English
Related papers

Related papers: Quadratic Matrix Factorization with Applications t…

200 papers

We propose SMMF (Square-Matricized Momentum Factorization), a memory-efficient optimizer that reduces the memory requirement of the widely used adaptive learning rate optimizers, such as Adam, by up to 96%. SMMF enables flexible and…

Machine Learning · Computer Science 2025-05-01 Kwangryeol Park , Seulki Lee

Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts. To be robust to outliers and differences in scale across features, a…

Machine Learning · Computer Science 2020-07-07 Marco Cuturi , Olivier Teboul , Jonathan Niles-Weed , Jean-Philippe Vert

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…

Machine Learning · Computer Science 2019-08-30 Gianna M. Del Corso , Francesco Romani

Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…

Methodology · Statistics 2021-07-05 Phillip Shreeves , Jeffrey L. Andrews , Xinchen Deng , Ramie Ali-Adeeb , Andrew Jirasek

Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…

Machine Learning · Computer Science 2021-11-30 Kai Liu

Many computer vision problems can be posed as learning a low-dimensional subspace from high dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF…

Computer Vision and Pattern Recognition · Computer Science 2016-09-21 Xiangyong Cao , Qian Zhao , Deyu Meng , Yang Chen , Zongben Xu

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…

Optimization and Control · Mathematics 2017-04-05 Martin Benning , Guy Gilboa , Joana Sarah Grah , Carola-Bibiane Schönlieb

First-order methods in convex optimization offer low per-iteration cost but often suffer from slow convergence, while second-order methods achieve fast local convergence at the expense of costly Hessian inversions. In this paper, we…

Machine Learning · Statistics 2025-07-08 Qiang Heng , Caixing Wang

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

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

Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based…

Computer Vision and Pattern Recognition · Computer Science 2024-09-17 Shiqi Li , Jihua Zhu , Yifan Xie , Naiwen Hu , Mingchen Zhu , Zhongyu Li , Di Wang

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

Optimization and Control · Mathematics 2015-07-01 Duy-Khuong Nguyen , Tu-Bao Ho

Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) decompose non-negative high-dimensional data into non-negative low-rank components. NMF and NTF methods are popular for their intrinsic interpretability and…

Machine Learning · Computer Science 2024-12-02 Alexander Sietsema , Zerrin Vural , James Chapman , Yotam Yaniv , Deanna Needell

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…

Machine Learning · Statistics 2020-12-08 Matthew Corsetti , Ernest Fokoué

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

Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the…

Machine Learning · Computer Science 2024-10-29 Yuheng Jia , Jia-Nan Li , Wenhui Wu , Ran Wang

Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…

Machine Learning · Computer Science 2017-08-29 Benjamin D. Haeffele , Rene Vidal

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Machine Learning · Statistics 2025-02-18 Stephen Zhang , Gilles Mordant , Tetsuya Matsumoto , Geoffrey Schiebinger

As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…

Quantum Physics · Physics 2026-05-25 Jiaqi Yao , Tianjian Huang , Zipeng Cai , Ding Liu

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…

Machine Learning · Statistics 2014-12-10 Nicolas Gillis