# Adversarially-Trained Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/2104.04757 · HTML: https://mlsanity.com/paper/2104.04757/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 10 Apr 2021.

## Builds on (most cited first, 10 of 10)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Generalizable Adversarial Training via Spectral Normalization](https://mlsanity.com/paper/1811.07457/) (2018)
- [Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning](https://mlsanity.com/paper/1402.4419/) (2014)
- [On the folded normal distribution](https://mlsanity.com/paper/1402.3559/) (2014)
- [Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization](https://mlsanity.com/paper/1401.5649/) (2014)
- [Online Nonnegative Matrix Factorization with Outliers](https://mlsanity.com/paper/1604.02634/) (2016)
- [Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization](https://mlsanity.com/paper/1901.10757/) (2019)

## Built on by (most cited first, 2 of 2)

- [A Dynamic Linear Bias Incorporation Scheme for Nonnegative Latent Factor Analysis](https://mlsanity.com/paper/2309.10618/) (2023)
- [LaFA: Latent Feature Attacks on Non-negative Matrix Factorization](https://mlsanity.com/paper/2408.03909/) (2024)

## Abstract (arXiv)

We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices with enhanced generalization abilities. Extensive simulations on synthetic and benchmark datasets demonstrate the superior predictive performance on matrix completion tasks of our proposed method compared to state-of-the-art competitors, including other variants of adversarial nonnegative matrix factorization.