Spectral Clustering and Block Models: A Review And A New Algorithm

TL;DR

This paper reviews spectral clustering methods for graph data, discusses their theoretical guarantees under block models, and introduces a new algorithm that performs optimally both theoretically and empirically.

Contribution

It provides a comprehensive review of spectral clustering in block models and proposes a novel algorithm with proven optimality.

Findings

The new algorithm achieves strong consistency in block model clustering.

Theoretical analysis confirms the algorithm's asymptotic optimality.

Empirical results demonstrate superior performance over existing methods.

Abstract

We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to perform optimally both theoretically using asymptotic theory and empirically.