Hearing the clusters in a graph: A distributed algorithm

TL;DR

This paper introduces a fast, distributed graph clustering algorithm that approximates spectral clustering without heavy computations, enabling efficient community detection and distributed processing in large-scale networks.

Contribution

A novel distributed algorithm that recovers spectral clustering results efficiently using local Fourier transforms, avoiding eigenvalue computations.

Findings

Orders of magnitude faster than random walk methods for large graphs

Proven equivalence to spectral clustering with convergence guarantees

Effective in community detection and distributed estimation tasks

Abstract

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies.