Convex Relaxation Methods for Community Detection

TL;DR

This survey reviews recent advances in convex optimization techniques for community detection, highlighting their theoretical foundations, advantages, and broad applicability in network analysis.

Contribution

It provides a comprehensive overview of recent theoretical developments and techniques in convex community detection, emphasizing their robustness and consistency.

Findings

Convex methods are robust against outliers.

They achieve consistency under weak assumptions.

They are adaptable to networks with heterogeneous degrees.

Abstract

This paper surveys recent theoretical advances in convex optimization approaches for community detection. We introduce some important theoretical techniques and results for establishing the consistency of convex community detection under various statistical models. In particular, we discuss the basic techniques based on the primal and dual analysis. We also present results that demonstrate several distinctive advantages of convex community detection, including robustness against outlier nodes, consistency under weak assortativity, and adaptivity to heterogeneous degrees. This survey is not intended to be a complete overview of the vast literature on this fast-growing topic. Instead, we aim to provide a big picture of the remarkable recent development in this area and to make the survey accessible to a broad audience. We hope that this expository article can serve as an introductory guide for readers who are interested in using, designing, and analyzing convex relaxation methods in network analysis.