Spectral Clustering for Multiple Sparse Networks: I

TL;DR

This paper extends spectral clustering methods to identify common community structures across multiple sparse networks, providing theoretical guarantees and demonstrating effectiveness even when individual networks are below detectability thresholds.

Contribution

It introduces spectral clustering extensions for multiple sparse networks with proven consistency under stochastic block models and degree-corrected models.

Findings

Spectral clustering achieves consistent community detection in multiple sparse networks.

Methods work under mild conditions even with networks below detectability thresholds.

Theoretical results are supported by simulation studies.

Abstract

Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of connection between each other are known as multiple or multi-layer networks. We consider the problem of identifying the common community structures for multiple networks. We consider extensions of the spectral clustering methods for the multiple sparse networks, and give theoretical guarantee that the spectral clustering methods produce consistent community detection in case of both multiple stochastic block model and multiple degree-corrected block models. The methods are shown to work under sufficiently mild conditions on the number of multiple networks to detect associative community structures, even if all the individual networks are sparse and most of the individual networks are below community detectability threshold. We reinforce the validity of the theoretical results via simulations too.