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Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for…

最优化与控制 · 数学 2015-03-19 Filippo Pompili , Nicolas Gillis , P. -A. Absil , François Glineur

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…

最优化与控制 · 数学 2012-08-13 Nicolas Gillis , François Glineur

Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilises the Bayesian non-negative matrix factorisation (NMF) model to produce a probabilistic…

机器学习 · 统计学 2010-09-28 Ioannis Psorakis , Stephen Roberts , Ben Sheldon

Hyperspectral image (HSI) unmixing is a challenging research problem that tries to identify the constituent components, known as endmembers, and their corresponding proportions, known as abundances, in the scene by analysing images captured…

图像与视频处理 · 电气工程与系统科学 2025-03-13 Chao Zhou , Wei Pu , Miguel Rodrigues

Hyperspectral unmixing aims at identifying a set of elementary spectra and the corresponding mixture coefficients for each pixel of an image. As the elementary spectra correspond to the reflectance spectra of real materials, they are often…

计算机视觉与模式识别 · 计算机科学 2020-02-17 Adrien Lagrange , Mathieu Fauvel , Stéphane May , Nicolas Dobigeon

Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best…

数值分析 · 数学 2015-10-28 Nicolas Gillis , Abhishek Kumar

Symmetric nonnegative matrix factorization (symNMF) is a variant of nonnegative matrix factorization (NMF) that allows to handle symmetric input matrices and has been shown to be particularly well suited for clustering tasks. In this paper,…

数值分析 · 数学 2020-03-11 François Moutier , Arnaud Vandaele , Nicolas Gillis

Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial…

计算机视觉与模式识别 · 计算机科学 2014-07-14 Feiyun Zhu , Ying Wang , Shiming Xiang , Bin Fan , Chunhong Pan

The establishment of robust target appearance model over time is an overriding concern in visual tracking. In this paper, we propose an inverse nonnegative matrix factorization (NMF) method for robust appearance modeling. Rather than using…

计算机视觉与模式识别 · 计算机科学 2016-01-13 Fanghui Liu , Tao Zhou , Keren Fu , Irene Y. H. Gu , Jie Yang

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…

机器学习 · 计算机科学 2025-02-04 Matej Mihelčić , Pauli Miettinen

A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with the constraint over an auxiliary matrix whose Boolean structure…

数据结构与算法 · 计算机科学 2021-08-27 Duc P. Truong , Erik Skau , Derek Desantis , Boian Alexandrov

The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve…

机器学习 · 计算机科学 2022-09-23 Rachid Hedjam , Abdelhamid Abdesselam , Abderrahmane Rahiche , Mohamed Cheriet

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…

机器学习 · 计算机科学 2020-03-20 Ioannis Panageas , Stratis Skoulakis , Antonios Varvitsiotis , Xiao Wang

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…

声音 · 计算机科学 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…

最优化与控制 · 数学 2016-11-02 Hideaki Iiduka , Shizuka Nishino

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is…

Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, $X$, by the product of two nonnegative factors, $WH$, where $W$ has $r$ columns and $H$ has $r$ rows. In this paper, we consider NMF using the component-wise L1 norm…

机器学习 · 计算机科学 2026-04-01 Giovanni Seraghiti , Kévin Dubrulle , Arnaud Vandaele , Nicolas Gillis

In this work we introduce a comprehensive algorithmic pipeline for multiple parametric model estimation. The proposed approach analyzes the information produced by a random sampling algorithm (e.g., RANSAC) from a machine…

计算机视觉与模式识别 · 计算机科学 2016-11-14 Mariano Tepper , Guillermo Sapiro

In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ find, for assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and $H\in\R_+^{k\times n}$…

最优化与控制 · 数学 2014-07-08 Lorenzo Finesso , Peter Spreij

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…

分布式、并行与集群计算 · 计算机科学 2015-10-01 Ramakrishnan Kannan , Grey Ballard , Haesun Park