# On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion

arXiv: https://arxiv.org/abs/1712.01628 · HTML: https://mlsanity.com/paper/1712.01628/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2017.

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

- [A Perturbation Bound on the Subspace Estimator from Canonical Projections](https://mlsanity.com/paper/2206.14278/) (2022)

## Abstract (arXiv)

In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling patterns in the absence of noise based on the geometric analysis on the Grassmannian manifold. A special case where each column has a certain number of noisy entries is considered, where our probabilistic analysis performs very efficiently. Furthermore, assuming that the rank of the original matrix is not given, we provide an analysis to determine if the rank of a valid completion is indeed the actual rank of the data corrupted with sparse noise by verifying some conditions.