On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion
This work addresses matrix completion under noise, which is incremental as it builds on existing noiseless methods.
The paper tackles robust low-rank matrix completion with sparse noise by extending deterministic sampling pattern analysis from noiseless cases, and provides probabilistic analysis for columns with noisy entries and rank verification without prior rank knowledge.
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.