Spectral clustering on spherical coordinates under the degree-corrected stochastic blockmodel

TL;DR

This paper introduces a spectral clustering method using spherical coordinates for community detection in graphs with heterogeneous degrees, improving accuracy and automating model selection.

Contribution

It proposes a novel spectral clustering algorithm based on spherical coordinate transformation under the degree-corrected stochastic blockmodel, enabling automatic community and dimension selection.

Findings

Enhanced community detection in computer networks.

Automatic selection of number of communities and latent space dimension.

Outperforms existing methods in heterogeneous degree graphs.

Abstract

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition of the matrix. Estimating correctly the number of communities and the dimension of the reduced latent space is critical for good performance of spectral clustering algorithms. Furthermore, many real-world graphs, such as enterprise computer networks studied in cyber-security applications, often display heterogeneous within-community degree distributions. Such heterogeneous degree distributions are usually not well captured by standard spectral clustering algorithms. In this article, a novel spectral clustering algorithm is proposed for community detection under the degree-corrected stochastic blockmodel. The proposed method is based on a transformation of the spectral embedding to spherical coordinates, and a novel modelling assumption in the transformed space. The method allows for simultaneous and automated selection of the number of communities and the latent dimension for spectral embeddings of graphs with uneven node degrees. Results show improved performance over competing methods in representing computer networks.