Fast Approximate Spectral Clustering for Dynamic Networks

TL;DR

This paper introduces a fast approximate spectral clustering method for dynamic networks that leverages past information and Chebyshev graph filtering to reduce computational complexity while maintaining high clustering quality.

Contribution

It presents a novel approach that reuses previous cluster information and employs Chebyshev filtering to efficiently approximate spectral clustering on evolving graphs.

Findings

Achieves clustering quality close to traditional spectral clustering.

Provides significant computational speedups for dynamic graphs.

Effective when graph changes are bounded over time.

Abstract

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by using fast Chebyshev graph filtering of random signals. We show that the proposed algorithm achieves clustering assignments with quality approximating that of spectral clustering and that it can yield significant complexity benefits when the graph dynamics are appropriately bounded.