Overlapping community detection in networks via sparse spectral decomposition

TL;DR

This paper introduces a computationally efficient spectral method for detecting overlapping communities in networks, focusing on sparse node memberships, and demonstrates its effectiveness through empirical evaluation.

Contribution

It proposes a novel sparse spectral decomposition algorithm that estimates overlapping community memberships without requiring additional clustering steps.

Findings

Algorithm accurately estimates node memberships in simulated networks.

Method performs well on real-world network data.

Computational cost is comparable to eigenvector estimation.

Abstract

We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on sparse node membership vectors. Our algorithm is based on sparse principal subspace estimation with iterative thresholding. The method is computationally efficient, with a computational cost equivalent to estimating the leading eigenvectors of the adjacency matrix, and does not require an additional clustering step, unlike spectral clustering methods. We show that a fixed point of the algorithm corresponds to correct node memberships under a version of the stochastic block model. The methods are evaluated empirically on simulated and real-world networks, showing good statistical performance and computational efficiency.