Fast cluster detection in networks by first-order optimization

TL;DR

This paper introduces a fast, optimization-based method for detecting clusters in networks using s-defective clique models, with tailored algorithms demonstrating strong practical performance and effectiveness.

Contribution

It presents a novel continuous formulation and tailored Frank-Wolfe variants for efficient detection of maximal s-defective cliques in networks.

Findings

Algorithms quickly find maximal s-defective cliques.

Numerical results show high effectiveness of the approach.

Method outperforms existing techniques in practical scenarios.

Abstract

Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we analyze some tailored variants of the Frank-Wolfe algorithm that enable us to quickly find maximal s-defective cliques. The good practical behavior of those algorithmic tools, which is closely connected to their support identification properties, makes them very appealing in practical applications. The reported numerical results clearly show the effectiveness of the proposed approach.