# Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion

arXiv: https://arxiv.org/abs/1910.09092 · HTML: https://mlsanity.com/paper/1910.09092/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

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

- [Matrix Completion with Heterogonous Cost](https://mlsanity.com/paper/2203.12120/) (2022)

## Abstract (arXiv)

We formulate the problem of matrix completion with and without side information as a non-convex optimization problem. We design fastImpute based on non-convex gradient descent and show it converges to a global minimum that is guaranteed to recover closely the underlying matrix while it scales to matrices of sizes beyond 105 × 105. We report experiments on both synthetic and real-world datasets that show fastImpute is competitive in both the accuracy of the matrix recovered and the time needed across all cases. Furthermore, when a high number of entries are missing, fastImpute is over 75% lower in MAPE and 15 times faster than current state-of-the-art matrix completion methods in both the case with side information and without.