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There are two problems need to be dealt with for Non-negative Matrix Factorization (NMF): choose a suitable rank of the factorization and provide a good initialization method for NMF algorithms. This paper aims to solve these two problems…

机器学习 · 计算机科学 2014-10-13 Hanli Qiao

Non-negative matrix factorization (NMF) is an important tool in signal processing and widely used to separate mixed sources into their components. Algorithms for NMF require that the user choose the number of components in advance, and if…

机器学习 · 计算机科学 2025-01-10 Youdong Guo , Timothy E. Holy

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…

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

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…

机器学习 · 计算机科学 2016-05-04 Mariano Tepper , Guillermo Sapiro

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…

最优化与控制 · 数学 2015-04-24 Yat Tin Chow , Kazufumi Ito , Jun Zou

The Nonnegative Matrix Factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem. In this paper we propose new methods based on the NMF of the rating matrix and we compare them with…

机器学习 · 计算机科学 2019-08-30 Gianna M. Del Corso , Francesco Romani

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…

数值分析 · 数学 2013-05-27 Shu-Zhen Lai , Hou-Biao Li , Zu-Tao Zhang

Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this…

机器学习 · 统计学 2014-12-10 Nicolas Gillis

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,…

数值分析 · 计算机科学 2017-12-07 Gabriele Torre , Michael Graber

We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…

机器学习 · 计算机科学 2011-12-19 Youngmin Cho , Lawrence K. Saul

Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical…

计算机视觉与模式识别 · 计算机科学 2022-04-19 Junhang Li , Jiao Wei , Can Tong , Tingting Shen , Yuchen Liu , Chen Li , Shouliang Qi , Yudong Yao , Yueyang Teng

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

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

Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…

天体物理仪器与方法 · 物理学 2016-12-20 Guangtun Zhu

Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a…

机器学习 · 计算机科学 2021-04-14 Junjun Pan , Nicolas Gillis

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define…

机器学习 · 计算机科学 2013-04-04 Jing-Yan Wang , Mustafa AbdulJabbar

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…

机器学习 · 计算机科学 2024-05-24 Prasun Dutta , Rajat K. De

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…

信息论 · 计算机科学 2021-08-23 Rami Nasser , Yonina C. Eldar , Roded Sharan

Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…

计算机视觉与模式识别 · 计算机科学 2013-04-10 Yao Nan , Qian Feng , Sun Zuolei

Recently, the problem of blind image separation has been widely investigated, especially the medical image denoise which is the main step in medical diag-nosis. Removing the noise without affecting relevant features of the image is the main…

计算机视觉与模式识别 · 计算机科学 2018-07-11 R. M. Farouk , M. E. Abd El-aziz , A. M. Adam

Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image…

机器学习 · 统计学 2020-12-08 Matthew Corsetti , Ernest Fokoué
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