English
Related papers

Related papers: Memory-Efficient Convex Optimization for Self-Dict…

200 papers

In this paper, we propose a novel recurrent neural network architecture for speech separation. This architecture is constructed by unfolding the iterations of a sequential iterative soft-thresholding algorithm (ISTA) that solves the…

Sound · Computer Science 2017-09-22 Scott Wisdom , Thomas Powers , James Pitton , Les Atlas

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

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

Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination…

Applications · Statistics 2013-12-19 Paul Fogel

Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability…

Machine Learning · Computer Science 2025-01-23 Juefei Chen , Longxiu Huang , Yimin Wei

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

We introduce regularized Frank-Wolfe, a general and effective algorithm for inference and learning of dense conditional random fields (CRFs). The algorithm optimizes a nonconvex continuous relaxation of the CRF inference problem using…

Machine Learning · Computer Science 2022-09-09 Đ. Khuê Lê-Huu , Karteek Alahari

In this paper, we introduce a class of nonsmooth nonconvex least square optimization problem using convex analysis tools and we propose to use the iterative minimization-majorization (MM) algorithm on a convex set with initializer away from…

Optimization and Control · Mathematics 2019-06-14 Azita Mayeli

In this paper we provide an introduction to the Frank-Wolfe algorithm, a method for smooth convex optimization in the presence of (relatively) complicated constraints. We will present the algorithm, introduce key concepts, and establish…

Optimization and Control · Mathematics 2023-11-30 Sebastian Pokutta

The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a compact convex set $\mathcal{C}$. While many convergence results have been derived in terms of function values, hardly nothing is known about…

Optimization and Control · Mathematics 2022-02-18 Jérôme Bolte , Cyrille W. Combettes , Édouard Pauwels

We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation ($1$-SVD) in Frank-Wolfe with a top-$k$ singular-vector…

Machine Learning · Computer Science 2017-11-10 Zeyuan Allen-Zhu , Elad Hazan , Wei Hu , Yuanzhi Li

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

Optimization and Control · Mathematics 2024-06-07 Wei Jiang , Sifan Yang , Wenhao Yang , Yibo Wang , Yuanyu Wan , Lijun Zhang

We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…

Optimization and Control · Mathematics 2023-05-12 Duy-Nhat Phan , Sedi Bartz , Nilabja Guha , Hung M. Phan

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean…

Machine Learning · Statistics 2012-07-17 Naiyang Guan , Dacheng Tao , Zhigang Luo , John Shawe-Taylor

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…

Machine Learning · Statistics 2018-11-07 Pierre Ablin , Dylan Fagot , Herwig Wendt , Alexandre Gramfort , Cédric Févotte

Nonnegative Matrix Factorization (NMF) is a data analysis technique which allows compression and interpretation of nonnegative data. NMF became widely studied after the publication of the seminal paper by Lee and Seung (Learning the Parts…

Numerical Analysis · Mathematics 2008-10-24 Nicolas Gillis , François Glineur

We prove that the block-coordinate Frank-Wolfe (BCFW) algorithm converges with state-of-the-art rates in both convex and nonconvex settings under a very mild "block-iterative" assumption. This appears to be the first result on BCFW…

Optimization and Control · Mathematics 2025-12-17 Gábor Braun , Jannis Halbey , Sebastian Pokutta , Zev Woodstock

The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. The simplicity of iteration and applicability to many…

Optimization and Control · Mathematics 2024-09-17 Ruslan Nazykov , Aleksandr Shestakov , Vladimir Solodkin , Aleksandr Beznosikov , Gauthier Gidel , Alexander Gasnikov

We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…

Optimization and Control · Mathematics 2017-05-08 Christoph Buchheim , Marianna De Santis , Francesco Rinaldi , Long Trieu

Neural networks are often challenging to work with due to their large size and complexity. To address this, various methods aim to reduce model size by sparsifying or decomposing weight matrices, such as magnitude pruning and low-rank or…

Machine Learning · Computer Science 2025-06-05 Vladimír Boža , Vladimír Macko