An improved spectral clustering method for community detection under the degree-corrected stochastic blockmodel

TL;DR

This paper introduces an improved spectral clustering method tailored for community detection in networks modeled by the degree-corrected stochastic blockmodel, demonstrating enhanced accuracy over classical methods.

Contribution

The paper proposes a novel spectral clustering approach using weighted eigenvectors of a regularized Laplacian, improving community detection under DCSBM.

Findings

ISC outperforms classical spectral clustering in simulations

ISC achieves lower error rates on empirical networks

Significant improvement on weak signal networks Simmons and Caltech

Abstract

For community detection problem, spectral clustering is a widely used method for detecting clusters in networks. In this paper, we propose an improved spectral clustering (ISC) approach under the degree corrected stochastic block model (DCSBM). ISC is designed based on the k-means clustering algorithm on the weighted leading K + 1 eigenvectors of a regularized Laplacian matrix where the weights are their corresponding eigenvalues. Theoretical analysis of ISC shows that under mild conditions the ISC yields stable consistent community detection. Numerical results show that ISC outperforms classical spectral clustering methods for community detection on both simulated and eight empirical networks. Especially, ISC provides a significant improvement on two weak signal networks Simmons and Caltech, with error rates of 121/1137 and 96/590, respectively.