Spectral Clustering of Signed Graphs via Matrix Power Means
This work addresses clustering in signed graphs, which model both attractive and repulsive relations, offering a novel method that improves over existing approaches in scenarios like the Stochastic Block Model.
The authors tackled the problem of clustering signed graphs by extending spectral clustering using Signed Power Mean Laplacians, showing that this approach captures ground truth clusters in expectation where state-of-the-art methods fail and confirming its effectiveness through experiments on random graphs and real-world datasets.
Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed Power Mean Laplacians, defined as the matrix power mean of normalized standard and signless Laplacians of positive and negative edges. We provide a thorough analysis of the proposed approach in the setting of a general Stochastic Block Model that includes models such as the Labeled Stochastic Block Model and the Censored Block Model. We show that in expectation the signed power mean Laplacian captures the ground truth clusters under reasonable settings where state-of-the-art approaches fail. Moreover, we prove that the eigenvalues and eigenvector of the signed power mean Laplacian concentrate around their expectation under reasonable conditions in the general Stochastic Block Model. Extensive experiments on random graphs and real world datasets confirm the theoretically predicted behaviour of the signed power mean Laplacian and show that it compares favourably with state-of-the-art methods.