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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

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 powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…

Computer Vision and Pattern Recognition · Computer Science 2017-07-27 Lihua Zhang , Shihua Zhang

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

Non-negative matrix factorization (NMF) is widely used for dimensionality reduction and interpretable analysis, but standard formulations are unsupervised and cannot directly exploit class labels. Existing supervised or semi-supervised…

Machine Learning · Computer Science 2025-10-14 Kenichi Satoh

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

Non-negative matrix factorization (NMF) is a prob- lem with many applications, ranging from facial recognition to document clustering. However, due to the variety of algorithms that solve NMF, the randomness involved in these algorithms,…

Numerical Analysis · Mathematics 2018-12-17 Connor Sell , 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

Brain tumor classification from magnetic resonance imaging, which is also known as MRI, plays a sensitive role in computer-assisted diagnosis systems. In recent years, deep learning models have achieved high classification accuracy.…

Computer Vision and Pattern Recognition · Computer Science 2026-04-21 Hiba Adil Al-kharsan , Róbert Rajkó

In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions,…

Numerical Analysis · Computer Science 2017-03-03 Nicolas Gillis

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) is a powerful tool for decomposing mixtures of audio signals in the Time-Frequency (TF) domain. In the source separation framework, the phase recovery for each extracted component is necessary for…

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

Language model based methods are powerful techniques for text classification. However, the models have several shortcomings. (1) It is difficult to integrate human knowledge such as keywords. (2) It needs a lot of resources to train the…

Computation and Language · Computer Science 2024-02-09 Weijie Xu , Jay Desai , Srinivasan Sengamedu , Xiaoyu Jiang , Francis Iannacci

Non-negative Matrix Factorization (NMF) methods offer an appealing unsupervised learning method for real-time analysis of streaming spectral data in time-sensitive data collection, such as $\textit{in situ}$ characterization of materials.…

Applied Physics · Physics 2024-06-12 Phillip M. Maffettone , Aidan C. Daly , Daniel Olds

In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…

Optimization and Control · Mathematics 2015-04-24 Yat Tin Chow , Kazufumi Ito , Jun Zou

We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity…

Machine Learning · Computer Science 2020-06-16 Nicolas Nadisic , Arnaud Vandaele , Jeremy E. Cohen , Nicolas Gillis

We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a…

Machine Learning · Computer Science 2018-01-08 Olivier Gouvert , Thomas Oberlin , Cédric Févotte

The California Innocence Project (CIP), a clinical law school program aiming to free wrongfully convicted prisoners, evaluates thousands of mails containing new requests for assistance and corresponding case files. Processing and…

In traditional Distributional Semantic Models (DSMs) the multiple senses of a polysemous word are conflated into a single vector space representation. In this work, we propose a DSM that learns multiple distributional representations of a…

Computation and Language · Computer Science 2019-04-12 Eleftheria Briakou , Nikos Athanasiou , Alexandros Potamianos

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