An overview of low-rank matrix recovery from incomplete observations

TL;DR

This paper surveys recent methods for recovering low-rank matrices from incomplete observations, highlighting algorithms, theoretical guarantees, and practical applications in signal processing and machine learning.

Contribution

It provides a comprehensive overview of current techniques and theoretical insights for low-rank matrix recovery from incomplete data.

Findings

Summarizes key algorithms used in practice

Reviews theoretical guarantees for recovery methods

Highlights applications in signal processing and machine learning

Abstract

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and one encounters the problem of recovering the matrix given only incomplete and indirect observations. This paper provides an overview of modern techniques for exploiting low-rank structure to perform matrix recovery in these settings, providing a survey of recent advances in this rapidly-developing field. Specific attention is paid to the algorithms most commonly used in practice, the existing theoretical guarantees for these algorithms, and representative practical applications of these techniques.