Spectral clustering on spherical coordinates under the degree corrected stochastic blockmodel
Date:
Spectral clustering is a popular method for community detection in networks. The nodes are clustered on a low dimensional representation of the graph, resulting from a truncated spectral decomposition of the adjacency matrix or one of its regularised versions. Estimating the number of communities and the dimensionality of the reduced latent space is crucial for a good performance of the spectral clustering algorithm in estimating stochastic blockmodels. Additionally, real-world networks often present heterogeneous within-community degree distributions, for example, in cybersecurity applications. This property is addressed within community detection by the degree corrected stochastic blockmodel. A novel model-based method for simultaneous and automated selection of the number of communities and latent dimensionality in spectral clustering under the degree-corrected stochastic blockmodel is proposed. The method is based on a transformation to spherical coordinates of the spectral embedding, and on a novel modelling assumption in the transformed space, then embedded into a model selection framework for the number of communities and latent dimensionality. Results show improved performance over competing methods on simulated and real-world computer network data.
Joint work with Professor Nick Heard (Imperial College London) and Dr Patrick Rubin-Delanchy (University of Bristol).