Overlapping stochastic block models with application to the French political blogosphere

TL;DR

This paper introduces the Overlapping Stochastic Block Model, enabling vertices in networks to belong to multiple clusters, addressing limitations of traditional clustering methods that assume disjoint groups.

Contribution

The paper presents a novel overlapping stochastic block model, proves its identifiability, and develops an approximate inference method, extending the classic SBM to overlapping community detection.

Findings

Successfully applied to real-world networks including political blogs and yeast transcriptional networks.

Demonstrated improved clustering performance over existing methods.

Validated the model's ability to identify overlapping communities.

Abstract

Complex systems in nature and in society are often represented as networks, describing the rich set of interactions between objects of interest. Many deterministic and probabilistic clustering methods have been developed to analyze such structures. Given a network, almost all of them partition the vertices into disjoint clusters, according to their connection profile. However, recent studies have shown that these techniques were too restrictive and that most of the existing networks contained overlapping clusters. To tackle this issue, we present in this paper the Overlapping Stochastic Block Model. Our approach allows the vertices to belong to multiple clusters, and, to some extent, generalizes the well-known Stochastic Block Model [Nowicki and Snijders (2001)]. We show that the model is generically identifiable within classes of equivalence and we propose an approximate inference procedure, based on global and local variational techniques. Using toy data sets as well as the French Political Blogosphere network and the transcriptional network of Saccharomyces cerevisiae, we compare our work with other approaches.