# Nonnegative/Binary Matrix Factorization for Image Classification using Quantum Annealing

arXiv: https://arxiv.org/abs/2311.01028 · HTML: https://mlsanity.com/paper/2311.01028/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 2 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [Nonnegative/binary matrix factorization with a D-Wave quantum annealer](https://mlsanity.com/paper/1704.01605/) (2017)
- [Image classification using quantum inference on the D-Wave 2X](https://mlsanity.com/paper/1905.13215/) (2019)
- [Towards Feature Selection for Ranking and Classification Exploiting Quantum Annealers](https://mlsanity.com/paper/2205.04346/) (2022)
- [Reverse Annealing for Nonnegative/Binary Matrix Factorization](https://mlsanity.com/paper/2007.05565/) (2020)
- [A Review of Machine Learning Classification Using Quantum Annealing for Real-world Applications](https://mlsanity.com/paper/2106.02964/) (2021)
- [Completely Quantum Neural Networks](https://mlsanity.com/paper/2202.11727/) (2022)
- [Image Analysis Based on Nonnegative/Binary Matrix Factorization](https://mlsanity.com/paper/2007.00889/) (2020)
- [Using machine learning for quantum annealing accuracy prediction](https://mlsanity.com/paper/2106.00065/) (2021)

## Built on by (most cited first, 4 of 4)

- [Quantum autoencoders for image classification](https://mlsanity.com/paper/2502.15254/) (2025)
- [Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization](https://mlsanity.com/paper/2501.02114/) (2025)
- [Collaborative filtering based on nonnegative/binary matrix factorization](https://mlsanity.com/paper/2410.10381/) (2024)
- [Layer-wise QUBO-Based Training of CNN Classifiers for Quantum Annealing](https://mlsanity.com/paper/2603.02958/) (2026)

## Abstract (arXiv)

Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute. Demonstrating the benefits of this integration now becomes essential. With the advance of quantum computing, several machine-learning techniques have been proposed that use quantum annealing. In this study, we implement a matrix factorization method using quantum annealing for image classification and compare the performance with traditional machine-learning methods. Nonnegative/binary matrix factorization (NBMF) was originally introduced as a generative model, and we propose a multiclass classification model as an application. We extract the features of handwritten digit images using NBMF and apply them to solve the classification problem. Our findings show that when the amount of data, features, and epochs is small, the accuracy of models trained by NBMF is superior to classical machine-learning methods, such as neural networks. Moreover, we found that training models using a quantum annealing solver significantly reduces computation time. Under certain conditions, there is a benefit to using quantum annealing technology with machine learning.