH$, where the factors $W$ and $H$ are…

Machine Learning · Computer Science 2026-02-06 Olivier Vu Thanh , Nicolas Gillis

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

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

Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to…

Machine Learning · Statistics 2018-03-19 M. Arjumand Masood , Finale Doshi-Velez