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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

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

Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…

Numerical Analysis · Computer Science 2017-12-07 Gabriele Torre , Michael Graber

Non-negative matrix factorization (NMF) is a common method for generating topic models from text data. NMF is widely accepted for producing good results despite its relative simplicity of implementation and ease of computation. One…

Machine Learning · Computer Science 2016-08-09 Brendan Gavin , Vijay Gadepally , Jeremy Kepner

Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…

Machine Learning · Computer Science 2016-05-04 Mariano Tepper , Guillermo Sapiro

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…

Machine Learning · Computer Science 2007-05-23 Patrik O. Hoyer

Non-negative matrix factorization (NMF) is a fundamental matrix decomposition technique that is used primarily for dimensionality reduction and is increasing in popularity in the biological domain. Although finding a unique NMF is generally…

Information Theory · Computer Science 2021-08-23 Rami Nasser , Yonina C. Eldar , Roded Sharan

Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy data sets with applications in data mining, text recognition, dimension reduction, face…

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 a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise)…

Machine Learning · Computer Science 2021-02-10 Nicolas Gillis , Le Thi Khanh Hien , Valentin Leplat , Vincent Y. F. Tan

Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…

Machine Learning · Computer Science 2017-11-21 Yuning Qiu , Guoxu Zhou , Kan Xie

We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification,…

Machine Learning · Computer Science 2023-03-02 Tyler Will , Runyu Zhang , Eli Sadovnik , Mengdi Gao , Joshua Vendrow , Jamie Haddock , Denali Molitor , Deanna Needell

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

Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-10-25 Wei Tan , Liangliang Cao , Liana Fong

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…

Machine Learning · Statistics 2014-01-10 Jason Gejie Liu , Shuchin Aeron

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…

Numerical Analysis · Computer Science 2013-03-19 Hugo Van hamme

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…

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

Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear…

Machine Learning · Computer Science 2012-04-12 Bin Shen , Luo Si , Rongrong Ji , Baodi Liu

Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…

Machine Learning · Statistics 2012-12-07 Nicolas Gillis

We propose an efficient, distributed, out-of-memory implementation of the truncated singular value decomposition (t-SVD) for heterogeneous (CPU+GPU) high performance computing (HPC) systems. Various implementations of SVD have been…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-18 Ismael Boureima , Manish Bhattarai , Maksim E. Eren , Nick Solovyev , Hristo Djidjev , Boian S. Alexandrov
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