On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion

TL;DR

This paper investigates deterministic sampling patterns for robust low-rank matrix completion, extending geometric analysis methods to noisy data and providing criteria to verify the true rank of completed matrices.

Contribution

It introduces new deterministic sampling strategies for robust matrix completion and offers analysis tools to determine the actual rank in noisy scenarios.

Findings

Probabilistic analysis shows efficiency in noisy column entries

Extended geometric analysis to noisy matrix completion

Criteria for verifying the true rank of completed matrices

Abstract

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.