# Accelerating Nonnegative Matrix Factorization Algorithms using Extrapolation

arXiv: https://arxiv.org/abs/1805.06604 · HTML: https://mlsanity.com/paper/1805.06604/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2018.

## Built on by (most cited first, 10 of 10)

- [Accelerated Algorithms for Nonlinear Matrix Decomposition with the ReLU function](https://mlsanity.com/paper/2305.08687/) (2023)
- [An extrapolated and provably convergent algorithm for nonlinear matrix decomposition with the ReLU function](https://mlsanity.com/paper/2503.23832/) (2025)
- [Quasi Non-Negative Quaternion Matrix Factorization with Application to Color Face Recognition](https://mlsanity.com/paper/2211.16739/) (2022)
- [Efficient algorithms for the Hadamard decomposition](https://mlsanity.com/paper/2504.13633/) (2025)
- [Non-negative matrix factorization algorithms generally improve topic model fits](https://mlsanity.com/paper/2105.13440/) (2021)
- [A Second-Order Majorant Algorithm for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2303.17992/) (2023)
- [Manifold-based Algorithms for the Hadamard Decomposition](https://mlsanity.com/paper/2605.28980/) (2026)
- [Block Majorization Minimization with Extrapolation and Application to β-NMF](https://mlsanity.com/paper/2401.06646/) (2024)
- [A Non-Negative Matrix Factorization Game](https://mlsanity.com/paper/2104.05069/) (2021)
- [An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2607.13919/) (2026)

## Abstract (arXiv)

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the two-block exact coordinate descent algorithms tackling the non-convex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms, namely, accelerated hierarchical alternating least squares (A-HALS) and alternating nonnegative least squares (ANLS), using synthetic, image and document data sets.