# Spectral Geometric Matrix Completion

arXiv: https://arxiv.org/abs/1911.07255 · HTML: https://mlsanity.com/paper/1911.07255/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2019.

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

- [Adaptive and Implicit Regularization for Matrix Completion](https://mlsanity.com/paper/2208.05640/) (2022)
- [Scalable unsupervised alignment of general metric and non-metric structures](https://mlsanity.com/paper/2406.13507/) (2024)
- [AIR-Net: Adaptive and Implicit Regularization Neural Network for Matrix Completion](https://mlsanity.com/paper/2110.07557/) (2021)

## Abstract (arXiv)

Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix. In this work we interpret the DMF model through the lens of spectral geometry. This allows us to incorporate explicit regularization without breaking the DMF structure, thus enjoying the best of both worlds. In particular, we focus on matrix completion problems with underlying geometric or topological relations between the rows and/or columns. Such relations are prevalent in matrix completion problems that arise in many applications, such as recommender systems and drug-target interaction. Our contributions enable DMF models to exploit these relations, and make them competitive on real benchmarks, while exhibiting one of the first successful applications of deep linear networks.