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Nonnegative matrix factorization (NMF), which is the approximation of a data matrix as the product of two nonnegative matrices, is a key issue in machine learning and data analysis. One approach to NMF is to formulate the problem as a…

Optimization and Control · Mathematics 2016-11-02 Hideaki Iiduka , Shizuka Nishino

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

Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative…

Machine Learning · Statistics 2013-12-06 Jim Jing-Yan Wang

We consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF) problem, encompassing various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem holds…

Machine Learning · Computer Science 2024-04-26 Nathanaël Perraudin , Adrien Teutrie , Cécile Hébert , Guillaume Obozinski

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define…

Machine Learning · Computer Science 2013-04-04 Jing-Yan Wang , Mustafa AbdulJabbar

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 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

Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization…

Optimization and Control · Mathematics 2019-12-09 Mahesh Chandra Mukkamala , Peter Ochs

Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a…

Optimization and Control · Mathematics 2019-05-14 R. Jyothi , P. Babu , R. Bahl

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

Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of…

Machine Learning · Computer Science 2019-04-18 Gordon E. Moon , Aravind Sukumaran-Rajam , Srinivasan Parthasarathy , P. Sadayappan

Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, $V$, as the product of two smaller nonnegative matrices, $W$ and $H$. In this paper, we introduce a general framework to design…

Machine Learning · Computer Science 2022-04-29 Valentin Leplat , Nicolas Gillis , Jérôme Idier

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

Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data…

Machine Learning · Statistics 2020-06-23 Alberto Lumbreras , Louis Filstroff , Cédric Févotte

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

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

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…

Numerical Analysis · Mathematics 2013-05-27 Shu-Zhen Lai , Hou-Biao Li , Zu-Tao Zhang

A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this…

Machine Learning · Statistics 2019-05-20 Karthik Devarajan

In this paper, we consider a class of nonsmooth nonconvex optimization problems whose objective is the sum of a block relative smooth function and a proper and lower semicontinuous block separable function. Although the analysis of block…

Optimization and Control · Mathematics 2022-04-27 Le Thi Khanh Hien , Duy Nhat Phan , Nicolas Gillis , Masoud Ahookhosh , Panagiotis Patrinos

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