Convex Formulation for Planted Quasi-Clique Recovery

TL;DR

This paper introduces a convex nuclear norm minimization approach for recovering planted quasi-cliques, extending the planted clique problem and demonstrating superior performance over existing methods when the quasi-clique density exceeds a threshold.

Contribution

It proposes a novel convex formulation for the NP-hard planted quasi-clique problem, improving recovery performance in community detection and related fields.

Findings

Convex formulation outperforms mixed integer programming methods for certain parameters.

The approach is effective in applications like community detection and biology.

Numerical experiments validate the method's efficiency and accuracy.

Abstract

In this paper, we consider the planted quasi-clique or {\gamma}-clique problem. This problem is an extension of the well known planted clique problem which is NP-hard. The maximum quasi-clique problem is applicable in community detection, information retrieval and biology. We propose a convex formulation using nuclear norm minimization for planted quasi-clique recovery. We carry out numerical experiments using our convex formulation and the existing mixed integer programming formulations. Results show that the convex formulation performs better than the mixed integer formulations when {\gamma} is greater than a particular threshold.