# Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds

arXiv: https://arxiv.org/abs/2502.14174 · HTML: https://mlsanity.com/paper/2502.14174/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 21 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 5 of 5)

- [Regularized Weighted Low Rank Approximation](https://mlsanity.com/paper/1911.06958/) (2019)
- [Matrix Completion in Almost-Verification Time](https://mlsanity.com/paper/2308.03661/) (2023)
- [Disjunctive Branch-and-Bound for Certifiably Optimal Low-Rank Matrix Completion](https://mlsanity.com/paper/2305.12292/) (2023)
- [A Stochastic Gradient Descent Theorem and the Back-Propagation Algorithm](https://mlsanity.com/paper/2104.00539/) (2021)
- [Fast gradient method for Low-Rank Matrix Estimation](https://mlsanity.com/paper/2211.16236/) (2022)

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

- [Retraction-Based Gradient Projection Algorithms on Manifolds](https://mlsanity.com/paper/2609.30885/) (2026)

## Abstract (arXiv)

We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for retraction-based stochastic gradient descents admitting confinements. On sample data from the Netflix Prize training dataset, our algorithm outperforms the existing stochastic gradient descent on Euclidean spaces. We also compare the accelerated line search on this manifold to the existing accelerated line search on Euclidean spaces.