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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

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-01 Ramakrishnan Kannan , Grey Ballard , Haesun Park

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

Machine Learning · Statistics 2014-05-27 Nicolas Gillis , Robert Luce

Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids, and find the optimal…

Image and Video Processing · Electrical Eng. & Systems 2021-03-26 Mulin Chen , Xuelong Li

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

Nonnegative Matrix Factorization (NMF) is a widely applied technique in the fields of machine learning and data mining. Graph Regularized Non-negative Matrix Factorization (GNMF) is an extension of NMF that incorporates graph regularization…

Machine Learning · Computer Science 2024-03-19 Zhen Wang , Wenwen Min

Nonnegative Matrix Factorization (NMF), first proposed in 1994 for data analysis, has received successively much attention in a great variety of contexts such as data mining, text clustering, computer vision, bioinformatics, etc. In this…

Numerical Analysis · Mathematics 2019-03-05 Paola Favati , Grazia Lotti , Ornella Menchi , Francesco Romani

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 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 explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the…

Artificial Intelligence · Computer Science 2009-04-22 Nikolaos Vasiloglou , Alexander G. Gray , David V. Anderson

Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major…

Signal Processing · Electrical Eng. & Systems 2019-03-27 Xiao Fu , Kejun Huang , Nicholas D. Sidiropoulos , Wing-Kin Ma

Non-negative matrix factorization (NMF) is an important tool in signal processing and widely used to separate mixed sources into their components. Algorithms for NMF require that the user choose the number of components in advance, and if…

Machine Learning · Computer Science 2025-01-10 Youdong Guo , Timothy E. Holy

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…

Machine Learning · Statistics 2014-04-07 Nicolas Gillis , Stephen A. Vavasis

We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research…

Machine Learning · Statistics 2015-03-06 Tomohiko Mizutani

Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…

Instrumentation and Methods for Astrophysics · Physics 2016-12-20 Guangtun Zhu

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

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

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 problem of finding overlapping communities in networks has gained much attention recently. Optimization-based approaches use non-negative matrix factorization (NMF) or variants, but the global optimum cannot be provably attained in…

Machine Learning · Statistics 2017-06-26 Xueyu Mao , Purnamrita Sarkar , Deepayan Chakrabarti

Collaborative filtering generates recommendations by exploiting user-item similarities based on rating data, which often contains numerous unrated items. To predict scores for unrated items, matrix factorization techniques such as…

Statistical Mechanics · Physics 2025-07-30 Yukino Terui , Yuka Inoue , Yohei Hamakawa , Kosuke Tatsumura , Kazue Kudo