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Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value…

Machine Learning · Computer Science 2024-10-30 Youdong Guo , Timothy E. Holy

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

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,…

Numerical Analysis · Mathematics 2020-03-11 François Moutier , Arnaud Vandaele , Nicolas Gillis

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…

Machine Learning · Statistics 2012-12-04 Prateek Jain , Praneeth Netrapalli , Sujay Sanghavi

Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, $V$, as the product of two smaller nonnegative matrices, $W$ and $H$. In this paper, we introduce a general framework to design…

Machine Learning · Computer Science 2022-04-29 Valentin Leplat , Nicolas Gillis , Jérôme Idier

Deep representations have shown promising performance when transferred to downstream tasks in a black-box manner. Yet, their inherent lack of interpretability remains a significant challenge, as these features are often opaque to human…

Machine Learning · Computer Science 2024-04-24 Yifei Wang , Qi Zhang , Yaoyu Guo , Yisen Wang

Nonnegative matrix factorization (NMF) has been successfully applied to many areas for classification and clustering. Commonly-used NMF algorithms mainly target on minimizing the $l_2$ distance or Kullback-Leibler (KL) divergence, which may…

Information Retrieval · Computer Science 2014-10-07 Le Li , Jianjun Yang , Yang Xu , Zhen Qin , Honggang Zhang

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…

Numerical Analysis · Mathematics 2025-11-11 Junjun Pan , Valentin Leplat , Michael Ng , Nicolas Gillis

Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…

Machine Learning · Computer Science 2022-06-08 Tingting Shen , Junhang Li , Can Tong , Qiang He , Chen Li , Yudong Yao , Yueyang Teng

This paper proposes a novel algorithm for training recurrent neural network models of nonlinear dynamical systems from an input/output training dataset. Arbitrary convex and twice-differentiable loss functions and regularization terms are…

Machine Learning · Computer Science 2022-10-18 Alberto Bemporad

Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning. Given a matrix $M \in \mathbb{R}^{n \times n}$, a non-negative weight matrix $W \in \mathbb{R}_{\geq…

Machine Learning · Computer Science 2025-02-18 Zhao Song , Mingquan Ye , Junze Yin , Lichen Zhang

This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…

Machine Learning · Computer Science 2015-06-18 Canyi Lu , Zhouchen Lin , Shuicheng Yan

Nonnegative matrix factorization (NMF) has been actively investigated and used in a wide range of problems in the past decade. A significant amount of attention has been given to develop NMF algorithms that are suitable to model time series…

Machine Learning · Computer Science 2017-09-04 Nasser Mohammadiha , Paris Smaragdis , Ghazaleh Panahandeh , Simon Doclo

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable…

Optimization and Control · Mathematics 2017-03-27 Songtao Lu , Mingyi Hong , Zhengdao Wang

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…

Optimization and Control · Mathematics 2015-03-19 Filippo Pompili , Nicolas Gillis , P. -A. Absil , François Glineur

This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data…

Computer Vision and Pattern Recognition · Computer Science 2023-07-19 Liansheng Zhuang , Shenghua Gao , Jinhui Tang , Jingjing Wang , Zhouchen Lin , Yi Ma

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…

Machine Learning · Computer Science 2013-03-20 Vamsi K. Potluru , Sergey M. Plis , Jonathan Le Roux , Barak A. Pearlmutter , Vince D. Calhoun , Thomas P. Hayes

We consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF) problem, encompassing various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem holds…

Machine Learning · Computer Science 2024-04-26 Nathanaël Perraudin , Adrien Teutrie , Cécile Hébert , Guillaume Obozinski

Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…

Computational Geometry · Computer Science 2016-11-17 Wajeb Gharibi , Omar Saeed Al-Mushayt

A fundamental problem in machine learning is to understand how neural networks make accurate predictions, while seemingly bypassing the curse of dimensionality. A possible explanation is that common training algorithms for neural networks…

Machine Learning · Statistics 2024-01-10 Adityanarayanan Radhakrishnan , Mikhail Belkin , Dmitriy Drusvyatskiy