Low-rank Matrix Completion with Noisy Observations: a Quantitative Comparison

TL;DR

This paper compares three advanced algorithms for low-rank matrix completion in noisy settings, demonstrating their effectiveness in reconstructing both real and synthetic data matrices across various practical applications.

Contribution

It provides a systematic numerical comparison of OptSpace, ADMiRA, and FPCA algorithms for noisy matrix completion, highlighting their practical performance.

Findings

Algorithms accurately reconstruct real data matrices.

Efficient algorithms perform well on synthetic matrices.

Comparison offers insights into practical applicability.

Abstract

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and wireless sensor networks. In this paper, we focus on the matrix completion problem in the case when the observed samples are corrupted by noise. We compare the performance of three state-of-the-art matrix completion algorithms (OptSpace, ADMiRA and FPCA) on a single simulation platform and present numerical results. We show that in practice these efficient algorithms can be used to reconstruct real data matrices, as well as randomly generated matrices, accurately.