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Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…

Machine Learning · Computer Science 2024-12-10 Olivier Vu Thanh

Factorization-based gradient descent is a scalable and efficient algorithm for solving low-rank matrix completion. Recent progress in structured non-convex optimization has offered global convergence guarantees for gradient descent under…

Optimization and Control · Mathematics 2021-02-09 Trung Vu , Raviv Raich

The so-called Burer-Monteiro method is a well-studied technique for solving large-scale semidefinite programs (SDPs) via low-rank factorization. The main idea is to solve rank-restricted, albeit non-convex, surrogates instead of the SDP.…

Optimization and Control · Mathematics 2019-08-29 Yulun Tian , Kasra Khosoussi , Jonathan P. How

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…

Numerical Analysis · Mathematics 2020-06-23 Melanie Beckerleg , Andrew Thompson

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

Information Theory · Computer Science 2016-11-18 Mohammadreza Malek-Mohammadi , Massoud Babaie-Zadeh , Mikael Skoglund

This paper develops a scalable new algorithm, called NysADMM, to minimize a smooth convex loss function with a convex regularizer. NysADMM accelerates the inexact Alternating Direction Method of Multipliers (ADMM) by constructing a…

Optimization and Control · Mathematics 2022-07-05 Shipu Zhao , Zachary Frangella , Madeleine Udell

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

Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for clustering, which typically uses the $k$-nearest neighbor ($k$-NN) method to construct similarity matrix. However, $k$-NN may mislead clustering since the neighbors…

Machine Learning · Computer Science 2024-12-06 Wenlong Lyu , Yuheng Jia

Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and…

Machine Learning · Computer Science 2019-07-09 Shuai Jiang , Kan Li , Richard Yida Xu

Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…

Machine Learning · Statistics 2021-09-24 Elena Tuzhilina , Trevor Hastie

The unconstrained binary quadratic programming (UBQP) problem is a class of problems of significant importance in many practical applications, such as in combinatorial optimization, circuit design, and other fields. The positive…

Optimization and Control · Mathematics 2024-08-12 Xinyue Huo , Ran Gu

Interest in unsupervised methods for joint analysis of heterogeneous data sources has risen in recent years. Low-rank latent factor models have proven to be an effective tool for data integration and have been extended to a large number of…

Methodology · Statistics 2024-05-20 Felix Held , Jacob Lindbäck , Rebecka Jörnsten

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

Numerical Analysis · Computer Science 2018-05-23 Longhao Yuan , Chao Li , Danilo Mandic , Jianting Cao , Qibin Zhao

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

We propose an asymmetric affinity score for representing the complexity of utilizing the knowledge of one task for learning another one. Our method is based on the maximum bipartite matching algorithm and utilizes the Fisher Information…

Machine Learning · Computer Science 2022-01-25 Cat P. Le , Juncheng Dong , Mohammadreza Soltani , Vahid Tarokh

Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…

Machine Learning · Computer Science 2021-04-23 Tian Tong , Cong Ma , Yuejie Chi

With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training…

Machine Learning · Computer Science 2026-02-24 Dayana Savostianova , Emanuele Zangrando , Gianluca Ceruti , Francesco Tudisco

The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…

Computational Complexity · Computer Science 2025-06-24 Dror Chawin , Ishay Haviv

A wide range of symbolic analysis and optimization problems can be formalized using polyhedra. Sub-classes of polyhedra, also known as sub-polyhedral domains, are sought for their lower space and time complexity. We introduce the Strided…

Symbolic Computation · Computer Science 2024-07-08 Arjun Pitchanathan , Albert Cohen , Oleksandr Zinenko , Tobias Grosser

Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$. SymNMF can be used for…

Numerical Analysis · Computer Science 2016-10-07 Arnaud Vandaele , Nicolas Gillis , Qi Lei , Kai Zhong , Inderjit Dhillon