Survey of Matrix Completion Algorithms

TL;DR

This survey reviews passive and adaptive matrix completion algorithms, highlighting recent advances and comparing their efficiency, with a focus on convex optimization and adaptive sensing techniques for low-rank matrix estimation.

Contribution

It provides a comprehensive overview of both passive and adaptive matrix completion methods, including recent algorithms and their comparative advantages.

Findings

Adaptive algorithms often outperform passive methods in efficiency.

Convex optimization remains a key approach in passive matrix completion.

Recent adaptive techniques show promising results in real-world datasets.

Abstract

Matrix completion problem has been investigated under many different conditions since Netflix announced the Netflix Prize problem. Many research work has been done in the field once it has been discovered that many real life dataset could be estimated with a low-rank matrix. Since then compressed sensing, adaptive signal detection has gained the attention of many researchers. In this survey paper we are going to visit some of the matrix completion methods, mainly in the direction of passive and adaptive directions. First, we discuss passive matrix completion methods with convex optimization, and the second active matrix completion techniques with adaptive signal detection methods. Traditionally many machine learning problems are solved in passive environment. However, later it has been observed that adaptive sensing algorithms many times performs more efficiently than former algorithms. Hence algorithms in this setting has been extensively studied. Therefore, we are going to present some of the latest adaptive matrix completion algorithms in this paper meanwhile providing passive methods.