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Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or…

Machine Learning · Statistics 2014-03-25 Jason Gejie Liu , Shuchin Aeron

We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…

Optimization and Control · Mathematics 2012-07-03 Vijay Krishnamurthy , Alexandre d'Aspremont

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) based topic modeling is widely used in natural language processing (NLP) to uncover hidden topics of short text documents. Usually, training a high-quality topic model requires large amount of textual…

Computation and Language · Computer Science 2022-05-27 Shijing Si , Jianzong Wang , Ruiyi Zhang , Qinliang Su , Jing Xiao

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

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

We consider the problem of sparse nonnegative matrix factorization (NMF) using archetypal regularization. The goal is to represent a collection of data points as nonnegative linear combinations of a few nonnegative sparse factors with…

Machine Learning · Statistics 2024-02-13 Kayhan Behdin , Rahul Mazumder

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

Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…

Machine Learning · Computer Science 2020-09-08 Khanh Luong , Richi Nayak

Non-negative Matrix Factorization (NMF) is a popular tool for data exploration. Bayesian NMF promises to also characterize uncertainty in the factorization. Unfortunately, current inference approaches such as MCMC mix slowly and tend to get…

Machine Learning · Statistics 2016-10-28 M. Arjumand Masood , Finale Doshi-Velez

Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm…

Machine Learning · Computer Science 2016-11-15 Yuanzhi Li , Yingyu Liang , Andrej Risteski

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent…

Machine Learning · Computer Science 2022-06-22 Jun Lu , Xuanyu Ye

In this article, we study algorithms for nonnegative matrix factorization (NMF) in various applications involving streaming data. Utilizing the continual nature of the data, we develop a fast two-stage algorithm for highly efficient and…

Optimization and Control · Mathematics 2021-01-22 Ran Gu , Qiang Du , Simon J. L. Billinge

Fully unsupervised topic models have found fantastic success in document clustering and classification. However, these models often suffer from the tendency to learn less-than-meaningful or even redundant topics when the data is biased…

Machine Learning · Computer Science 2021-02-08 Joshua Vendrow , Jamie Haddock , Elizaveta Rebrova , Deanna Needell

Mixed pixels are presented in hyperspectral images due to low spatial resolution of hyperspectral sensors. Spectral unmixing decomposes mixed pixels spectra into endmembers spectra and abundance fractions. In this paper using of robust…

Computer Vision and Pattern Recognition · Computer Science 2012-12-06 Roozbeh Rajabi , Hassan Ghassemian

Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in…

Machine Learning · Computer Science 2023-07-18 Sebastian Dalleiger , Jilles Vreeken

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

Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…

Computer Vision and Pattern Recognition · Computer Science 2016-09-20 Reza Borhani , Jeremy Watt , Aggelos Katsaggelos

Airborne gamma-ray surveys are useful for many applications, ranging from geology and mining to public health and nuclear security. In all these contexts, the ability to decompose a measured spectrum into a linear combination of background…

Data Analysis, Statistics and Probability · Physics 2020-06-24 M. S. Bandstra , T. H. Y. Joshi , K. J. Bilton , A. Zoglauer , B. J. Quiter

Learning multi-view data is an emerging problem in machine learning research, and nonnegative matrix factorization (NMF) is a popular dimensionality-reduction method for integrating information from multiple views. These views often provide…

Machine Learning · Statistics 2023-04-26 Shuo Shuo Liu , Lin Lin