Spectral Clustering of Signed Graphs via Matrix Power Means

Abstract

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 behavior of the signed power mean Laplacian and show that it compares favorably with state-of-the-art methods.

Please cite this work as:

@InProceedings{icml2019mercado,
  title = {Spectral Clustering of Signed Graphs via Matrix Power Means},
  author = {Mercado, Pedro and Tudisco, Francesco and Hein, Matthias},
  booktitle = {Proceedings of the Twenty-Sixth International Conference on Machine Learning},
  year = {2019 (to appear)}
}

Keywords: Spectral clustering signed networks networks graph Laplacian matrix means power mean