Eigenvector Computation and Community Detection in Asynchronous Gossip Models

TL;DR

This paper introduces a simple distributed algorithm for eigenvector computation in asynchronous gossip models, enabling effective community detection in stochastic block models and related communication frameworks.

Contribution

It presents a novel connection between asynchronous eigenvector computation and Oja's streaming PCA algorithm, simplifying and generalizing prior methods.

Findings

Achieves state-of-the-art community detection in asynchronous models

Connects eigenvector computation with Oja's algorithm for streaming PCA

Simplifies analysis of asynchronous gossip algorithms

Abstract

We give a simple distributed algorithm for computing adjacency matrix eigenvectors for the communication graph in an asynchronous gossip model. We show how to use this algorithm to give state-of-the-art asynchronous community detection algorithms when the communication graph is drawn from the well-studied stochastic block model. Our methods also apply to a natural alternative model of randomized communication, where nodes within a community communicate more frequently than nodes in different communities. Our analysis simplifies and generalizes prior work by forging a connection between asynchronous eigenvector computation and Oja's algorithm for streaming principal component analysis. We hope that our work serves as a starting point for building further connections between the analysis of stochastic iterative methods, like Oja's algorithm, and work on asynchronous and gossip-type algorithms for distributed computation.