# Quartic First-Order Methods for Low-Rank Minimization

arXiv: https://arxiv.org/abs/1901.10791 · HTML: https://mlsanity.com/paper/1901.10791/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2019.

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

- [Symmetric Sparse Boolean Matrix Factorization and Applications](https://mlsanity.com/paper/2102.01570/) (2021)
- [SymNMF-Net for The Symmetric NMF Problem](https://mlsanity.com/paper/2205.13214/) (2022)

## Abstract (arXiv)

We study a generalized nonconvex Burer-Monteiro formulation for low-rank minimization problems. We use recent results on non-Euclidean first order methods to provide efficient and scalable algorithms. Our approach uses geometries induced by quartic kernels on matrix spaces; for unconstrained cases we introduce a novel family of Gram kernels that considerably improves numerical performances. Numerical experiments for Euclidean distance matrix completion and symmetric nonnegative matrix factorization show that our algorithms scale well and reach state of the art performance when compared to specialized methods.