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Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this…

Machine Learning · Statistics 2014-12-10 Nicolas Gillis

Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to…

Machine Learning · Computer Science 2021-09-07 Junjun Pan , Michael K. Ng

In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \times r$ and $r…

Data Structures and Algorithms · Computer Science 2011-11-04 Sanjeev Arora , Rong Ge , Ravi Kannan , Ankur Moitra

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

Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations…

Machine Learning · Computer Science 2017-10-06 Paris V. Giampouras , Athanasios A. Rontogiannis , Konstantinos D. Koutroumbas

Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for…

Optimization and Control · Mathematics 2015-03-19 Filippo Pompili , Nicolas Gillis , P. -A. Absil , François Glineur

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

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

Nonnegative matrix factorization (NMF) is a known unsupervised data-reduction method. The principle of the common cause (PCC) is a basic methodological approach in probabilistic causality, which seeks an independent mixture model for the…

Machine Learning · Computer Science 2025-09-09 E. Khalafyan , A. E. Allahverdyan , A. Hovhannisyan

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…

Machine Learning · Computer Science 2024-05-07 Farid Saberi-Movahed , Kamal Berahman , Razieh Sheikhpour , Yuefeng Li , Shirui Pan

In this work, we consider nonnegative matrix factorization (NMF) with a regularization that promotes small volume of the convex hull spanned by the basis matrix. We present highly efficient algorithms for three different volume…

Numerical Analysis · Computer Science 2020-01-14 M. S. Ang , Nicolas Gillis

Non-negative matrix factorization (NMF) is widely used for parts-based representations, yet formal inference for covariate effects is rarely available when the basis is learned under non-negativity. We introduce non-negative matrix…

Methodology · Statistics 2026-03-03 Kenichi Satoh

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

In this paper, we address a statistical model extension of multichannel nonnegative matrix factorization (MNMF) for blind source separation, and we propose a new parameter update algorithm used in the sub-Gaussian model. MNMF employs…

In an effort to develop topic modeling methods that can be quickly applied to large data sets, we revisit the problem of maximum-likelihood estimation in topic models. It is known, at least informally, that maximum-likelihood estimation in…

Machine Learning · Statistics 2026-02-10 Peter Carbonetto , Abhishek Sarkar , Zihao Wang , Matthew Stephens

Dimensionality reduction is considered as an important step for ensuring competitive performance in unsupervised learning such as anomaly detection. Non-negative matrix factorization (NMF) is a popular and widely used method to accomplish…

Machine Learning · Computer Science 2021-02-08 Imtiaz Ahmed , Xia Ben Hu , Mithun P. Acharya , Yu Ding

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

In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the…

Computation · Statistics 2011-01-24 Elizabeth D. Schifano , Robert L. Strawderman , Martin T. Wells

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) has attracted much attention in the last decade as a dimension reduction method in many applications. Due to the explosion in the size of data, naturally the samples are collected and stored…

Machine Learning · Computer Science 2018-02-27 Tianxiang Gao , Chris Chu