# Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization

arXiv: https://arxiv.org/abs/2501.02114 · HTML: https://mlsanity.com/paper/2501.02114/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 3 Jan 2025.

## Builds on (most cited first, 11 of 11)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Traffic flow optimization using a quantum annealer](https://mlsanity.com/paper/1708.01625/) (2017)
- [Nonnegative/binary matrix factorization with a D-Wave quantum annealer](https://mlsanity.com/paper/1704.01605/) (2017)
- [Control of automated guided vehicles without collision by quantum annealer and digital devices](https://mlsanity.com/paper/1812.01532/) (2018)
- [Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer](https://mlsanity.com/paper/1508.06182/) (2015)
- [Item Listing Optimization for E-commerce Websites based on Diversity](https://mlsanity.com/paper/1903.12478/) (2019)
- [Reverse Annealing for Nonnegative/Binary Matrix Factorization](https://mlsanity.com/paper/2007.05565/) (2020)
- [Quantum Annealing Implementation of Job-Shop Scheduling](https://mlsanity.com/paper/1506.08479/) (2015)
- [Nonnegative/Binary Matrix Factorization for Image Classification using Quantum Annealing](https://mlsanity.com/paper/2311.01028/) (2023)
- [Travel time optimization on multi-AGV routing by reverse annealing](https://mlsanity.com/paper/2204.11789/) (2022)
- [Routing and Scheduling Optimization for Urban Air Mobility Fleet Management using Quantum Annealing](https://mlsanity.com/paper/2410.11231/) (2024)

## Built on by (most cited first, 1 of 1)

- [Non-Negative Matrix Factorization Using Non-Von Neumann Computers](https://mlsanity.com/paper/2512.00675/) (2025)

## Abstract (arXiv)

Quantum annealing has garnered significant attention as meta-heuristics inspired by quantum physics for combinatorial optimization problems. Among its many applications, nonnegative/binary matrix factorization stands out for its complexity and relevance in unsupervised machine learning. The use of reverse annealing, a derivative procedure of quantum annealing to prioritize the search in a vicinity under a given initial state, helps improve its optimization performance in matrix factorization. This study proposes an improved strategy that integrates reverse annealing with a linear programming relaxation technique. Using relaxed solutions as the initial configuration for reverse annealing, we demonstrate improvements in optimization performance comparable to the exact optimization methods. Our experiments on facial image datasets show that our method provides better convergence than known reverse annealing methods. Furthermore, we investigate the effectiveness of relaxation-based initialization methods on randomized datasets, demonstrating a relationship between the relaxed solution and the optimal solution. This research underscores the potential of combining reverse annealing and classical optimization strategies to enhance optimization performance.