Revisiting Spectral Graph Clustering with Generative Community Models

TL;DR

This paper introduces SGC-GEN, a unified spectral graph clustering framework that combines model-based guarantees with model-free flexibility, providing theoretical detectability conditions and robust performance on real-world data.

Contribution

The paper proposes SGC-GEN, a novel community detection method that integrates model mismatch analysis with spectral clustering, offering theoretical guarantees and practical effectiveness.

Findings

SGC-GEN outperforms baseline methods on real-world datasets.

It provides a theoretical condition for community detection under GCMs.

SGC-GEN has comparable computational complexity to existing methods.

Abstract

The methodology of community detection can be divided into two principles: imposing a network model on a given graph, or optimizing a designed objective function. The former provides guarantees on theoretical detectability but falls short when the graph is inconsistent with the underlying model. The latter is model-free but fails to provide quality assurance for the detected communities. In this paper, we propose a novel unified framework to combine the advantages of these two principles. The presented method, SGC-GEN, not only considers the detection error caused by the corresponding model mismatch to a given graph, but also yields a theoretical guarantee on community detectability by analyzing Spectral Graph Clustering (SGC) under GENerative community models (GCMs). SGC-GEN incorporates the predictability on correct community detection with a measure of community fitness to GCMs. It resembles the formulation of supervised learning problems by enabling various community detection loss functions and model mismatch metrics. We further establish a theoretical condition for correct community detection using the normalized graph Laplacian matrix under a GCM, which provides a novel data-driven loss function for SGC-GEN. In addition, we present an effective algorithm to implement SGC-GEN, and show that the computational complexity of SGC-GEN is comparable to the baseline methods. Our experiments on 18 real-world datasets demonstrate that SGC-GEN possesses superior and robust performance compared to 6 baseline methods under 7 representative clustering metrics.