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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

Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and…

Machine Learning · Computer Science 2019-07-09 Shuai Jiang , Kan Li , Richard Yida Xu

We introduce NPEFF (Non-Negative Per-Example Fisher Factorization), an interpretability method that aims to uncover strategies used by a model to generate its predictions. NPEFF decomposes per-example Fisher matrices using a novel…

Machine Learning · Computer Science 2025-05-12 Michael Matena , Colin Raffel

Non-negative matrix factorisation (NMF) is a widely used tool for unsupervised learning and feature extraction, with applications ranging from genomics to text analysis and signal processing. Standard formulations of NMF are typically…

Machine Learning · Computer Science 2026-03-11 Elisabeth Sommer James , Asger Hobolth , Marta Pelizzola

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

Time-frequency representation (TFR) is often used for non-stationary signal analysis. The most intuitive and interpretable TFR is the spectrogram. Recently, a concept of non-negative matrix factorization (NMF) has been successfully applied…

Signal Processing · Electrical Eng. & Systems 2024-03-20 Mateusz Gabor , Rafal Zdunek , Radoslaw Zimroz , Agnieszka Wylomanska

Nonnegative Matrix Factorization(NMF) is a common used technique in machine learning to extract features out of data such as text documents and images thanks to its natural clustering properties. In particular, it is popular in image…

Computer Vision and Pattern Recognition · Computer Science 2016-08-05 Giovanni Barbarino

Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical…

Machine Learning · Computer Science 2022-02-16 Joshua Vendrow , Jamie Haddock , Deanna Needell

Non-negative matrix factorization (NMF) is a popular unsupervised learning approach widely used in image clustering. However, in real-world clustering scenarios, most existing NMF methods are highly sensitive to noise corruption and are…

Computer Vision and Pattern Recognition · Computer Science 2025-05-01 Jingjing Liu , Nian Wu , Xianchao Xiu , Jianhua Zhang

Nonnegative Matrix Factorization (NMF) is a powerful tool for decomposing mixtures of audio signals in the Time-Frequency (TF) domain. In applications such as source separation, the phase recovery for each extracted component is a major…

Sound · Computer Science 2016-11-17 Paul Magron , Roland Badeau , Bertrand David

Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of…

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

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean…

Machine Learning · Statistics 2012-07-17 Naiyang Guan , Dacheng Tao , Zhigang Luo , John Shawe-Taylor

Nonnegative matrix factorization (NMF) has been successfully applied in several data mining tasks. Recently, there is an increasing interest in the acceleration of NMF, due to its high cost on large matrices. On the other hand, the privacy…

Machine Learning · Computer Science 2020-09-08 Yuqiu Qian , Conghui Tan , Danhao Ding , Hui Li , Nikos Mamoulis

Non-negative matrix factorization (NMF) minimizes the Euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper,…

Machine Learning · Computer Science 2019-06-04 Naiyang Guan , Tongliang Liu , Yangmuzi Zhang , Dacheng Tao , Larry S. Davis

Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is…

Machine Learning · Computer Science 2015-07-09 Rong Ge , James Zou

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…

Machine Learning · Statistics 2018-11-07 Pierre Ablin , Dylan Fagot , Herwig Wendt , Alexandre Gramfort , Cédric Févotte

Nonnegative matrix factorization (NMF) is a popular data embedding technique. Given a nonnegative data matrix $X$, it aims at finding two lower dimensional matrices, $W$ and $H$, such that $X\approx WH$, where the factors $W$ and $H$ are…

Machine Learning · Computer Science 2026-02-06 Olivier Vu Thanh , Nicolas Gillis

Nonnegative matrix factorization (NMF) methods have proved to be powerful across a wide range of real-world clustering applications. Integrating multiple types of measurements for the same objects/subjects allows us to gain a deeper…

Machine Learning · Computer Science 2014-09-16 Daniel Hidru , Anna Goldenberg

In this paper, a whitening-based algorithm has been applied to sparse non-negative matrix factorization (NMF) as a preprocessing practice enhancing the identification of buried object, significantly. In fact, without utilizing a suitable…

Signal Processing · Electrical Eng. & Systems 2019-10-17 Ali Gharamohammadi , Fereidoon Behnia , Arash Shokouhmand
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