An Overview of Robust Subspace Recovery

TL;DR

This paper introduces robust subspace recovery, discussing its challenges, existing methods, and unresolved issues in identifying low-dimensional structures within corrupted datasets.

Contribution

It provides a comprehensive overview of the field, highlighting the advantages, disadvantages, and open problems of current approaches.

Findings

Summarizes key methods and their limitations.

Identifies open problems and future research directions.

Highlights the nonconvexity challenge in algorithm development.

Abstract

This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due to its underlying nonconvexity. This work emphasizes advantages and disadvantages of proposed approaches and unsolved problems in the area.