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Independent low-rank matrix analysis (ILRMA) is a fast and stable method for blind audio source separation. Conventional ILRMAs assume time-variant (super-)Gaussian source models, which can only represent signals that follow a…

Audio and Speech Processing · Electrical Eng. & Systems 2018-08-27 Shinichi Mogami , Norihiro Takamune , Daichi Kitamura , Hiroshi Saruwatari , Yu Takahashi , Kazunobu Kondo , Hiroaki Nakajima , Nobutaka Ono

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

This paper investigates a non-negative matrix factorization (NMF)-based approach to the semi-supervised single-channel speech enhancement problem where only non-stationary additive noise signals are given. The proposed method relies on…

Sound · Computer Science 2013-09-25 Nikolay Lyubimov , Mikhail Kotov

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 data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this paper, we…

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

Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale…

Machine Learning · Computer Science 2026-02-27 Jichao Zhang , Ran Miao , Limin Li

This article proposes new multiplicative updates for nonnegative matrix factorization (NMF) with the $\beta$-divergence objective function. Our new updates are derived from a joint majorization-minimization (MM) scheme, in which an…

Machine Learning · Computer Science 2023-04-18 Arthur Marmin , José Henrique de Morais Goulart , Cédric Févotte

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…

Machine Learning · Statistics 2015-01-26 Paul Honeine , Fei Zhu

Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive…

Machine Learning · Computer Science 2020-03-20 Ioannis Panageas , Stratis Skoulakis , Antonios Varvitsiotis , Xiao Wang

In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…

Machine Learning · Computer Science 2019-11-15 Anthony Degleris , Nicolas Gillis

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

Symmetric nonnegative matrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix…

Numerical Analysis · Computer Science 2017-10-11 Qingjiang Shi , Haoran Sun , Songtao Lu , Mingyi Hong , Meisam Razaviyayn

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

Hyperspectral unmixing (HU) is a critical yet challenging task in remote sensing. However, existing nonnegative matrix factorization (NMF) methods with graph learning mostly focus on first-order or second-order nearest neighbor…

Computer Vision and Pattern Recognition · Computer Science 2025-09-26 Hui Chen , Liangyu Liu , Xianchao Xiu , Wanquan Liu

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) 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

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

The so-called independent low-rank matrix analysis (ILRMA) has demonstrated a great potential for dealing with the problem of determined blind source separation (BSS) for audio and speech signals. This method assumes that the spectra from…

Sound · Computer Science 2024-01-04 Jianyu Wang , Shanzheng Guan , Jingdong Chen , Jacob Benesty

Non-negative matrix factorization (NMF) has become a popular method for representing meaningful data by extracting a non-negative basis feature from an observed non-negative data matrix. Some of the unique features of this method in…

Optimization and Control · Mathematics 2022-11-15 Sajad Fathi Hafshejani , Zahra Moaberfard

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