# Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlations

arXiv: https://arxiv.org/abs/1706.04097 · HTML: https://mlsanity.com/paper/1706.04097/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2017.

## Built on by (most cited first, 3 of 3)

- [Crowdsourcing via Annotator Co-occurrence Imputation and Provable Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2106.07193/) (2021)
- [Learning Polynomial Transformations](https://mlsanity.com/paper/2204.04209/) (2022)
- [Efficient Matrix Factorization Via Householder Reflections](https://mlsanity.com/paper/2405.07649/) (2024)

## Abstract (arXiv)

Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear whether such algorithms can recover the ground-truth feature matrix when the weights for different features are highly correlated, which is common in applications. This paper proposes a simple and natural alternating gradient descent based algorithm, and shows that with a mild initialization it provably recovers the ground-truth in the presence of strong correlations. In most interesting cases, the correlation can be in the same order as the highest possible. Our analysis also reveals its several favorable features including robustness to noise. We complement our theoretical results with empirical studies on semi-synthetic datasets, demonstrating its advantage over several popular methods in recovering the ground-truth.