English
Related papers

Related papers: Frank-Wolfe Optimization for Symmetric-NMF under S…

200 papers

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more…

Machine Learning · Computer Science 2024-12-02 Koby Hayashi , Sinan G. Aksoy , Grey Ballard , Haesun Park

We consider convex optimization problems which are widely used as convex relaxations for low-rank matrix recovery problems. In particular, in several important problems, such as phase retrieval and robust PCA, the underlying assumption in…

Optimization and Control · Mathematics 2022-06-22 Dan Garber

Nonnegative Matrix Factorization (NMF), first proposed in 1994 for data analysis, has received successively much attention in a great variety of contexts such as data mining, text clustering, computer vision, bioinformatics, etc. In this…

Numerical Analysis · Mathematics 2019-03-05 Paola Favati , Grazia Lotti , Ornella Menchi , Francesco Romani

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

Optimization and Control · Mathematics 2026-02-19 Shota Takahashi , Sebastian Pokutta , Akiko Takeda

Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and…

Machine Learning · Statistics 2015-10-27 Emanuele Frandi , Ricardo Nanculef , Stefano Lodi , Claudio Sartori , Johan A. K. Suykens

This article presents a novel approach to solving the sparsity-constrained Orthogonal Nonnegative Matrix Factorization (SCONMF) problem, which requires decomposing a non-negative data matrix into the product of two lower-rank non-negative…

Data Structures and Algorithms · Computer Science 2025-04-07 Salar Basiri , Alisina Bayati , Srinivasa Salapaka

This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank-Wolfe algorithm and its variants already avoid…

Optimization and Control · Mathematics 2024-09-04 Kamiar Asgari , Michael J. Neely

We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…

Optimization and Control · Mathematics 2019-12-10 Ilnura Usmanova , Andreas Krause , Maryam Kamgarpour

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration,…

Optimization and Control · Mathematics 2020-12-11 Bingcong Li , Lingda Wang , Georgios B. Giannakis , Zhizhen Zhao

We present and analyze a new generalized Frank-Wolfe method for the composite optimization problem $(P):{\min}_{x\in\mathbb{R}^n}\; f(\mathsf{A} x) + h(x)$, where $f$ is a $\theta$-logarithmically-homogeneous self-concordant barrier,…

Optimization and Control · Mathematics 2021-12-07 Renbo Zhao , Robert M. Freund

The Frank-Wolfe algorithm is a classic method for constrained optimization problems. It has recently been popular in many machine learning applications because its projection-free property leads to more efficient iterations. In this paper,…

Optimization and Control · Mathematics 2020-10-23 Cheng Chen , Luo Luo , Weinan Zhang , Yong Yu

Non-negative Matrix Factorization (NMF) is one of the most popular techniques for data representation and clustering, and has been widely used in machine learning and data analysis. NMF concentrates the features of each sample into a…

Image and Video Processing · Electrical Eng. & Systems 2021-03-26 Mulin Chen , Maoguo Gong , Xuelong Li

We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given…

Optimization and Control · Mathematics 2025-11-05 Dan Garber

The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…

Machine Learning · Computer Science 2023-01-26 Xiao Li , Zhihui Zhu , Qiuwei Li , Kai Liu

In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…

Optimization and Control · Mathematics 2020-09-10 Hamed Hassani , Amin Karbasi , Aryan Mokhtari , Zebang Shen

Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While…

Optimization and Control · Mathematics 2021-10-20 Thomas Kerdreux , Alexandre d'Aspremont , Sebastian Pokutta

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 $H\in\R_+^{k\times n}$…

Optimization and Control · Mathematics 2007-05-23 Lorenzo Finesso , Peter Spreij

As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants…

Optimization and Control · Mathematics 2021-05-11 Mingrui Zhang

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of…

Machine Learning · Computer Science 2021-03-03 Yuheng Jia , Hui Liu , Junhui Hou , Sam Kwong , Qingfu Zhang

Federated learning (FL) has gained a lot of attention in recent years for building privacy-preserving collaborative learning systems. However, FL algorithms for constrained machine learning problems are still limited, particularly when the…

Machine Learning · Computer Science 2024-08-20 Ali Dadras , Sourasekhar Banerjee , Karthik Prakhya , Alp Yurtsever