Poster
Spectral Clustering of Signed Graphs via Matrix Power Means
Pedro Mercado · Francesco Tudisco · Matthias Hein

Thu Jun 13th 06:30 -- 09:00 PM @ Pacific Ballroom #190

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.

Author Information

Pedro Mercado (Saarland University / University of Tübingen)
Francesco Tudisco (University of Strathclyde)
Matthias Hein (University of Tübingen)

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